Seven Card Stud High-Low Poker

Stealing Antes

2012-01-04T10:06:00.000-08:00

Of the Stud variants of poker, Seven-Card Stud High/Low is the hardest game in which to steal antes. For example in Razz, the bring-in is usually a face card, and very rarely will the bring-in defend against a complete bet from an exposed low card. In Razz you can have wired kings with an exposed 2 and steal the antes. It is more difficult to steal antes in high-only Seven-Card Stud because bring-ins can have many possible card combinations worth defending. In fact, in high-only Seven-Card Stud a bring-in with a pair or high-cards in the hole, will usually defend against someone she believes is trying to steal the antes. However, a bring-in in high-only Stud will usually not defend complete garbage.

However, in Seven-Card Stud High/Low, the bring-in will often defend against a player that she believes is stealing the antes. If the bring-in has an exposed low-card and picks up a second exposed low-card, she can become very aggressive. An opponent trying to steal antes with garbage might find himself in an uncomfortable situation, because the bring-in’s low-cards could allow her to freeroll on later streets. In Seven-Card Stud High/Low, low-cards because of the their dual roles in both high and low hands, have greater value than mid-range cards, which can only contribute to high-hands. A bring-in with an exposed 2 and 6, 7, in the hole has a better starting hand than an opponent with an exposed K and Q, 8, in the hole, even though the bring-in has no over cards. Attempting to steal antes with uncoordinated high-cards will not work in Stud-High/Low as often as it will in Stud-high. A significant fraction of the time, the bring-in will have a hand worth defending, or even raising with in response to a completed bet.

Calling versus Raising on Seventh Street

2011-07-05T19:28:00.000-07:00

If you are debating whether to call or raise, it often means that you have a chance to scoop or it is a multi-way pot for which you expect to win half and therefore seek to maximize the pot size. If you have a lock on both halves of the pot, raising is automatic and no decision needs to be made. But, when the outcome is not clear, you need to consider which action is most likely to maximize your earnings. Consider these situations:

Nut low-hand versus a better high-hand in a heads-up pot: This is a common occurrence and often the low-hand cannot beat the board, which means that you know that a split-pot will result at showdown. Many players in this situation simply call. However, this is a mistake. If you have the nut-low you should raise for two reasons. First it often forces your opponent to make a difficult decision because his high holding might not be that strong. For example, a low pair showing in his hand that you cannot beat might be all he has for high. His initial bet might be a bluff and a raise could induce a fold. Second you do not want to develop a pattern of raising in situations in which your low-hand scoops and calling when it does not. Obviously, when your low-hand scoops you want your raise called. Only raising when you want to be called will soon result in no callers in those circumstances. That might be useful for inducing a fold later on when you need an opponent to fold. But, in general it is better to keep up the pressure on your opponents. It is better over the long run to have a table image in which you are feared because opponents will check to you more often and allow you to drive the action.

Nut low-hand versus a better high-hand in a multi-way pot: Raising might not be the way to extract maximum value in a multi-way pot if it drives out paying customers. If an opponent acts after you, and has to cold-call two large bets, she is more likely to fold than if only one bet is required. Consider a three-way pot in which you act second after an initial bet from Bob but before Alice. Consider these possible outcomes:

1. You call, Alice folds (no additional gain).
2. You call, Alice calls (you gain half a large bet).
3. You raise, Alice folds (no additional gain).
4. You raise, Alice calls, and Bob calls (you gain one large bet).
5. You raise, Alice calls, Bob re-raises, you cap the action, and Alice and Bob both call (you gain two large bets).

Obviously, since you have the nut low-hand, scenario 5 is the one you desire. But, that requires a raise on your part, and with it a risk of scenario 3 in which Alice folds leaving you with no additional gain. On the other hand, if you call Alice might still fold (scenario 1) leaving you with no gain. That means that if you decide to call you are hoping for scenario 2 as opposed to scenario 1.

You need to judge how much Alice likes her hand. She will need a lot of confidence for scenarios 4 or 5 to play out. But, if Alice doesn't like her hand it will not matter if you call or raise. Therefore, the only reason to call is if you think Alice is unsure of her hand but willing to make a crying call at the end if the price stays low.

The situation is of course different if you act after Alice, and she already called Bob's initial bet. In that case you have nothing to lose by raising and everything to gain.

Non-nut low-hand versus a potential better low-hand: As a general rule you should call with any qualified low-hand at the end. Pots are usually large by the end and it is never a certainty that anyone else has a qualified low-hand. A single incorrect fold can be very costly in relation to the cost of calling one last bet.

However, cold-calling raises from players with potentially better low-hands is problematic. These can be some of the toughest decisions that you will make. Suppose you have a weak low-hand such as an 8-6 high against an opponent showing a 6, 4, J, 9 on the board who suddenly raises on the end. In this circumstance the chances are high that your low-hand is beat. If the player who initiated betting appears confident in a high-hand you have to weigh the loss of four large bets against the reduced chance of winning back anything. Folding in these situations will most likely save money over the long run.

It is to avoid these expensive traps that you should not routinely play weak low-hands such as 8-7 or 8-6 high. When you play 8-high low cards you will face these kind of tough decisions often. There will of course be times that you back into an 8-high low with legitimate starting cards such as 3, 4, 5, 6, but those will be less frequent occurrences.

I have seen players automatically raise on the end with any qualified low-hand, no matter how weak. This is often a costly mistake. Weak low-hands lose frequently in Stud-Eight so you should not get too confident with an 8-high or even 7-high low-hand unless no other low-hands are possible. Remember that it is possible for any player with two wheel cards on the board to have a wheel. Also remember that if you are showing cards such as 8, 5, J, K, a player with a 7-high low or better can raise back because he will know that his low-hand is better.

Calling versus Folding on Seventh Street

2011-05-31T13:44:00.000-07:00

If you are deciding between calling and folding on Seventh Street, it means that you do not like your holdings. One of the toughest decisions in Stud-Eight is whether to call on the end with a hand that finished “one-way,” meaning that the hand can only take half the pot. By Seventh Street, the pot can be very large, so losing even half the pot to an incorrect fold can be costly. In many cases, weak one-way hands can hold up for half the pot, if the action came from players vying for the other half. Here are some of the more uncomfortable circumstances to be in at the end.

A weak low versus a potential low: This situation arises with hands such as (5, 6) 7, A, K, 9 (8). By picking up an 8 on the end you are saddled with one of the worse possible low-hands and a terrible high-hand. Some one showing (X, X) 7, 4, 2, A (X) can easily have you beat. However, as a general rule, if you have a qualifying low-hand, and there is a large pot at the end, you should call because it never certain that four scary looking low-cards in an opponent’s hand are part of a qualified low-hand. An exception can be made, if it is a multi-way pot with a lot of raising, in which case it is not a bad play to fold. Good hand reading ability is vital in making the decision because there are times when the player with the low cards has a wired high-pair and little chance completing a low-hand. In heads-up play don’t fold if your opponent appears to be playing for low and you can beat the board for high. In the example above, the A, K might hold up for the high-pot if the other hand hasn’t paired. If the other hand has paired, it will be less likely to qualify for the low-pot.

Two pair versus a potential straight: If the straight cards are high and the player holding them bets or raises into a threatening board, you can confidently muck the two pair. Some one checking and calling with (X, X) J, 10, 9, K, (X) who suddenly bets on the end into a possible low-hand, made the straight. A more difficult situation is when the straight cards are low. For example, you have (A, 2) A, 3, 6, 2 (J) against a player with (X, X) 4, 5, 6, 2 (X), who bets out on the end without having made any prior raises. You lost your chance for a low-hand when the Jack hit, and there is a good chance your Aces-up are no longer good for high. Generally you should call here, unless it is a multi-way pot with a lot of jamming on the end, in which case your hand is clearly no good for high. Again, in making this decision, watch for the 4s and 5s and the connectedness of the cards. For example, your chances are much better for taking the high-pot if you have (A, 4) A, 4, 5, 6 (J) and your opponent has (X, X) 2, 3, 7, 9 (X), than in first example in which all your opponent needs is a hidden 3 to scoop.

One small pair versus a potential low: This is often an apparently hopeless situation, but surprisingly it might not be and you can give up a lot of equity by routinely folding. Suppose you have (3, 4) 5, 6, J, 9, (5) versus (X, X) 7, 3, 2, K (X) and your opponent bets. You missed both the straight draw and the low-hand draw and have nothing but a pair of 5s for a high-hand. However, if your opponent played only for low he might not have any paired cards, which means that your 5s are good for high. In fact, I’ve been in hands in which calling with the 5s scooped for me because the bet was a semi-bluff from an opponent who also missed the low-hand and had an even lower pair.

Trips or less versus another hand betting into a low-hand: A frustrating occurrence is to start with rolled trips or two small pair that do not fill up or make a low-hand. Finishing with (3, 3) 3, 4, 5, J (K) or (A, A) 2, 2, 5, 6, (Q) are frequent outcomes from promising starting cards. These kinds of hands are still strong, but qualify only for the high-pot which limits your implied pot odds on the end. In a heads-up pot, you would simply call. The difficult decision arises in multi-way pots in which a player bets into a potential low-hand, who either raises or might raise when her turn comes. What to do depends on your judgment of whether the player making the bet is representing a high-hand or a low-hand.

If the bettor is representing a high-hand, she has you beat because she wouldn’t bet unless she has better than a low straight. There are exceptions, such as players who bet two pair aggressively in this situation anticipating that for this board you and the other player each have low-hands. However, if you played your early cards aggressively, which you should have, that usually dissuades most players from betting into you on the end unless they hit a monster hand. As painful as it might be, it is better to fold in this situation rather than get jammed by the low-hand.

An extremely uncomfortable situation arises if the bettor is representing a better low-hand than the other player’s low-hand. If each opponent thinks that his or her low-hand is the best, each will want to cap the raising. In that case you will have to go along and hope that neither holds a low straight. Again your aggressive play early in the hand because of the strength of your starting cards means that the pot prior to Seventh Street betting is already large.

A Clever Bluff

2011-04-26T06:04:00.000-07:00

One of the smartest Seventh Street plays I’ve witnessed occurred in a three-way hand in which I had a lock on the low-pot, against two players vying for the high-pot. On Fifth and Sixth Streets the action began with Player 1, showing a high-hand on the board, who checked to Player 2, who checked to me. I bet and both players called. But on Seventh Street, Player 1 checked, and Player 2, who appeared to be on some sort of draw, bet. I raised because I thought Player 1, who clearly had the best hand all along, would call. But, Player 1, who did not want to get jammed by Player 2 and me, folded. I split the pot with Player 2 who had a high hand that could not have beat the high-hand Player 1 showed on the board. Player 2 said to me: “I was hoping that you would raise.”

Of course, I would not have raised had I known Player 1’s response would be to fold. Who won the high pot made no difference to me, I just wanted the pot to be as big as possible and driving Player 1 out reduced my winnings. Had Player 1 called the raise it would have increased my winnings. It is always difficult predicting your opponent’s response.

However, Player 2’s bluff was a smart play. In limit poker it is difficult to pull off successful bluffs late in the hand because the pot is usually large in relation to the cost of the single bet needed to call. Had Player 1 and 2 been heads-up, or playing high-only Seven-Card Stud, the bluff would not have worked. But, with me in between them holding the power to cap raises with no risk to myself, Player 1 had to consider the possibility of calling four large bets before showdown, which is a significant cost. By manipulating my action in the way that Player 2 did, he essentially used one bet to make a four-bet bluff. That is leverage not available in no-limit games in which a bluff with say an amount equal to half the pot, requires a bet equal to half the pot. Player 2 made a clever play that must have high expected value.

This events of this hand also illustrate the dangers inherent in playing a one-way high-hand in a situation in which everyone knows that it is a one-way high-hand. Player 1 did not bet, or check-raise my bets for two reasons. First he needed Player 2 to stay in order to make any money at all. Second, I would certainly re-raise, and Player 1 did not want to be heads-up against me for a huge pot, because I might be freerolling. The net result was that Player 1 was trapped into tentative play. He wanted Player 2 in the hand, but he did not want to be outdrawn for the high-pot. He wanted a large pot because he can only win half, but not too large because he might get scooped. He repeatedly checked and called, hoping for the best, but in the end was run off the pot by the more aggressive players.

If Player 1 had had a one-way high-hand with appearances of possibly qualifying for the low-pot, it would have discouraged Player 2 from trying his bluff, and caused me to think more carefully about raising given that I might not have a lock on the low-pot.

Fifth Street Decisions: Betting into Three Exposed Low-Cards

2011-03-31T18:23:00.000-07:00

The balance of power can shift dramatically on Fifth Street because it is now possible for a player to have a qualifying low-hand and potentially a lock on half the pot if no one else can make a better low. Prior to Fifth Street it is usually the high hands that drive the action. A player holding the best high hand will not want to give free draws to the low hands prior to Fifth Street. But, if at Fifth Street a player has accumulated three low-cards the high hand needs to be careful. The player with the best high-hand has a conundrum with two mutually exclusive goals for continuing.

Betting to protect the high hand and building a pot.
Checking to reduce risk if the low-hand is freerolling for a better high-hand in order to scoop.

Many players lean toward the cautious side and automatically check to a hand with three exposed low cards. However, that kind of routine play becomes predictable and cedes too much power to opponents with hands that could be mediocre at best. The highest hand scoops by default if no low-hand qualifies, and not every hand with three exposed low-cards on Fifth Street is a qualified low.

Consider a hand with four unpaired low-cards after Fourth Street such as (2, 3) 5, 7. If the low cards are live, 22 remain that are not 5s or 7s. Of these 22 cards, six will be 2s and 3s and will pair the hole cards. That means 6 out of 22 times, or 27% of the time, a low-card falling on Fifth Street will pair a hole card. If you are looking at an opponent's hand that consists of (X, X) 5, 7, 2 and believe that the hole cards are low and unpaired, the 2 represents a completed low-hand at most 73% of the time. Depending on the cards already played and your opponent's prior hand history, that percentage might be less.

For example, consider the hand (2, 3) 5, 7 with a board showing that two of the 6s, two of the 4s, and two of the 8s, dead. That leaves 16 remaining low-cards, not ranked 5 or 7, of which 6, or 37.5% will pair the 2 or the 3. That means in many hands in which significant numbers of low-cards are dead, the odds could tilt more towards the possibility that (X, X) 5, 7, 2 is a small pair rather than a qualified low-hand. To know how much the odds tilt requires some knowledge of your opponent because she might be more likely to draw with a four-low if many of the dead cards don't match her hole cards and reduce the possibility of pairing.

It's also possible that your opponent already has a pair-split or wired-going into Fifth Street and cannot complete a low-hand on that street. Sometimes the pair consists of wired high cards, in which case completing a low-hand at all is unlikely. If you have a better high hand you definitely want to bet. That means knowing your opponent's range of playable hands is necessary.

Given these considerations, here are some general guidelines for betting into a hand with three exposed low-cards on Fifth Street.

Situations to check:

* Your opponent has a very tight hand range that does not include small pairs and uncoordinated low-cards.

* The exposed cards include a 4 and a 5. Because these cards are necessary to complete low straights, hands with 4s and 5s can be dangerous holdings to bet into.

* The exposed cards are sequential.

* The exposed cards are suited

* It is a multi-way pot and your high holding is vulnerable in relation to the other hands in play.

Situations to bet:

* Your opponent has a wide hand range that includes any pair and any four low-cards.

* The 4s and 5s are dead or nearly so, in which case a split-pot is more likely if you have a solid high hand and your opponent does complete a qualified low-hand.

* You are playing heads-up, which reduces that chance of being out-drawn for the high-pot by the other players.

* You still have a chance to win the low-pot yourself. If you have Aces-up containing a low-pair and in addition a low kicker, or you have trips low-cards with two additional low-cards, you could still scoop against a qualified low-hand.

In summary, the decision to check or bet should be carefully considered. Do not get into the predictable habit of automatically checking to any hand with three exposed low-cards.

Betting versus Checking on Seventh Street

2011-02-28T17:44:00.000-08:00

The usual rationale for checking on the end is that in many circumstances, it risks money for no gain. If you believe that your opponents are on a draw against you, they will fold if they miss, or raise if they hit. In high-only poker variants, players check on the end for this reason. But, in high-low games, a hit draw might be for only half the pot. In these cases a raise does not necessary mean you lose everything. This is why having a good read on the end is so important. It is always dangerous to bet with a high-only hand into a made low-hand because your opponent has nothing to loose by raising and could have you beat. However, not every hand that shows low cards on the board represents a qualified low-hand. Many times these are high-only hands that will still call your bet when you have them beat. Here are some cues for reading hands.

Suited cards: Obviously, an opponent showing four, or even three suited cards on the board is a threat to make a flush on the end. However, two suited cards can be threat if one of them includes a high door card, especially if that high door card was either dead, or an under-card after the deal. For example, a person playing a Queen, when other Queens are exposed and/or higher cards such as Aces or Kings are exposed, is almost always playing three suited cards. Even though, in most instances this is a bad play, three suited cards is an irresistible starting hand for most players. If a second card with a suit matching the door card appears, that person will stay to the end looking to complete the flush. Pay attention to how live your opponent's flush draw remains when deciding if you want to bet into this kind of hand at the end.

Sequential cards: Opponents showing sequential mid-range cards, such as 8, 9, 10, or even cards with a gap, such as 7, 9, 10, are usually on a straight draw because that is one of the principal reasons for continuing with mid-range cards that have little value for a low-hand and are often dominated for high hand. Often the straight-draw is backed into from a hand that started as a potential low-hand. Many times these straight-draws can be live and open-ended, so proceed with caution on the end if you do not finish with a qualified low-hand, and cannot beat a mid-range straight.

The exposure of 4s and 5s: As pointed out in a previous post, the completion of a straight that simultaneously qualifies as a low-hand requires 4s and 5s. If you do not see any of the 4s or 5s, any two exposed low-cards in an opponent's hand can be a threat to make a low straight on the end, because most likely the straight-draw is live.

Paired door cards that prompt raising: A hand such as (X, X) 5, 7, K, 5 (X) in which the player suddenly started raising on Sixth Street when the second 5 appeared, has usually made trip 5s. The hand cannot qualify for low on Sixth Street and if there are trips 5s it will not qualify for low. Unless you can beat 5s-full you should probably check to this hand on the river.

Paired door cards that are high in a hand that did not raise on prior streets: Consider a hand such as (X, X) K, K, 7, 5 (X). When a high door card such as this is paired, the possibility of trips must be considered, but usually the player will begin raising immediately. If a raise does not occur when the card is paired, that is often sign of a wired pair, and the player now has two pair. Players with two pair are often aggressive when there are no potential low-hands, but if there are one or more potential low-hands, two pair is a vulnerable holding and many players check and call while hoping to fill-up. What this means is that if you finish with two pair, you need to be able to beat a hand with two pair that includes the pair on the board.

Paired door cards that are low in a hand that did not raise on prior streets: A hand such as (X, X) 4, 4, J, 10 (X) that checked and called all the way, most likely went to the river as a pair 4s with hopes of making two-pair or trips on the end. Most likely this hand started as three small cards but never improved for low. If you can beat two small pair you should bet because this player will call with any two pair, no matter how small, and might even call with the pair of 4s if the 4s beat the board.

Paired cards for Fourth Street and later: For hands such as (X, X) 3, 4, J, J (X) or (X, X) 3, 4, Q, 4 (X) it is unlikely that the player had anything better than the single pair going to the river. The player is hoping to make two pair, or trips on the end, or complete a low-hand. If you have a two pair that can beat the pair on the board it is usually worth it to bet.

Low door cards that remain in the hand after picking up high cards: A player with a hand such as (X, X) 5, J, Q, K, almost always started with a low pair, either split or wired, because if the starting hand had been 4, 5, 6, it would have been abandoned. This player is hoping make two pair, or trips on the end. You should not have to worry about the straight. If you are heads-up against this kind of hand and have two small pair, you should check. This is the kind of hand that will often fold to a bet unless it makes Jacks-up or better, in which case you are beat.

Any two exposed wheel cards, especially on early streets: A player with (X, X), 5, 4, J, Q (X) is going to the river looking to complete a low-hand at the minimum, and possibly a low straight. You should check to this hand unless you have a high hand that can beat a low straight because you have nothing to gain from a bet. The player will fold to any bet unless he completed a low-hand.

Four exposed low-cards in a hand that did not raise on prior streets: Hand such as (X, X) 2, 5, 6, 7 (X) that did not raise earlier have not qualified for the low-pot before the river. Clearly the hand could be a qualified low-hand after the river, but frequently the last card is a brick, especially if many of the low cards are dead. If the hand is not already a qualified low-hand before the river, it is because low hole cards paired, resulting in two small pair, or there was a wired pair to begin with that did not make trips. Often in these situations the wired pair is high, which meant the player never expected to get a low-hand. If you have a hand with a reasonably high two pair or better, you should bet because often you will scoop in this situation, even with all the scary looking low-cards.

The High-Only Four-Flush

2011-01-30T08:20:00.000-08:00

One of the most misunderstood hands in Seven-Card Stud High-Low is the high-only four-flush. These are hands such as 2, 9, Q, K suited that can never qualify for the low-pot, but need just one additional suited card to complete a flush for a powerful high-hand. These hands occur frequently on Fourth Street when players who automatically play any three suited cards catch their suit. These players almost always stay to the end no matter what action follows.

In high-only Seven-Card Stud, a four-flush is usually a positive expectation holding. With a live draw and three cards to come, the probability of completing the flush by the end is about 50%. That means as long as the pot is paying better than even money--which it always is because of the antes--you will win money over the long run. It is the equivalent of betting on coin-flips that pay back more than you wager.

But the math is very different if you are in a Stud High-Low game and completing the flush will only win half the pot. If you win half the pot, half the time, your pot equity is only 25%. The pot must be paying at 3 to 1 for you to just break-even on a wager. That means heads-up play against a player with a better high hand who is also drawing to the low-pot is usually not worth the risk, unless you have some other way of backing into the high-hand.

To get the proper pot odds to play a high-only four-flush usually requires a multi-way pot. With three or more players your bets are being multiplied, not just matched. But, even then it is difficult to get a positive expectation. For example, in a three-way pot your bets are essentially being matched 2 for 1, which is not the 3 for 1 payoff needed to break even. Imagine a betting game in which three players put up equal amounts of money and 50% of the time you win 50% of the amount wagered. If the bets were $10 it would cost you $100 to play this game 10 times. Your expected winning of 5 x $15, or $75, doesn't cover your cost.

Playing a high-only four-flush against two other players with possible low-hands is essentially this kind of a betting game. The difference is that in poker, there is usually some dead money in the pot from antes and bets on prior streets. But, the dead money has to be large and your cost small to profitably compete for it.

To see how this works lets consider a specific example. Consider a Fifth Street scenario with the following conditions.

Stakes: $1-2
Hands Dealt: Seven
Current pot size: $10

Remaining hands:

You (2-Diamonds, 3-Diamonds) K-Diamonds, 10-Diamonds, 9-Spades
Alice (X, X) A-Clubs, 6-Spades, 7-Clubs
Bob (X, X) 2-Spades, A-Hearts, A-Spades

The number of exposed cards is 11 plus the 4 door cards that were dealt and mucked, a total of 15. If none of the mucked door cards were diamonds, you have 9 outs with 2 cards to come and 37 unseen cards. Under these circumstances, the probability of completing the flush by the end is 43%. But, this board appears to give someone a low-hand and you are currently behind for high. You are attempting a draw for half of a $10 pot. The expected values for some possible betting scenarios can be calculated.

Scenario 1: You believe Bob will lead the betting for the next three streets and Alice will call, in which case you will call (likely to happen if Alice is drawing for a low-hand). If this happens the final pot will be $28 ($10 + $2 x 3 players x 3 streets). You will have to invest $6 for a 43% chance of winning $14. Because 43% of $14 is $6.02 this is essentially a break-even proposition.

Scenario 2: You believe Bob will lead the betting for the next three streets and Alice will raise, and if you call, Bob will re-raise and Alice will cap (likely if Alice already has a lock on the low-pot and is free-rolling. If this happens the final pot will be $82 ($10 + $2 x 3 players x 4 bets x 3 streets). You will have to invest $24 for a 43% chance to win $41. Because 43% of $41 is $17.63 this is a losing proposition.

These scenarios are all thinking ahead after seeing the fifth card, but prior to any Fifth Street action. At that moment your expected return from further investment in the hand is between break-even and negative. It will require more than $10 of dead money to shift Scenario 1 to a positive expectation and much more to shift Scenario 2 to your favor.

The lesson from this analysis is that you should not automatically play any three suited cards if one or more is high. If Alice and Bob are showing high door cards go ahead. A low-hand is unlikely to develop and if you catch your suit on Fourth Street, you have an advantage. Plus if the King is the high card on the board, you can represent it as a pair of Kings and put pressure on Bob and Alice to fold without completing the flush. But, if Alice and Bob have low door cards and/or Aces, even catching your suit might leave you with a negative expectation if Alice and Bob develop viable low-hands. You cannot pressure anyone with a lock on the low-pot, so your fold equity is gone.

All this re-enforces the fundamental concept for playing Stud High-Low that is: if you can't foresee a scenario in which you have a high probability of scooping, don't play the hand.

Fifth Street Tactics: Keeping opponents in versus driving them out

2010-12-27T14:01:00.000-08:00

If you have a made low on Fifth Street and no one else does, it is often advantageous to keep players in the hand contributing to the pot. If the high hand is willing to bet, calling might be a more profitable option because you do not want to just get your money back if it becomes a heads-up contest with the high hand. However, there are situations where raising with the intent of driving others out of hand is preferable. Some examples:

-- Your low is vulnerable to another player with a low draw. Suppose you have (2, 4) A, 7, 8 and another player has an exposed 6, 3, 3. The pair means a low has not been made, but she could have a draw to a better low and she holds three cards that would improve your low. Your low hand is very vulnerable to becoming second best later in the hand. If the high bets you should raise and attempt to force her out.

-- You can freeroll your low for a powerful high hand and do not want other hands to compete against it for high. Suppose you have (2, 5) 3, 4, 7 in a multi-way pot in which one of the players appears to be on a flush draw. Another player with an exposed pair of 8s bets. You should raise to force out the flush draw. If you make your straight, you want it to hold up for high.

-- The high hand appears weak and possibly the result of a busted low. Suppose you have (6, 3) A, 5, 7 against a player with an exposed 2, 2, J. The pair of 2s might be the only thing he has going for him and pairing any one of your cards could lead to a better high. Aggressive raising might win the pot outright. He could judge that it is too risky to pursue the hand for high.

-- You have a lock on low in a multi-way pot in which raising will not drive the others out. There could be several powerful high hands that have developed or are developing in such a way that your opponents will pay any price to stay in the hand. Obviously in that situation, raising will maximize the amount in the pot and comes with no risk, even if you are drawing dead to high.

Missed Opportunities on the River

2010-11-29T05:42:00.000-08:00

Extracting maximum value from winning hands is as important as limiting financial damage from losing hands. Here are some examples of mistakes I've made on the end.

Missing an extra bet

Opponent: (X, X) A-Clubs, A-Spades, 10-Hearts, 10-Spades, (X)
Me: (3-Clubs, 5-Hearts) 4-Clubs, 6-Spades, 5-Diamonds, 5-Clubs, (J-Clubs)

Action: Obviously I was unhappy to see the brick on the end that denied me a qualifying low-hand. My opponent had led all the way in this hand with the exposed pair of Aces, and I had serious doubts that my trip 5s would hold up for high. But, on the river my opponent checked and after I thoughtlessly checked back, I won the entire pot.

Analysis: I missed picking up an extra bet on the end because it is not possible for my opponent to have trip Aces or trip 10s. If he has three of either rank his hand would be a full house, which is a holding that he would certainly bet. In fact he would bet quads, a full house, a flush, or an Ace-high straight. The only reason for a check is that he has none of these holdings, and fears losing to a possible small straight. Therefore my trip 5s has to be the nuts and I should bet. With Aces-up, he has to call because the pot was large and I could be betting with only a low-hand.

Missing a chance at half the pot

Opponent: (X, X) 10-Clubs, 9-Hearts, 8-Spades, 7-Clubs, (X)
Me: (2-Spades, Q-Clubs) Q-Spades, 5-Spades, 6-Spades, A-Clubs, (7-Diamonds)

Action: This was a heads-up hand, that because of the high door-cards, I bet out thinking that no qualified low-hand would result. I checked on Sixth Street and when my opponent responded by betting into my Queens, I read him for a straight and stayed because of my flush draw. I missed the flush-draw on the river but backed into a 7-high nut-low. My opponent bet on the end and I made the mistake of calling. He won the high-pot with two pair 10s and 7s.

Analysis: There was no reason for me not to raise in this situation. I have no risk of being scooped by a straight and a raise would force him to make a difficult decision if he missed his draw, which in this case he did. Do you call someone raising on the end with two overcards, when all you have is two small pair? He's not expecting a low-hand on my side anymore than I did. Most likely he would fold because his river bet amounts to a semi-bluff.

Part of the reason for my errors in both these cases was backing into a different kind of hand than what I had sought. In the latter case I had too much mental focus on playing a high-hand without thinking about the backdoor low possibilities. The call was an afterthought because I had not been looking for a low-hand. In the former case I was looking for a low straight because I believed trip 5s and even 5s-full would lose. But, backdoor low-hands and backdoor high-hands occur frequently in Stud-Eight. You need to quickly switch your thought processes when they occur and think about the new tactical possibilities that they present.

The problem with one-way low-hands

2010-10-14T06:57:00.000-07:00

Many players who have four low-cards after Fourth Street in Seven-Card Stud High-Low will stay until the end, and even raise before completing a low-hand. However, a hand with four low-cards and nothing else going for it has more problems than you might imagine. Consider a common scenario in which four unconnected low-cards are heads-up against a high pair. Consider this example:

You: (8, 7) 3, 2
Alice: (Q, K) K, 9

If your hand is completely live there are 16 outs to complete low-hand. That means that by the end you should complete a low-hand 73% of the time. The majority of hands, in which you split the pot, will return your money plus half the money already present from the antes and bring-ins. However, 27% of the time you lose all the money you invested on the later streets. Clearly this is a negative expectation contest because you win no additional money from your later bets the 73% of the time that you succeed, but 27% of the time you will lose all the money you invested. The money that already exists in the pot from antes and Third Street betting is rarely so large that half will offset this negative expectation.

In a three-way pot, your expectation is positive, but not as high as you might think.

You: (8, 7) 3, 2
Alice: (Q, K) K, 9
Bob: (J, J) 10, Q

If you, Alice, and Bob, each contribute $50 to see the final three cards, there will be $150 at stake. If this situation is played 100 times, you will have spent a total of $5000 to win half of $150, or $75 for the 73 low-pots that you will win on average. Your total return is $5475, which is less than a 10% return on your investment, barely enough to cover the rake. However, if you are in a hand such as this against two one-way high hands, there is the possibility of making your low-hand early and being able to freeroll on later streets.

However, a dangerous situation arises when you have a one-way low-draw against a high hand and another low-draw. In this case the probability of making a low-hand decreases because your draw is usually not completely live. The reduction in outs can be exacerbated by mucked low-cards after the deal. Consider a deal in which a 5 and 6 are mucked on Third Street and the following three-way hand develops:

You: (8, 7) 3, 2
Alice: (7, 5) 4, A
Bob: (J, J) 10, Q

This is a terrible situation to be in. Alice has three of your outs and two other outs are dead. There are only 11 cards available to complete your low-hand, which means the probability has decreased to 59%. While this is still a better than even chance it shifted your expectation to negative. If you, Alice, and Bob, each contribute $50 to see the final three cards, there will be $150 at stake. If this situation is played 100 times, you will have spent a total of $5000 to win $75 for the 59 low-pots that you will win on average. Your total return is $4425, a loss of $575 or 11.5%. That figure optimistically assumes that you win the low-pot each time that you make a qualifying low-hand. In fact, Alice is drawing to a better low-hand than yours, and a significant fraction of the time she will win the low-pot even if you qualify. That means that your expected losses will be much worse than 11.5%.

However, if your hand has scoop potential the expectation shifts to your favor. Consider having connected low-cards:

You: (3, 4) 5, 6
Alice: (Q, K) K, 9

Alice will still scoop the 27% of the time that you fail to make a low-hand. But 44% of the time you will complete a straight that most likely will scoop, and 29% of the time you will win the low pot. If you and Alice each contribute $50, there will be $100 at stake. Consider 100 trials of this scenario. At $50 for each trial it will cost you $5000 total. On average, you will win $100 the 44 times you hit the straight, and $50 the 29 times you make a low-hand only. Your total winnings over 100 trials will average $5850,which is a return of 17%

In a three-way pot against two high hands your positive expectation is even greater if both high hands stay until the end and a straight holds up for high. Consider this example:

You: (3, 4) 5, 6
Alice: (Q, K) K, 9
Bob: (J, J) 10, Q

If you, Alice and Bob each contribute $50, it will cost you $5000 to play this scenario 100 times. On average, you will win $150 the 44 times you hit the straight, and $75 the 29 times you make a low-hand only. Your total winnings over 100 trials will average $8775,which is a return of 75%. In practice this large positive expectation will be offset by the times when the high-hands improve to better than a 7-high straight which will still result in a split-pot.

These examples show how important the possibility of a scoop is to determining expectation. The challenge when you play the high side of these scenarios is to judge if your opponent has scoop potential so that you can avoid playing a hand in which you have a negative expectation. In the examples discussed, I specified the hole cards so that I could present a precise calculation of expectation. In practice you don't see your opponent's hole cards and must infer the values. In you fold a high pair any time that your opponent has two exposed low-cards, you are giving up in a situation in which you have positive expectation. However, anytime you are playing into a sequence of four connected low-cards, or four suited low-cards, you have a negative expectation.

Here are some guidelines for making that judgment.

Count your opponent's outs for a low-hand. If many of the low-cards needed are dead the probability that your opponent will qualify for the low-pot by the end drops considerably.
Note possible implied outs. A hand with a low door-card that limped in on Third Street and mucked after catching a high card on Fourth Street, probably removed two additional low-cards from play, not just the one exposed.
Pay attention to the blockers and take special note of the 4s and 5s. As explained in the previous section if the either rank-4s or 5s-are dead, low straights cannot occur.
Note gaps in exposed low-cards. An 8, 2 showing is much less of a threat than an exposed 3, 2.
Most importantly, track your opponent's tendencies. A tough, aggressive opponent who always plays to scoop is much more likely to have connected low-cards than an opponent who consistently limps in with any random set of low-cards.

The common Fourth Street confrontation between a high-hand and a draw to a low-hand has a precarious balance. The player with the low-hand has more information because it is difficult to hide a high-hand, while the player with the high hand must guess at the quality of the low-hand. However, no qualified low-hand can exist on Fourth Street which means that high hand is poised to scoop unless drawn out against.

Counting Outs in Seven-Card Stud High-Low

2010-09-15T13:51:00.000-07:00

Having identified the different kinds of drawing hands last month, we can now count the outs available in order to determine likelihood of improvement. However, Stud games, in contrast to flop games, usually have many more exposed cards to account for when adding up outs. As a result, counting outs is much more situational in Seven-Card Stud High-Low than in Hold'em.

Consider the following extreme example. For the coordinated high example of 2-clubs, 3- clubs, 4-clubs, 5- clubs, 5-diamonds, 5-spades there are a total of 31 cards that will improve its high ranking, qualify the hand for the low-pot, or do both. But the 31 total is an upper limit on the number of outs available to improve the hand. Suppose the 9- clubs, 7- clubs, 4-diamonds, and 6-spades are exposed other hands. All these cards are no longer available as outs, so the count needs to be reduced by four to a total of 27

Let us also suppose that another player has all four Aces exposed in her hand. Now not only must the Aces be removed from the total outs, but most of the high draws for this hand are now dead. There is only one out available for this hand to take the high-pot-the 6-clubs-and for the low pot all that remain are the two other 6s, three other 7s, and the four 8s. Instead of 31 outs available, there are actually only 10 cards that matter, because if someone already has quad Aces hitting quad 5s or any of the full houses, or high flushes, will not win anything.

The consideration of this extremely unlikely scenario is useful because it illustrates four important points about counting outs. You need to subtract from the total for the following reasons.

Dead cards: You must subtract from the total available outs all the helpful cards that you see in other hands because they are no longer available. This is different than in Hold'em, in which every card that you see is potentially playable.

Dead draws: You must subtract from the total available outs all the cards that you see that improve your hand but do not win. Again in contrast to Hold'em, you can often see in a Stud game when you are drawing dead, because certain improvements will not beat your opponent's exposed cards ("beat the board").

Weighted outs: Not all outs are of equal value. In high-low games some outs win the entire pot while other outs win just half. In the example of the straight flush draw versus quads, the 6-clubs wins it all while the nine available low cards win just half the pot. To account for this difference, in this book I introduce the concept of counting "weighted outs." To count weighted outs, add 1 for each out that scoops, and 1/2 for each out that only wins half the pot. For this example there is one out that scoops and nine outs that take the low-pot, so the total number of weighted outs is 1 + 9 x (1/2), or 5.5. I will show in a future post how a count of weighted outs can be used to determine pot equity, which is a measure of how much you should invest when betting on a hand.

Implied outs: You can often subtract from the total number of outs, cards that you cannot see because your opponent's actions imply the contents of their hole cards. Suppose three players in the hand after Fourth Street show 2-3, 5-7, and A-2, and all act as if they are on draws to low-hands. If you are looking for a low-card, it is clear that six of them are dead, but in this situation you can imply that 12 are dead, because the six unseen hole cards are most likely low.

Once an accurate count of outs is determined, the probability for improvement can be found by dividing the total outs by the number of unseen cards.

Kinds of Drawing Hands in Seven-Card Stud High-Low (Stud-Eight)

2010-08-15T13:36:00.000-07:00

In high only poker the concept of drawing to improve the rank of your hand is simple--the hand can only increase in rank. Therefore, cards drawn either raise the rank of your hand or they do not. But, in high-low forms of poker, defining improvement is more complicated because there are three kinds of improvement--increasing the rank of your high-hand, qualifying for a low-hand, and improving your low-hand. All hands, no matter how low, have the potential to win the high-pot, but not all hands qualify for the low-pot. To complicate matters further, some drawn cards can simultaneously improve your high and low hands, while some drawn cards can improve your high hand at the expense of disqualifying you from holding a low-hand. To account for these complexities we will define two categories of hands--half-made hands and drawing hands, and within each of these categories define three kinds of hands. That makes a total of six different kinds of drawing hands.

Half-made hands are holdings that can win half the pot, but need improvement to win the other half. The three kinds of half-made hands in order of desirability are:

Coordinated highs are hands that still need to qualify for the low-pot, but have outs for a low-hand that will improve the rank of the high hand. For example consider the best possible coordinated high that you could hold on Sixth Street--2-clubs, 3-clubs, 4-clubs, 5-clubs, 5-diamonds, 5-spades. This hand is already trip 5s, but it has four sequential suited low-cards. It can improve its high ranking to quads, a full house, or a 9-high flush or better without qualifying for the low-pot. But, it can also improve it high ranking to a 5-high or 6-high straight flush, 7-high or 8-high flush, 5-high or 6-high straight and at the same time qualify for a low-hand. It can also qualify for low without improving its high ranking. For example it can become a 7-high or 8-high low-hand, and remain trip 5s.

Uncoordinated highs still need to qualify for the low-pot, but in doing so cannot improve their high ranking. While coordinated highs might have some outs to qualify for the low-pot that do not improve the high ranking, for uncoordinated highs none of the outs for a low-hand improve the high hand. Consider the best uncoordinated high-hand that you can hold--A-spades, 2-spades, 3-spades, 5-diamonds, Q-spades, K-spades. This hand is an A-K-Q-high flush with four low-cards. There are 16 outs to qualify this hand for the low-pot--any of the 4s, 6s, 7s, or 8s--but none of these outs will change the fact that the high hand is a flush.

Lows are hands that qualify for the low-pot, but rank poorly as high hand. For these hands you are drawing for the high half of the pot. For example the holding--2-hearts, 3-hearts, 4-hearts, 5-hearts, 7-diamonds, 8-spades is a qualified 7-high low-hand, but only an 8-high high hand. However, it has many outs available to improve its high ranking. An A-hears or 6-hearts would result in a straight flush, a K-hearts, Q-hearts, J-hearts, 10-hearts, 9-hearts, 8-hearts, or 7-hearts, would make it a flush, while an A-clubs, A-diamonds, A-spades, 6-clubs, 6-diamonds, or 6-spades, would make it a straight. Any of the remaining 2s, 3s, 4s, 5s, or unsuited 8s or 7s would make it one pair.

Drawing hands are holdings that need improvement to win any part of the pot. In order of desirability the kinds or drawing hands are:

Scoop draws have outs available that can simultaneously win the high and low pots. Consider a Sixth Street holding of 2-clubs, 3-clubs, 4-clubs, 5-clubs, 9-hearts, 10-spades. This open-ended straight flush-draw has outs that will improve to a high-only flush (K-clubs, Q-clubs, J-clubs, 9-clubs, 10-clubs), outs that will qualify for the low-pot (7-hearts, 7-spades, 7-diamonds, 8-hearts, 8-spades, 8-diamonds) along with outs that qualify for the low-pot and improve the high hand. The 7-clubs or 8-clubs completes a flush and qualifies for low; the A-clubs or 6-clubs completes a straight flush and qualifies for low; the A-diamonds, A-hearts, A-spades, 6-diamonds, 6-hearts, 6-spades, would all complete a straight and qualify for low.

One-way high-draws can never qualify for the low-pot. The only outs available improve the high-ranking. Consider K-spades, K-diamonds, K-hearts, Q-hearts, J-hearts, 10-hearts, played against a 3-hearts, 4-diamonds, 5-spades, 6-clubs, 7-diamonds, 8-hearts, 8-spades. The trips Kings will lose to the 8-high straight, but the hand has many outs for a better high hand. It can improve to a straight flush, quads, full house, flush, or straight, and all of these hands would beat a low straight for the high-pot. However, the 8-high straight has a lock on the low-pot because a hand with trip Kings can never qualify.

One-way low-draws are drawing dead for the high-pot, but can still qualify for the low-pot. For example the hand A-clubs, 2-spades, 4-diamonds, 7-hearts, J-clubs, K-spades can never make a high hand better than one pair. If it plays against an opponent showing two pair--10s and 9s--on the board the hand is drawing dead for the high-pot, but drawing any of the remaining 3s, 5s, 6s, or 8s will win the low-pot.

Drawing Hands in Seven-Card Stud High-Low

2010-07-14T07:28:00.000-07:00

In high only poker the concept of drawing to improve the rank of your hand is simple. The hand can only increase in rank; cards drawn either raise the rank of your hand or they do not. But, in high-low forms of poker, defining improvement is more complicated because there are three kinds of improvement—increasing the rank of your high-hand, qualifying for a low-hand, and improving your low-hand. All hands, no matter how low, have the potential to win the high-pot, but not all hands qualify for the low-pot. To complicate matters further, some drawn cards can simultaneously improve your high and low hands, while some drawn cards can improve your high hand at the expense of disqualifying you from holding a low-hand. To account for these complexities we will define two categories of hands—half-made hands and drawing hands, and within each of these categories define three kinds of hands.

Half-made hands are holdings that can win half the pot, but need improvement to win the other half. The three kinds of half-made hands in order of desirability are:

Coordinated highs are hands that still need to qualify for the low-pot, but have outs for a low-hand that will improve the rank of the high hand. For example consider the best possible coordinated high that you could hold on Sixth Street—2-clubs, 3-clubs, 4-clubs, 5-clubs, 5-diamonds, 5-spades. This hand is already trip 5s, but it has four sequential suited low-cards. It can improve its high ranking to quads, a full house, or a 9-high flush or better without qualifying for the low-pot. But, it can also improve it high ranking to a 5-high or 6-high straight flush, 7-high or 8-high flush, 5-high or 6-high straight and at the same time qualify for a low-hand. It can also qualify for low without improving its high ranking. For example it can become a 7-high or 8-high low-hand, and remain trip 5s.

Uncoordinated highs still need to qualify for the low-pot, but in doing so cannot improve their high ranking. While coordinated highs might have some outs to qualify for the low-pot that do not improve the high ranking, for uncoordinated highs none of the outs for low improve the high hand. Consider the best uncoordinated high-hand that you can hold—A-spades, 2-spades, 3-spades, 5d, Q-spades, K-spades. This hand is an A-K-Q-high flush with four low-cards. There are 16 outs to qualify this hand for the low-pot—any of the 4s, 6s, 7s, or 8s—but none of these outs will change the fact that the high hand is a flush.

Lows are hands that qualify for the low-pot, but rank poorly as high hand. For these hands you are drawing for the high half of the pot. For example the holding—2-hearts, 3-hearts, 4-hearts, 5-hearts, 7-diamonds, 8-spades is a qualified 7-high low-hand, but only an 8-high high hand. However, it has many outs available to improve its high ranking. An A-hearts or 6-hearts would result in a straight flush, a K-hearts, Q-hearts, J-hearts, 10-hearts, 9-hearts, 8-hearts, or 7-hearts, would make it a flush, while an A-clubs, A-diamonds, A-spades, 6-clubs, 6-diamonds, or 6-spades, would make it a straight. Any of the remaining 2s, 3s, 4s, 5s, or unsuited 8s or 7s would make it one pair.

Drawing hands are holdings that need improvement to win any part of the pot. In order of desirability the kinds or drawing hands are:

Scoop draws have outs available that can simultaneously win the high and low pots. Consider a Sixth Street holding of 2-clubs, 3-clubs, 4-clubs, 5-clubs, 9-hearts, 10-spades. This open-ended straight flush-draw has outs that will improve to a high-only flush (K-clubs, Q-clubs, J-clubs, 9-clubs, 10-clubs), outs that will qualify for the low-pot (7-hearts, 7-spades, 7-diamonds, 8-hearts, 8-spades, 8-diamonds) along with outs that qualify for the low-pot and improve the high hand. The 7-clubs or 8-clubs completes a flush and qualifies for low; the A-clubs or 6-clubs completes a straight flush and qualifies for low; the A-diamonds, A-hearts, A-spades, 6-diamonds, 6-hearts, 6-spades, would all complete a straight and qualify for low.

One-way high-draws can never qualify for the low-pot. The only outs available improve the high-ranking. Consider K-spades, K-diamonds, K-hearts, Q-hearts, J-hearts, 10-hearts, played against a 3-hearts, 4-diamonds, 5-spades 6-clubs, 7-diamonds, 8-hearts, 8-spades. The trips Kings will lose to the 8-high straight, but the hand has many outs for a better high hand. It can improve to a straight flush, quads, full house, flush, or straight, and all of these hands would beat a low straight for the high-pot. However, the 8-high straight has a lock on the low-pot because a hand with trip Kings can never qualify.

One-way low-draws are drawing dead for the high-pot, but can still qualify for the low-pot. For example the hand A-clubs, 2-spades, 4-diamonds, 7-hearts, J-clubs, K-spades can never make a high hand better than one pair. If it plays against an opponent showing two pair—10s and 9s—on the board the hand is drawing dead for the high-pot, but drawing any of the remaining 3s, 5s, 6s, or 8s will win the low-pot.

Betting on the end into a heads-up split-pot

2010-02-28T13:21:00.000-08:00

I frequently see players berate other players for betting, or raising, a heads-up hand on the end in situations in which the pot is split. The complaint is that such an action costs both players money by contributing unnecessarily to the rake. The thinking goes that if a player knows that the pot will be split, it is foolish to throw additional money on the table for the house to rake before giving it back to the players. I've witnessed some very nasty comments directed at players who have made bets on the end with full knowledge that calling the bet would result in a split-pot. I've also witnessed players thank an opponent for not betting on the end and accepting the split-pot without further action.

Actually the players making these kinds of comments frequently misunderstand how the rake is calculated. In many of these situations the additional action is not generating rake for the house. The rake structure at most cardrooms usually includes a cap on the total rake taken from a single pot. Once a pot becomes large enough that the rake is capped, further bets and raises do not cost the players additional money. However, the cap depends on the number of players dealt into the hand (not the number seated at the table) which makes knowing when the cap is in effect difficult at times.

For example, consider the rake structure of a $2-4 Stud-Eight game at Full Tilt Poker . The rake is 5%, or $0.50 per $10 in the pot. But, if only two players are dealt into the hand the rake is capped at $0.50. In heads-up play, with the two players betting on every street, the cap will be reached by Fifth Street. That means action before a showdown will not cost the players or benefit the house. But, if it's the same $2-4 limits with seven players dealt into the hand, the rake is still 5%, but the cap rises to $3.00. It now takes a $60 pot to cap the rake. In a $2-4 game $60 is a large pot, even with seven players dealt in because most will fold early in the hand. In most cases, additional action on the end will generate more rake for the house.

The reason for the discrepancy is that in a two-player hand, it is common to see each player make $2 Fourth Street bets followed by $4 Fifth Street bets and a $10 pot that caps the rake is reached. But is very rare in a seven-player hand to see every single player contribute $2 on Fourth Street and $4 on Fifth Street. Even if that happened, the $42 contributed is still less than the $60 needed to cap the rake.

The situation is a little different in the $2-4 games at Poker Stars. In a two-player game the rake cap is $1, however, only $0.50 is taken from the first $20 in the pot. In a seven-player game the rake is capped at $3.00, but $1.00 is taken from a $20 pot, which is the same as at Full Tilt.

What is important to realize is that the $3 cap at Full Tilt and Poker Stars applies to all games at $2-4 limits and higher. In $5-10 games, in which $60 pots would be common, the same 5% of the pot up to $3.00 applies. Also, both cardrooms reduce the rake cap for limits less than $2-4. For $1-2 games the maximum rake at each site is $1.00, and for $0.50-1 games is it $0.50.

This means that the rake structure for the $2-4 game is the least favorable for the players because at that limit, the $3.00 cap on the rake will rarely be reached. Additional bets on the end will generate more rake for the house. You are better off playing at either a higher or lower limit than $2-4.

Both sites, by the way, have policy of not raking a hand unless it gets to Fourth Street. No money is raked if no one calls the bring-in, or if everyone folds to a raise on Third Street.

It is clear from examining the rake structures, that the complaints that players are wasting money with bets on the end are not always true. For low-limit games-$1-2 and below-a pot size of 10 large bets caps the rake. For medium to high-limit games-$3-6 and above-a pot size of 10 large bets or less caps the rake. It is only at the $2-4 limit that extra action at the end costs the player money.

Of course, even if the action on the end is generating more rake for the house, players need to be careful about automatically assuming that their opponent will not fold to a bet. Even if the bettor can't beat the board, that doesn't mean that the opponent will have enough confidence in a small pair showing along with a missed low-hand to call. That situation occurs frequently in Stud-Eight. Inducing a single fold of a better high hand could pay for all of the additional rake spent on hands in which the other player did not fold.

Low Hands in Seven-Card Stud High-Low Eight-or-Better

2010-02-18T18:26:00.000-08:00

I often see a great deal of confusion about the ranking of low-hands in Seven-Card Stud High-Low (Stud-Eight). This post is meant to explain the rankings.

When ranking low-hands, an Ace is always ranked as the lowest card. In Stud-Eight, a low hand must "qualify" to win the low pot. In contrast, the game of Razz awards the entire pot to the lowest hand with no conditions attached. To qualify for the low-pot, a low-hand must contain five cards with none paired, and none ranked higher than an 8. For example: 8, 5 4, 2, A and 7, 6, 4, 3, 2 are qualifying low hands. A hand such as 9, 4, 3, 2, A does not qualify for low. When comparing low hands, the high cards are compared first. Therefore 8, 4, 3, 2, A would loose to 7, 6, 4, 3, 2. When high cards match the second highest cards are compared and so on until there is a discrepancy. For example 8, 7, 4, 3, 2 would loose to 8, 6, 4, 3, 2 and 8, 6, 4, 3, A would beat 8, 6, 4, 3, 2. If all cards in two or more qualifying low hands match, the players split the low pot.

Straights and flushes do not disqualify a hand from low. As a result, the best possible low hand is 5, 4, 3, 2, A, a hand that could also compete for the high pot as a 5-high straight. A hand such as A, 2, 4, 5, 7 all in spades, could compete as an Ace-high flush for the high pot, and 7-high low for the low pot. In high-only poker, the dream hand is the "royal flush" (Ace-high straight flush) because it out-ranks all other hands. In high-low games, the dream hand is the "steel wheel" which is an A, 2, 3, 4, 5, all in the same suit. Simultaneously it serves as the best possible low hand, and as a 5-high straight flush. Even thought it is the lowest-ranked straight flush, it would win high against any player with four-of-a-kind.

There are a total of 56 qualified low hands in Stud-Eight. Ranked from best (lowest), to worse (highest), the low hands can be categorized by the highest card in the group. Here is a listing of the low-hands in order of rank, with the total number of each kind of hand in parenthesis.
.

5-high hands (1)

5, 4, 3, 2, A

6-high hands (5)

6, 4, 3, 2, A

6, 5, 3, 2, A
6, 5, 4, 2, A
6, 5, 4, 3, A
6, 5, 4, 3, 2

7-high hands (15)

7, 4, 3, 2, A

7, 5, 3, 2, A
7, 5, 4, 2, A
7, 5, 4, 3, A
7, 5, 4, 3, 2

7, 6, 3, 2, A
7, 6, 4, 2, A
7, 6, 4, 3, A
7, 6, 4, 3, 2
7, 6, 5, 2, A
7, 6, 5, 3, A
7, 6, 5, 3, 2
7, 6, 5, 4, A
7, 6, 5, 4, 2
7, 6, 5, 4, 3

8-high hands (35)

8, 4, 3, 2, A

8, 5, 3, 2, A
8, 5, 4, 2, A
8, 5, 4, 3, A
8, 5, 4, 3, 2

8, 6, 3, 2, A
8, 6, 4, 2, A
8, 6, 4, 3, A
8, 6, 4, 3, 2
8, 6, 5, 2, A
8, 6, 5, 3, A
8, 6, 5, 3, 2
8, 6, 5, 4, A
8, 6, 5, 4, 2
8, 6, 5, 4, 3

8, 7, 3, 2, A
8, 7, 4, 2, A
8, 7, 4, 3, A
8, 7, 4, 3, 2
8, 7, 5, 2, A
8, 7, 5, 3, A
8, 7, 5, 3, 2
8, 7, 5, 4, A
8, 7, 5, 4, 2
8, 7, 5, 4, 3

8, 7, 6, 2, A
8, 7, 6, 3, A
8, 7, 6, 3, 2
8, 7, 6, 4, A
8, 7, 6, 4, 2
8, 7, 6, 4, 3
8, 7, 6, 5, A
8, 7, 6, 5, 2
8, 7, 6, 5, 3
8, 7, 6, 5, 4

Notice that in each grouping, the low-hand that also competes for the high-pot as a straight is the worse low-hand that you can have. An 8-high straight loses the low pot to all other 8-high low-hands, a 7-high straight loses the low-pot to all other 7-high low-hands, and a 6-high straight loses the low-pot to all other 6-high low-hands. Also notice how common an 8-7 high low-hand is compared to the other low-hands. Of the 56 possible low-hands, 20 are 8-7 high low-hands, which is more than all the 7-high low-hands combined (15 total).

Note for Omaha High-Low players:

Low-hands are ranked the same in Omaha High-Low and in Stud-Eight, but I've seen players become confused in determining the rank of their low-hands. In Omaha High-Low, you must use three community cards combined with two in your hand. That means that if the community cards include an 8, 7, 6, and you hold an A, 2, your hand is the best possible low-hand. It is still an 8-high low-hand, but no one can make a better low given the community cards. That rule makes an A, 2 a powerful holding in Omaha High-Low. But in Stud-Eight, if you have an 8, 7, 6, A, 2, you lose the low-pot to a player with a 7, 6, 5, 4, 3. You have an 8-high low-hand and your opponent has a 7-high low-hand. The 7-high bests the 8-high for the low-pot. The fact that you have A, 2, for your lowest cards, does not matter because it is the high card in the hand that counts.

It is also worth noting, that in contrast to Omaha High-Low, being "quartered" in Stud-Eight is a rare event. In Omaha High-Low, it is common for two players to each have the best possible low-hand and split the low-pot (each receive one-quarter of the total pot). For example if two players each have an A, 2, and the community cards included 8, 7, 6, each player has the same low-hand. But, in Stud-Eight there are no community cards, which means that to split a low-pot all five cards in the players' low-hands must match. A single un-matched card will decide the low-pot. For example, a player with 7, 6, 5, 3, 2 would lose the low-pot to a 7, 6, 5, 3, A, because the Ace beats the 2 for low.

Low Straight Blockers

2010-01-31T12:45:00.000-08:00

When betting on a high pair in Seven-Card Stud High-Low, against a player showing a bunch of scary-looking low-cards, the possibility of being scooped by a low straight must be considered. Conversely, if you have a bunch of low-cards, how likely is it that your hand will also fill out into a low straight? The chances of a bunch of low-cards turning into a low straight depend on the availability of the "blockers." That is the location of cards that are necessary for a low straight to form. If the needed cards are dead, the low straight is blocked, and the relative value of the high-hand goes way up in relation to the low-hand.

That means that when reading the board, you should look for exposed cards that block the completion of low straights. For example, if you started with 2, 3, 4, and picked up a 6 on Fourth Street, be on the lookout for the 5s. If three of the 5s are exposed on the board, your hand has gone way down in value. Your straight potential is down to just one out. You are essentially drawing for just one half the pot, which is a violation of the most fundamental principle of high-low poker, that you should always play to scoop.

Knowing the blockers is also important if you are going high. Suppose your hand is (4, 4,) 4, J and Bob raises with (X, X) 3, 5. You see the remaining 4 in Alice's hand. Your draw for quads might be dead, but more importantly; Bob's draw for any kind of low straight is completely dead. He will not hit a wheel, or even an 8-high straight. You can re-raise Bob all you want, because he will not beat you with a straight.

Here is a table of blockers for low straights (8-high or less):

Dead Rank	straights blocked	straights possible
A	5-high	6-high, 7-high, 8-high
2	5-high, 6-high	7-high, 8-high
3	5-high, 6-high, 7-high	8-high
4	5-high, 6-high, 7-high, 8-high	none
5	5-high, 6-high, 7-high, 8-high	none
6	6-high, 7-high, 8-high	5-high
7	7-high, 8-high	5-high, 6-high
8	8-high	5-high, 6-high, 7-high

It is important to note in the above table the critical role of the 4s and 5s. If either rank is dead, no low straights (8-high or less) are possible. If the 4s are dead the minimum allowed straight is a 9-high, and for the 5s the minimum is a 10-high. Players with exposed low cards (8s and less) are less likely to reach straights that high.

Also note from the table that these two-card combinations that will block all low straights.

A, 6
2, 6
3, 6
2, 7
3, 7
3, 8

In other words, if any single wheel card plus the 6s are dead, no low straights are possible. Dead 2s or dead 3s combined with dead 7s block all low straights. Dead 3s and 8s block all low straights.

Keeping track of blockers is especially important on later streets in determining hand values. Two 5s might be gone on by Fourth Street, but if all are dead by Sixth Street, that is useful information for deciding whether to value bet on the end.

Key Concepts in High-Low Poker: Part II

2009-12-29T07:49:00.000-08:00

This is a continuation of a post in October on concepts for high-low poker. If you have only played variants of poker in which the high-hand wins the entire pot, and are trying to learn some of the split-pot games, here are some key concepts for high-low play that apply to Seven-Card Stud High-Low Eight-or Better Poker (Stud-Eight), as well as Omaha High-Low Eight-or-Better.

Split-pots generate action: Many players complain about split-pot games, because it is possible for a powerful (monster) hand, such as quads, to split a heads-up pot resulting in a slight loss after the rake is subtracted. It seems unfair that you can hit a hand as rare as quads, and have to share the winnings. But, while winning the hand isn't a problem when you hit a monster, getting action on that hand often is a problem.

Consider holding pocket Aces in Hold'em or Omaha and flopping quads. Pairs on the board are scary enough, and since no one else has Aces you are unlikely to generate much action. Even someone with a full boat might be cautious. The same problem exists in Seven-Card Stud. It is possible to hold quads, or a boat, without showing a pair, but unlikely. If you have an exposed pair of Aces your action will dry up.

But, in split-pot games, action is possible in these circumstances because potential lows might try to draw. Sometimes they will hit the low, and you will have to share. But a certain fraction of the time, the low will not qualify, and you keep it all. Just remember, in each case you are receiving action that might not have occurred in a high-only game. If more than one low-draw joins the fray, you are assured of winning money, and can raise without risk of losing or driving out paying customers.

It might be frustrating to share large pots with a nut-high, but remember the pot might not have had any value had competition for a low-pot not been possible.

Starting card requirements should be tighter: Split-pot games have different starting card requirements than high-only games, because the goal is to scoop. Starting hands must have the potential to win the high-pot or low-pot, and ideally both. Because high-low games offer so many different kinds of drawing opportunities, many players think that starting hand requirements can be looser than for high-only games, such as Seven-Card Stud or Hold'em. Actually, the reverse is true. Starting hand requirements need to be much tighter, because coordinated starting cards that have the potential to attack both sides of the pot are rare holdings. In Hold'em, each player receives just two cards, and that makes just about any pair, or any two high-cards a potential winner. But, in Stud-Eight, three starting cards are less likely to coordinate than two. Starting hand requirements are discussed at great length at StudHighLow.com. However, there are some general principles.

-- Aces, either singly or paired, are the most valuable starting cards because of their potential to complete both a high-hand, and a low-hand.

-- Connected low-cards, suited low-cards, and connected-suited low-cards have the greatest potential to scoop large multi-way pots.

-- Mid-range cards, especially 9s, 10s, Js, play poorly, and should be avoided. However, even 8s, Qs, and Ks can lead to problems.

Strong starting hands in Stud-Eight also need to be "live," meaning that the cards needed to improve must not exposed in other hands. An A, 2, 3, all in Clubs is a great looking starting hand in Stud-Eight, unless you are looking out at a board with the 5, 6, 9 in Clubs, and two of the remaining Aces. It is frequent to receive starting cards that look great, but need to be mucked, because too many of the cards needed to improve are exposed in other hands.

Fold equity is reduced: There are two ways to win a pot in poker-have the best cards at showdown, or induce the other players to fold before a showdown happens. The act of betting is intended to put more money in the pot to win when you have the best cards. But, betting also forces opponents to make decisions, and folding is one alternative when confronted with a bet. The chance that a bet will win the pot uncontested is known as "fold equity." Bets in high-low games have much less fold equity than bets in high-only games, especially late in the hand if the pot is large. Players that failed to improve for the high-pot, might still have many outs available for the low-pot, so it is not in their long-term interests to fold to hands that will clearly win the high-pot. The reduced fold equity means that aggression, and bluffing, must be combined with cards that work together to attack both sides of the pot. Aggression will not win by itself, because players call much more frequently in high-low games.

Most fold equity in Stud-Eight is available early in the hand, when players with marginal cards will fold to bets and raises, because they do not want to be sucked too deeply into a hand with limited opportunities. However, players, who stay until Sixth Street, are usually in it until the end. Part of the problem, is that by Sixth Street, many pots become so large, that drawing to half the pot becomes mathematically correct. This is especially true for players who missed their high chances, but still have ten or more outs for a low-hand. Contesting a small pot on Third Street, with a hand that can only compete for the low-pot makes no sense mathematically. But, a large multi-way pot on Sixth Street is a different case, particularly if a draw to a low-hand is still live. My own experience, playing Stud-Eight, is that fold equity on Sixth Street is close to zero. Opponents willing to call a large bet on Fifth Street, almost never fold to a Sixth Street bet. An opponent willing to fold on Seventh Street is slightly more common, because of missed low-draws, but it is still an uncommon event. The fact is that you will show down more hands in Stud-Eight compared to most other variations of poker.

For big money invest in low-straights and low-flushes: In high-only games, when you think of monster hands, what come to mind are full houses and quads. Ironically, in high-low games filling up can often be detrimental to your financial outcome. For example, in Stud-Eight, if you hold A, A, 3, 3, 4, 6 going to the river, a final card of 2 might scoop the pot with Aces-up for a high-hand, and a 6-high for a low-hand. But, if an A, or 3, hits the full house disqualifies your hand from competing for the low-pot. Because two-pair, and trips are vulnerable hands in games with many competitors going to the river, the hands that have the best change of holding up for the high-pot, and winning the low-pot are the small straights, and Ace-high flushes with a complement of small cards. A hand such as 6, 5, 4, 3, 2, is simultaneously a 6-high low-hand, and a 6-high straight. The hand A, 2, 4, 5, 7, all is Spades is simultaneously a 7-high low-hand, and an Ace-high flush. In both of these examples, the hand is simultaneously a powerful low-hand and a powerful high-hand. In the case of the straight, it beats anyone holding two pair or trips, and in the case of the flush it beats anyone holding a straight.

Low-straights and low-flushes are also rare hands that can never be completely exposed, because five cards are required. That means if the pot is large, any player with two pair, or trips, will have to call you down at the end to make sure that your hand is not just a low-hand. Draws to these hands also offer excellent freeroll opportunities. Suppose after Fifth Street, you have A-Hearts, 2-Hearts, 4-Hearts, 5-Hearts, 6-clubs. Your hand is a 6-high low-hand, that might have a lock on the low-pot. At the same time you have two cards to come, and any Heart gives you an Ace-high flush, a 3-Diamonds, 3-Spades, or 3-Clubs, gives you a 5-high straight, and a 3-Hearts gives you a 5-high straight flush. The draws to all of these possibilities are risk-free.

Catching Bad versus Catching Good on Fourth Street

2009-12-07T13:16:00.000-08:00

Fourth Street is a point in the hand when it is easy to get out before becoming too committed to the pot. Many players who catch a bad card on Fourth Street will make quick exits, and many times, a raise will hasten the exit of marginal hands. Before betting or raising into multi-way pots, it is important to think ahead about how potential raises will effect the action.

Consider these scenarios:

High-pair with no low:

You (J, K) K, 10
Alice (X, X) 2, 3
Bob (X, X) 4, 8

You have a big pair with no hope of a low-hand, against two players who have each caught low cards. However, neither Alice nor Bob has a low-hand yet, and your pair would stand a better chance of scooping in heads-up play. You should lead with a bet. If Alice has four little cards, she will raise to force Bob, her other low-hand competitor, off the hand. Then you can re-raise Alice, to make her pay to draw out on you for the low-pot. If you instead check to the lows in this hand, Alice will bet, Bob will call, and you won’t have much better to do but call and hope for the best. A check-raise after Alice bets and Bob calls, will probably not force anyone off the hand. Bob will stay at that point, even if Alice raises, because he is into the hand too deep.

A low-draw:

You (4, 5) 6, A
Alice (X, X) K, 9
Bob (X, X) Q, 10

You have caught a decent card, although, it does not connect with your initial three and that lessens the chance of scooping with a low straight. The Ace does act first on this board. It would be tempting to bet, but then Alice might raise Bob off the hand. If that happened, you would be drawing for just one-half the pot, heads-up against Alice. It would be better to check to Alice, let her bet and Bob call. Then you could call and keep both players in. Most likely, Alice and Bob each have a big pair and no chance for a low-hand. If you pickup a low hand later on, then you can drive the action make it difficult for both Bob and Alice.

Small pair:

You (4, 5) 4, J
Alice (X, X) K, Q
Bob (X, X) 6, 5

In this situation, you should check-fold your hand no matter how Alice or Bob play. Your hand is unlikely to make low, which means that all you really have is a pair of 4s for high against a probable pair of Kings. You will be playing catch up for one-half the pot, a terrible situation to be in. But, I’ve seen many players continue in the hand until the end with any kind of pair, a pattern that is sure to lose money over the long-run.

Second-best low:

Alice (X, X) K, Q
You (A, 3) 4, 8
Bob (X, X) 6, 5

If Alice leads with a bet in this situation, you should fold because of your position. You never want to be in the middle between the best high-hand and best low-hand because it will cost you four bets to see every card. If you call Alice, Bob will raise and Alice will re-raise. If you cold-call that two-bet raise, Bob will cap it. Your best hope after that is that Bob catches bad on 5th street and does not complete the low-hand, but you catch good and do. But, even if that happens—for example Bob gets a Jack while you get a 7—you are still in a tough spot because you have the worse possible low-hand—an 8-7—while Bob has a draw to a better low. If you both catch good cards—for example both you and Bob get 7s—you are in a terrible position on Fifth Street because you are not sure where your low-hand ranks and you have almost no chance of scooping. It is best to get out cheaply on Fourth Street before being faced with all these difficult and expensive decisions.

Potential monster with a brick:

Alice (X, X) Q, 7
You (3d, 4d) 5d, Ks
Bob (X, X) 6, 5

Alice leads with a bet and you are faced with a situation similar to the previous one, in which a call could lead to capped action. The difference is that you’ve caught a bad card for one of the best three-card starting hands. Your hand could develop into a monster, which means that you do not want to be raised out of it. At the same time, the bad card means that you do not want to put a lot of money in the pot. One possible solution is for you to make the raise. That might cause both Alice and Bob to pause. They would have to consider the possibility that you have wired Kings and just completed trips. If Bob raised, Alice might leave the hand and you might even have the highest hand at that point. If Bob called and Alice called, you would make it to Fifth Street for the cost of two small bets, instead of four, and could decide what to do from there. You might even get free cards on Fifth Street if Alice and Bob don’t improve.

Overplaying the Eight

2009-11-27T18:35:00.000-08:00

One of the most common mistakes I see in Seven-Card Stud High-Low, is overplaying 8-high low-hands. Many players raise the moment they make any kind of low-hand, even if it's on the river, and cold-call raises with a draw to any kind of low-hand, even if its an 8-high.

The problem is that the 8 is actually one of the deadliest cards you can hold, because an 8-high is the worse possible low-hand. Remember, that a low of 8, 4, 3, 2, A, loses the low-pot to 7, 6, 5, 4, 2, because low-hands are ranked by the highest card, not the lowest.

I once saw a player river an 8-high low-hand and fire an immediate raise. He was promptly called and scooped by an opponent with a 7-high low-hand and an exposed pair of 3s for high. The raiser could not beat the board for high, and yet raised on the basis a weak low-hand.

A river raise will hardly ever move a bettor off a hand in Seven-Card Stud High-Low. In fact, you will show more hands at the end then just about any other form of poker. Most players who bet until the end have something going for at least one-half of the pot. Remember, it is a fixed-limit game with pots that can grow very large by the end. With only one bet to call at the end, players with any kind of chance for any half of the pot usually pay to see the raiser's holdings. Many players with a small pair such as 3s, will call if they can beat the board for high, even if they miss a low-hand. The call often works because if multiple players are competing for low-hands only, it is not uncommon for a small pair, or even A-K, to take the high-pot at the end.

Because hands with an 8 qualify for low, many players automatically play them aggressively and often set themselves up for disaster. In one hand, I bet out a 7-5 low-hand on Fifth Street and was promptly raised by an opponent with an 8, 7, 5, showing on the board. Knowing it would be difficult for her to better my low-hand, I re-raised and ended up scooping the entire pot when at the end, I completed a 7-high straight.

In another hand my opponent was luckier. I had completed a 9-high straight on Fifth Street, and my opponent, who had an 8, 6, 10 exposed, cold-called my two-bet raise to draw to an 8-high low. On Sixth Street I picked up the 4 to make it 6 sequential cards, while my opponent hit a King and kept calling. He saved half the pot on the end when I caught a Queen that failed to improve my 8-7 low-hand and he picked up a 2 to complete an 8-6 low-hand. He got his money back, but calling all those raises in order to draw to second-worse low-hand that you can have, (the 8-high straight I held is the worse) will not win over the long-run.

The pitfalls of 8s, means that many of the so-called "Razz hands," such as starting cards of 8, 2, 3, or 8, 7, 3, or even 8, 2, A, should not be played. These hands are playable in Razz because the lowest hand takes the entire pot with no qualifier necessary. But, in Seven-Card Stud High-Low these cards are competing for one-half the pot, and are often second best for that half of the pot. If you play low starting cards, the cards should have some possibility of "connecting," that is complete a low straight, and rank better than an 8-high for the low-hand.

Probabilities for Simultaneous High and Low-Draws: Weighted Outs

2009-11-19T13:48:00.000-08:00

The big-money hands in Seven-Card Stud High-Low are the low straights and low flushes. These hands often scoop and better yet, usually get paid. Any player with at least two-pair will pay if the pot is large, because it is not possible to know for certain that the hand qualifies for low, let alone know that it is a straight or flush.

However, if you start with connected or suited cards, and then pick up a helpful card on Fourth Street, you still do not have a winning hand. Here is a summary of the outs available to complete the low-hand, high-hand, or both for some common Fifth Street-draws. For these tabulations I will introduce the concept of "weighted outs". In many cases the total number of outs to make a high-hand, low-hand, or both, are the same. But some circumstances are more favorable than others, because the numbers of outs that can make both a high-hand and a low-hand are greater than the number that make high-hand only or low-hand only.

To reflect this discrepancy, I define a "weighted out" as equal to 1 if the out completes a high-hand and a low-hand, and one-half (0.5) if the out completes a high-hand or a low-hand. Totaling "weighted outs" is a better measure of your actual equity in the pot. For example, if you have seen 16 cards after Fourth Street, there are 36 unseen cards. If your total weighted outs are 12, you have 33% equity in the pot. Some of the outs might result in winning only half the pot, and some the entire pot, but on average you can expect to pick up 33% of the money on the table if the scenario is repeated many times.

Here are the tabulations:

Open-ended straight-flush with low-draw

Example: 3, 4, 5, 6 all in Spades

Improve to:	Outs	Weighted Outs
Straight-Flush	2	2
Straight	6	6
Low-flush	2	2
High-flush	5	2.5
Low-hand	6	3
Totals	21	15.5

Four-flush with inside straight and low-draw

Example: A, 3, 4, 5 all in Hearts

Improve to:	Outs	Weighted Outs
Straight-Flush	1	1
Straight	3	3
Low-flush	3	3
High-flush	5	2.5
Low-hand	9	4.5
Totals	21	14

Four-flush with low-draw

Example: A, 3, 5, 6 in Hearts

Improve to:	Outs	Weighted Outs
Low-flush	4	4
High-flush	5	2.5
Low-hand	12	6
Totals	21	12.5

Open-ended straight with low-draw

Example: 3, 4, 5, 6 rainbow

Improve to:	Outs	Weighted Outs
Straight	8	8
Low-hand	8	4
Totals	16	12

Inside straight with low-draw

Example: 3, 4, 6, 7 rainbow

Improve to:	Outs	Weighted Outs
Straight	4	4
Low-hand	12	6
Totals	16	10

All of these tabulations count the maximum number of outs possible, which only occurs when the draw is completely live. It is rare that a Fifth Street draw, in which 10 to 15 cards are already exposed, would be completely live. That is why counting weighted outs on the later streets is so important. Consider the most favorable draw-an open-ended straight-flush with low-draw. If the 6 outs to a low-hand are missing, the weighted outs drop by 3 to a total of 12.5. But, if the 6 outs for the straight are missing, the total weighted outs drops by 6 to 9.5.

The tabulations above are still valid on later streets. In all likelihood there would be fewer unseen cards on later streets, but more missing outs. As is usually the case in Seven-Card Stud High-Low, pot equity can change drastically from street-to-street as cards are exposed.

Cold-Calling a Blocking-Raise with a Low-Draw: Scenario 2

2009-11-10T06:44:00.000-08:00

Last week, I analyzed a tactic in Seven-Card Stud High-Low Poker I call a "blocking-raise," in which a player with a made low-hand on Fifth or Sixth Street, raises a bet from a high-hand to force out a player on a draw to a better low. The issue is whether it is correct for the player on a draw to cold-call the raise. Analysis showed that if a scoop is possible for the player on a draw, cold-calling does gain equity. The amount of equity depends on the number of outs that are still live. But what happens if no scoop is possible?

Consider a second scenario:

After Fifth Street you are in a three-way pot with the following (hole cards are in parenthesis):

You (A, 2) 6, 7, J
Bob (x, x) 3, 4, 8
Alice (x, x) K, 9, J

Action: Alice leads with a $2 bet; Bob raises to $4. It is your turn to act.

Again for computational purposes we will assume a $1-2 game with eight players dealt into the hand.

Total seen cards = 16 (Eleven that you are looking at, plus five mucked door cards).
Total unseen cards = 36.

A scoop is less likely in this case because you cannot complete a straight. Your only hope to scoop is to pair the Ace and hope it holds up against the high-hand. If your hand is completely live, your outs to make low-hand are as follows:

Outs to make a 7-high low=10 (three 3s, plus three 4s, plus four 5s)
Outs to make an 8-high low = 3 (three 8s)

Again we can divide the number of outs by 36 to arrive at Sixth Street probabilities. Your chances on Sixth Street of having a:

7-high low = 28%
8-high low = 8.3%

Again we can approximate your equity in the pot by making the following assumptions:

A 7-high will win the low-pot.
An 8-high will win the low-pot about half of the time.

Then if (P) represents the pot-size, and (E) represents the equity in the pot, then under these assumptions:

E = (0.28)P/2 + (0.083)P/4 = (0.16)P

Because you are on a draw for only one-half the pot, your equity is only one-sixth of its value. To break-even on this play you need a pot-size of about $24. Unless there was a great deal of prior action on the early streets in the hand, it is unlikely that the pot is that large. It is also unlikely that your low-draw is completely live if Bob already has a low-hand. In this scenario, without a possibility of a scoop, it is best to fold to the raise.

Cold-Calling a Blocking-Raise with a Low-Draw: Scenario 1

2009-11-02T20:19:00.000-08:00

A tactic, that Seven-Card Stud High-Low (Stud-Eight) players frequently encounter, is what I call a “blocking-raise.” This is a raise intended to force out a player on a low-draw. Usually, a player who has just made a low-hand, and wants to force out a player drawing to a better low, executes this kind of raise. Blocking-raises occur most often on Fifth or Sixth Streets, when a player has completed a weak low—such as an 8-high—and wants to force out a player showing two undercards, but no other low-cards. Any player, with only two exposed low-cards, cannot have a low-hand until the river. In this post, I will analyze a scenario to determine if cold-calling a blocking-raise is a correct response. As is usually the case in high-low poker, whether or not a scoop is possible, has large effect on the expected value for a play.

For these computations, I will assume a $1-2 game with eight players dealt into the hand. Hole cards are in parentheses.

After Fifth Street you are in a three-way pot with the following:

You (2, 3) 4, 5, J
Bob (x, x) 3, 4, 8
Alice (x, x) K, 9, J

Action: Alice leads with a $2 bet; Bob raises to $4. It is your turn to act.
Total seen cards = 16 (Eleven that you are looking at, plus five mucked door cards).
Total unseen cards = 36.

If your hand is completely live, your outs are as follows:

Outs to make a straight=8 (four As plus four 6s)
Outs to make a better low = 4 (four 7s)
Outs to make comparable low = 3 (three 8s)

That means we can divide the number of outs by 36 to arrive at Sixth Street probabilities. Your chances on Sixth Street of having a:

Straight = 22%
7-high low = 11%
8-high low = 8.3%

We can approximate your equity in the pot by making the following assumptions:

A straight will scoop.
A 7-high will win the low-pot.
An 8-high will win the low-pot about half of the time.

Then if (P) represents the pot-size, and (E) represents the equity in the pot, then under these assumptions:

E = (0.22)P + (0.11)P/2 + (0.083)P/4 = (0.296)P

You expect about 30% equity in the total pot after the action is completed. If you cold-call the $4-raise and Alice closes the action with a call, the total pot-size needs to be at least $13 for your equity to equal the $4 call. We know that the antes and Fifth Street action alone is equal to $13. If there was any prior action on Third and Fourth Streets, the pot is larger than $13. Cold-calling the raise is a profitable response. Not only is the current pot-size large enough, but also the implied pot-size from action on Sixth and Seventh Streets is greater still. And you get a second chance to make the hand if you miss on Sixth Street. Depending on the exposed Sixth Street cards, a cold-call might still be favorable.

However, it is rare that your hand is completely live. The kinds of missing outs make a big difference in your pot-equity. If the 7s and 8s are dead, but the straight draw is live, your pot-equity falls to 22%. That means you need to take down an $18 pot to make a $4 investment worth it. But, if your straight-draw has missing outs, your pot-equity is considerably reduced. Suppose you only have four outs left for your straight, but the 7s and 8s are live. Now your pot-equity is 18.5%. You need a pot in excess of $21 to break-even. That could be a stretch. You might only get that kind of action if the high-hand can beat a low straight, in which case you have only half the equity that you thought you did.

Also keep in mind, that if Alice jams you, that is not close the action by calling, she might be unafraid of a low straight because she can already beat one. The kind of player Alice is has a big effect on your equity. Some players with high-hands are timid in response to a possible low-hand because they are afraid of being freerolled. These players will call the low-hand down, unless they can beat a low straight, in which case they will raise. Other players are more afraid of giving free cards than being freerolled, and will jam anyone raising with a low-cards, even if all they have is one or two pair. In that case your scoop possibility is still live.

Next week we’ll look at a scenario in which scooping is not a possibility.

Key Concepts for High-Low Poker, Part I

2009-10-26T08:51:00.000-07:00

If you have only played high-only variants of poker, and are trying to learn some of high-low games, here are some key concepts you need to know. These concepts apply to both Omaha High-Low and Seven-Card Stud High-Low Eight-or-Better (referred to as "Stud-Eight" in the post).

Scooping: Routinely playing for high-hand only, or low-hand only, leads to trouble. Splitting the pot should be a saving out, not the reason for playing the hand. As a general rule, you do not want to be on a draw for half the pot. The goal should be to have a hand that is on track to win the entire pot. Ideally, opponents drawing against your hand should only win half the pot when their hands hit.

For example in Stud-Eight, many players routinely play uncoordinated low cards with the intention of winning low-only. But consider going the river with A, A, 5, 5, K against an opponent with 2, 3, 5, 7, J. The King on Sixth Street caused you to miss a chance at low, but you have a lock on high. Your opponent is hoping to pick up either an A, 4, 6, or 8 to hit low. Depending on the number cards exposed, that could be as many as 14 outs. But your opponent will only get half the pot if he or she hits, you get the entire pot if he or she misses. Repeat this scenario enough times and you will accrue much more money.

The value of Aces: Compared to high-only poker, Aces have even greater value in high-low games, although not for the usual reasons. Understanding the role of Aces is critical to success. In Hold'em a pair of "bare" Aces is a powerhouse, because it can often win on its own without improvement. In high-low games, bare Aces rarely win without improvement. Many players transitioning from high-only games over value pairs of Aces, and loose money by overplaying them. But Aces are the most important cards in high-low games because they are simultaneously the lowest and highest card in your hand. Having an Ace is the equivalent of having an extra card.

In Omaha High-Low, a starting hand such as A, 2, 3, J, can be part of a nut-low such as A, 2, 3, 4, 5 or a nut-straight A, K, Q, J, 10, depending on the board. In Stud-Eight, an Ace can be part of an Ace-high flush such as A, 3, 4, 5, 6 all in Spades, and these same cards also qualify for a 6-high low. Correct strategy that emphasizes playing coordinated cards that can scoop, relies on the dual capabilities of Aces.

Qualifying for Low: Most high-low forms of poker require that the low hand "qualify." In Stud-Eight and Omaha High-Low, the qualification is that a low-hand must contain five cards with none higher than an eight. If no hand qualifies for low, the high-hand takes the entire pot. It is sometimes possible to know that no hand qualifies for low. In Omaha High-Low, players must use two of their cards to form hands. Low hands are impossible if three cards appear on the board higher than an 8, and in that case, competition is only for the high hand. In Stud-Eight, any player with three exposed cards higher than an 8, cannot have a qualifying low. If all players have three exposed cards higher than an 8, the game reverts to ordinary Seven-Card Stud. But even if a low is possible, that does not guarantee that someone has a qualifying low. Judging when an opponent has a low is an important skill to develop.

Driving players out is not always correct: In high-only poker when you have the best hand, you want to make it expensive for the others to stay and draw out on you. Betting and raising are the usual actions. That is usually the case in high-low games, but not always. If you have a nut-low and are up against a high-hand that you cannot beat or move off the pot, the only way to profit is to keep others in the game. If the other players will cold-call raises, then by all means raise. But, if raising will drive them away, calling is the best play.

Freerolling: This term refers to situations where you can make risk-free bets that will payoff if your hand improves. Freerolls occur in all variants of poker, but the number of freeroll opportunities is much greater in Stud-Eight.

Consider the following situation in Pot-Limit Omaha. You hold A-Spades, Q-Hearts, J-Diamonds, 10-Spades. Your opponent holds A-Diamonds, 3- Diamonds, J-Hearts, 10-Spades. The flop is 9-Spades, 8-Spades, 7-Hearts. Both of you flopped the nuts. But your opponent's hand cannot improve. Yours can improve to the nut-flush, if any Spade hits later on, or a Queen-high straight, if a 10 hits. If a Queen hits you both have Queen-high straights but if it's the Queen of Spades you have made the nut-flush. Your opponent's nut-flush possibility in Diamonds is dead. That means if you raise all-in against each other, the worse that can happen to you is a split-pot where you recover your investment. But, you get two additional cards that might improve your hand so that you can take the entire pot. Your opponent risks his entire stack for half the pot. You risk nothing for a significant chance of taking the entire pot.

Freerolls occur more frequently in Stud-Eight. In high-only Seven-Card Stud, it is difficult to know if you have the nuts. After all, in Seven-Card Stud it is possible for an opponent to have a full house or quads without showing an open pair on the board. But in Stud-Eight it is possible to know if you have the nut-low. That often puts the player with a made nut-low in the drivers seat, with a re-draw to a possible high. Consider having A, 4, 5, 6, 7 against K, 4, 10, 10, K. If this were high-only Seven-Card Stud the player with the open-ended straight would have to call bets from the player with the two-pair in hopes of improving. But, in Stud-Eight the situation is reversed. The player with the two-pair can never make a low-hand and the player with the made low-hand knows that. With the low already made, that player can bet and raise with no risk, because half the pot is assured. If the straight hits and the two-pair do not improve, the entire pot goes to the straight.

The situation in Stud-Eight can get more interesting with multi-way pots. Consider having A, 2, 5, 6, 8 against two opponents with, A, A, J, 10, 10 and Q, 9, 9, Q, 9. Your opponents with well-hidden high hands, might start a raising war that you can encourage with additional re-raises, at no risk to yourself. You know that you get half the pot no matter which high-hand holds up. Put in all the raises you can, because the hand is guaranteed to make you money.

Reasons to Limp-in on Third Street

2009-10-19T14:51:00.000-07:00

In the previous post, I concluded that you gain an edge from attacking players who limp-in on Third Street with three low-cards, and fold immediately if hit with a high-card on Fourth Street. That raises the question: Are there situations where it is correct to limp-in on Third Street? As a general rule, open-limping is a weak play. If you intend to play the hand, and have the first opportunity to complete the bet, you should complete and force the players acting later to define their hands. It is also risky to allow the bring-in a free card. However, there are situations when limping has advantages. The situations I will analyze are when you act after multiple limpers, and you (1) hold a live-pair other than Aces (2) hold the lowest hand.

These situations occur frequently in low-limit Seven-Card Stud High-Low (Stud-Eight) games, when it is common for several players to limp-in holding just about anything. These players are hoping for a cheap card on Fourth Street that will somehow improve their mediocre starting cards. As a general rule, completing the bet after these players have limped-in, will not drive them out. Even though they would have folded, if a bet were placed before they had a chance to act, they now feel committed to the hand, and will call, if you bet.

(1) Pairs other than Aces. In Stud-Eight, pairs can present problems because they are a poor start for a low-hand, and in many cases, a poor start for high-hand. Mid-pairs, such as 9s and 10s are almost unplayable against a large field. The hand is unlikely to make low, and stands a good chance of being dominated by for high. A low-pair with a low-kicker, has a better chance of making a low-hand, but a greater chance of being dominated for high-hand. However, rolled-trips are powerful holdings, and in cases when the trips are low, an extremely deceptive holding. Rolled low-trips often look like the best low-hand, when in reality it might be the best high-hand.

Consider a $1-2 Stud-Eight game with a $0.20 ante and a $0.25 bring-in. Eight hands are dealt, and three players limp after the bring-in. You hold a low-pair with a low-kicker and your cards are completely live. Therefore, when it is your turn, the pot has $2.60. If by limping, you end the action, the pot is offering 10 to 1 on your $0.25 payment. What are the odds of making trips? You have seen 10 cards--the three in your hand, plus the other seven door cards. Only two of the remaining 42 unseen cards make trips, so the odds against trips are 20 to 1. However, the implied pots odds are much greater than the current 10 to 1 the pot is paying. If you make trips, a strong possibility exists for you to scoop what could be a $20 to $30 pot. You will have to contribute a minimum of $7 to reach a showdown, but with trips after Fourth Street, you are a heavy favorite.

However, if you complete the bet, instead of limping, your initial pot odds are greatly reduced. If you complete, and the other three players call, you have contributed $1, while the others contributed $4.85. The pot is now paying about 5 to 1, while the possibility of making trips on Fourth Street remains 20 to 1. You need much greater implied pot odds to have an edge compared to the case of limping. And remember, rolled-trips is not a lock, the hand will be outdrawn at times.

This analysis assumes that you will fold on Fourth Street, if your hand does not improve to trips. Against a large field this will often be the case. Limping, followed by a quick fold in the case of no improvement, is a viable strategy in circumstances when aggression will not drive players out. You will almost always need to have strong cards against a large field of limpers, because, in most cases, at least one person will improve, and stay until the end.

(2) Holding the lowest hand. Low-cards, that are unsuited and unconnected, are generally weak starting cards in Stud-Eight. These cards usually compete for just one half of the pot, so the pot odds are greatly reduced in comparison to a hand that can scoop. However, if you are the lowest hand on the board, against a number of players who have limped-in with high cards, it can be worth limping to pick up a cheap Fourth Street card. In this case you are looking to pick up a low-draw, not to make a low-pair. If your low-draw is completely live, there are 20 unknown cards that can help (the 9 other low cards will pair your hand). In an eight-handed game with seven other door cards, 42 cards remain unseen. You are looking at "coin-flip" chances of picking up a low-draw on Fourth Street--20 out of 42, or 47.6%. However, a low-draw is not yet a qualified low, so you will be investing money on the later streets before you know if the hand has any value. But on later streets, a low-hand against multiple highs, can be a profitable holding because it can freeroll and jam the high hands.

However, limping with low-cards, after multiple players with low cards have also limped, is a questionable play. Even if your hand is the lowest of the lows on Third Street, the numbers of outs that you have to make a "viable" low-draw on Fourth Street is greatly reduced. By "viable," I mean a card that will allow your hand to remain the lowest on the board. Being second-best low is a dangerous position in Stud-Eight. Suppose you limp-in with a 6-high, such as 2, 3, 6. There are only 12 cards that can maintain a 6-high low-draw after Fourth Street (As, 4s, 5s). Even if none of those cards are on the board, chances are that some of the limpers with low door cards, have some of your outs for hole cards. The realistic chances of having a 6-high low-draw after Fourth Street are only about 25%.

In summary, I think there are some situations where late limping is a viable strategy. But, those situations are ones when a questionable holding after Third Street, has a small chance to improve to a powerful holding on Fourth Street. Because the improvement chance is small, the Fourth Street Card should be seen cheaply.

Attacking Third Street Limpers

2009-10-12T18:00:00.000-07:00

Of the board games, Seven-Card Stud High-Low (Stud-Eight) attracts the most Third Street limpers. By "limpers," I refer to players who call the bring-in bet, rather than raise to the complete bet allowed by the limit. I am not referring to callers of a completed bet.

Limping is rarely seen in Razz because there is no reason not to show aggression with an exposed low-card. The hole-cards are almost immaterial in the early part of a Razz hand. In Stud-high, limping is seen, but it is generally regarded as a weak play. Even if a starting hand is marginal, aggression should be used early on to force the other players to define their hands.

But, in Stud-Eight, there are certain types of hands in which it is advantageous to entice a large number of competitors, rather than drive opponents out. The ideal situation is a low hand versus two or more high hands. In that situation, the low-hand can jam the others while being assured of half the pot.

As a result, it is common to see many players with three low-cards limping, in the hope that they can pick up a fourth low-card cheaply, and see if the hand develops into the only viable low. Many of these players will make a quick exit if their fourth cards are high.

Of course in poker, any player showing a predictable pattern should be a target. The question is what is the best way to get an edge? Should you attack or limp-in yourself? Here is a mathematical analysis of a typical scenario.

Assumptions:

$1-2 Stud-Eight game with a $0.20 ante and $0.25 bring-in. (These limit values are computationally convenient because they scale easily to higher and lower limit games.)
You act near the end, and after one player, who has limped-in.
That player has demonstrated a pattern of limping with three low-cards, and only continuing in the event of making a low-pair or low-draw on Fourth Street.
The bring-in folds in response to a completion.

Scenario 1: Full table with eight players making antes.

Suppose you attack the limper with a complete bet while holding three low-cards; the bring-in folds and the limper calls. The pot size is the $1.60 in antes, plus the $0.25 bring-in, plus the $2 in bets, for a total of $3.85. You have bet $1 for a chance to win the $2.85 on the table uncontested if your opponent's next card is high. The pot is paying 2.85 to 1. What is your chance of succeeding?

The deck contains 32 low cards and 20 high cards. The minimum number of low cards in play is 7. There are three low-cards in your hand, three for the limper, and the bring-in must have had one low-card exposed to be the bring-in. (If not you or the limper would be the bring-in, because you each have three low-cards.)Your worse case scenario is that the five hands that mucked on Third Street, all had door-cards that were high. That means, that if we total the known and unknown cards, there are 25 low-cards that are unknown, and15 high-cards that are unknown. The chances that an unknown card will be high are 15 out of 40, or 37.5%. That means, the odds against this play succeeding are 1.67 to 1. Because the pot pays 2.85 to 1, the play has a positive expectation. It cost $8 to make this play 8 times, but it brings back $3.85 three times out of eight, for a total of $11.55. We expect to receive back about $1.44 for every $1 invested. The expected value (E. V.) of the bet is $0.44.The edge increases if more low cards are exposed in the five mucked hands.

No. Low-Cards Mucked	Fraction High-Cards Remaining (%)	Odds Against High-Card	E. V.
0	37.5	1.67:1	$0.44
1	40	1.50:1	$0.54
2	42.5	1.35:1	$0.63
3	45	1.22:1	$0.73
4	47.5	1.10:1	$0.83
5	50	1:1	$0.92

That means that in the ideal situation of five mucked low-cards, the locations of 12 of the 32 low-cards are known. Because no high-cards are visible, we are getting coin-flip chances on an outcome that pays 2.85 to 1. That is a significant edge.

Scenario 2: Three-player game.

Interestingly, the edge does not go away if the game becomes shorthanded, even though the sum of the antes at stake is smaller. For example, a three-player game would have $1 less in antes in the pot. You would now be wagering $1 to win $1.85. The pot is now paying 1.8 to 1. We still know about the 7 low-cards, but have no information on the high cards. There are now 45 unknown cards. The chances of the play succeeding are 20/45 or 44.4% or 1.25 to 1 odds. In other words, 4 out of 9 times the limper will be hit with a high-card and fold immediately to a Fourth Street bet. You spend $9 making this Third Street-play 9 times, but it wins back 4 times on average, an amount of $2.85, or $11.44 total. You expect to receive back $1.27 for every $1 invested-an E. V. of $0.27.

Of course these calculations assume an idealized situation, in which the bring-in folds, and the limper is completely predictable. Often the bring-in will defend in these situations because he or she has observed the same pattern from the limper. Also, the limper might have a wider range of hands than three low cards. Split or wired-pairs might be included and a quick exit on Fourth Street not planned if he or she has a pair.

But those are all reasons to show aggression and not limp as well. Completing the bet forces the bring-in and the limper to define their hands. If they don't back down on Fourth Street, you will know something is up, and can proceed more cautiously.

In summary, if you see a player exhibiting this pattern, attacking on Third Street will give you an edge. Conversely, if you exhibit the pattern, alert players can gain an edge against your play.

The Possible and the Impossible in Seven-Card Stud High-Low Poker

2009-10-05T06:42:00.000-07:00

Every variation of poker has conditions on the kinds of hands possible, given the exposed cards (the board) and rules of the game. For example, in Hold'em full houses and quads are possible only if the board is paired. Knowledge of the possible is vital throughout the hand, when deciding to place or call bets. Here is a summary of what is possible and impossible in Seven-Card Stud High-Low.

High Hands

It is possible for a player to have a full house or quads without an exposed pair. The three hidden cards can combine with any one or two of the four exposed cards to make these kinds of hands.

If just two of the four exposed cards have matching suits, a flush is possible.

It is impossible for a player to have a flush when all four exposed cards are in different suits.

It is always possible for a player to have a straight, because the four exposed cards can never be arranged in such a way, that the three hidden cards couldn't fill a gap.

It is impossible for two players to have trips of the same rank. As a result, kickers never play when trips are compared. (The same is true for quads.)

It is possible for two players to have two-pair of identical ranks. In that case, the kickers decide the hand.

Exposed Hands

The following kinds of hands require all five cards and can never be completely exposed on the board:

Full houses
Flushes (including straight-flushes)
Straights
Qualified lows (low hands that meet the eight-or-better condition)

The following kinds of hands require less than five cards and can be exposed on the board:

Quads
Trips
Two-pair
One-pair

Low Hands

It is impossible for a player with three exposed high cards to have a qualified low.

It is impossible to have a qualified low and a full house or quads

It is impossible to have a qualified low with an exposed low-pair and two high cards. For example, a player with 5, 5, J, K, cannot make low.

For the same reason, it is impossible to have a qualified low with an exposed two-pair, when one of the pairs is high. For example, a player with J, J, 8, 8, cannot make low.

A player with an exposed high-pair and two low cards can have a qualified low-hand. However, the low-hand cannot be better than the highest exposed low card. For example, 9, 9, 7, 3 cannot be better than a 7-high low-hand.

A player with an exposed two-pair, with both pairs low, can have qualified low-hand, but it cannot be better than the rank of the highest pair. For example, 3, 3, 8, 8, cannot make a low-hand better than an 8-high.

It is always possible for a player with two exposed wheel cards to make a wheel. For example, a player with J, J, 2, 5, could have an A, 3, 4 hidden.

Similarly it is impossible to have a low hand better than the two lowest exposed low-cards. For example a player with 8, 7, 6, J exposed, can have at best a 7-6-high low.

Boats and Quads in Stud-Eight

2009-09-28T11:47:00.000-07:00

A complaint I've heard from poker players about high-low poker, is that it frustrates them to win little or nothing with a rare monster hand because of the split-pot rule. Competing heads-up with quads against a low hand, generates rake for the house, but no income for the players. This frustrating feature of high-low poker can be especially aggravating in Seven-Card Stud High-Low (Stud-Eight) because holding a full house (boat) or four-of-a-kind (quads) disqualifies the hand from claiming the low pot. In contrast, Omaha High-Low allows the possibility of holding a qualified low and a full house or quads at the same time. Ironically, in Stud-Eight, filling up can actually reduce the monetary value of a hand. If you hold trip 4s with an Ace, 2, 3, 6, you can win the low half of the pot with a 6-high. However, trip 4s with an Ace, 2, 3, 3, means no low hand is possible. If the trip 4s alone are good enough for high, filling up at the end might lose half the pot to another player who qualifies for low.

However, there is a flip side to the split-pot rule. The possibility of a low hand will generate action in many instances that would not have happened otherwise. You can start with rolled-trips in Stud-Eight and have it hold up for high without improvement. However, no one starts with a qualified low. A player competing for the low pot will be on a draw until at least fifth street and sometimes all the way to the river. Many of these draws will not materialize, but the player contributes to the pot on every street. When the draw succeeds a player with quads or a boat feels extremely frustrated. But, had the draw not been possible, no action would have occurred.

In one session of Stud-Eight, I had a sudden run of good cards. In a period covering just ten hands, I received a full house three times. In each case I had just one opponent calling me down. Twice the pot was split netting me nothing, and once I got to scoop. It sounds like little reward for such a great run of cards. But, consider what would have happened in a Seven-Card Stud high-only game. Absolutely no action would have occurred at all. No one holding 2, 3, 4, 7 after fourth street is going to call someone with an exposed pair in a high-only game. In fact, the hands would never have gone on long enough for me to fill up, so I wouldn't even be recalling such a great run of cards.

In multi-way pots with more than one opponent competing for low, if you're lucky enough to be receive a boat or quads early on, you can be hyper-aggressive without driving away action. A decision on whether to slow-play, that players in high-only games must make, is unnecessary. Raising and re-raising can build an enormous pot, of which you might only get half, but again, without the low possibilities your total action might be much less than half of the large pot generated by the competing lows.

You do need to be cautious with big hands when the possibility of being second best arises. It is much more costly to be second best in Stud-Eight than in other limit forms of poker, because simply calling another player down is often not an option. For example, in one hand I played, I started with rolled-trip 6s, followed by a Jack on Fourth Street and a second Jack on Fifth Street. I was confidently betting and raising with my boat against two other players. One player had a Queen for a door card and picked up a pair of 7s on Fourth and Fifth Streets. He respected my raises leading me to believe he had two-pair, Queens and 7s. The other player had three exposed low cards, including the fourth 6, was re-raising, and appeared to have no intention of leaving the hand. Clearly he had a made low hand.

But, on Sixth Street, a second Queen appeared in my opponent's hand, giving him Queens and 7s on the board, that he immediately bet out. The other player raised and now I had to make a decision. It is not possible for my hand to improve to beat his most likely holding, Queens-full. Even though the pot is large, I cannot call him down to be sure. It will cost me eight big-bets to make showdown because if I cold-call the two bets at the moment, he will re-raise and the low will cap it. That same four-bet action will occur again before showdown. I mucked my boat rather than risk getting caught in between a better high and a made low.

My assessment turned out to be correct. But, had it not been correct I would have only lost half of the pot, rather than the entire pot. In a high-only game, holding a boat with the entire pot at stake, and only two-large bets needed because no low hand would be raising, I would have simply called him down.

A full house or better plays differently in Seven-Card Stud High-Low than in high-only Seven-Card Stud. Yes, it is frustrating to split large pots when you have such a powerful hand, but you will get action that you otherwise might not have had. You need to stay alert to the reasons for that action and keep out of the middle between a possibly better high hand and made low hand.

Terminology for Seven-Card Stud High-Low

2009-09-21T07:27:00.000-07:00

Seven-Card Stud High-Low Eight or Better Poker is one of the most complex, intricate and least understood variations of poker. For those reasons it is a profitable game to master. This Blog will be an ongoing discussion of the strategies and tactics of this game that I will refer to simply as “Stud-Eight.” This short form makes the most sense to me because it is the “E” from the word eight that is used in acronyms for mixed-game poker formats to represent this high-low variation of Seven-Card Stud. Mixed-game poker competitions have become more popular recently. The $50,000 HORSE championship at the World Series of Poker is eclipsing the no-limit Texas Hold’em event in prestige. In the HORSE acronym: H=Hold’em, O=Omaha High-Low Eight or Better, R=Razz, S=Seven-Card Stud, and E=Seven-Card Stud High-Low Eight or Better.My first post is a brief overview of the terminology I will use in writing about Stud-Eight. A more extensive glossary of terms can be found at StudHighLow.com.

Poker, like all other activities, has a technical jargon that allows its participants to concisely communicate situations, actions and ideas. As with any jargon, it is gibberish to the uninitiated even though the words often have simple meanings. Poker vocabulary is extensive and cryptic at times. However, because it simplifies the writing I will make frequent use of some terms that describe key ideas in Stud games and High-Low games in particular. The terms explained below are used throughout the site.

The seven-card games of Seven-Card Stud (high-only wins) Stud-Eight (high and low split the pot), and Razz (low-only wins) all begin with each player being dealt three cards—two down and one exposed. The exposed card is referred to as the “door card” and determines the player forced to make the “bring-in” bet. In Seven-Card Stud and Stud-Eight the low door card has the bring-in while in Razz it is the high card that must bring-in.

In the rare event that all three cards are of the same rank, the three-of-a-kind or “trips” are said to be “rolled.” A more common event is for the first three cards to include two of the same rank or a “pair.” If the pair includes the door card it is a “split-pair.” If the two down cards or “hole cards” are paired it is a “wired-pair.”

Consider having three cards that include a pair. If you randomly turn one over, two out of three times you will split the pair and the other one-third of the time you will be left with a wired-pair. That means a pair is two times more likely to be split than wired. As a result, when a player bets to represent a pair, the opponents will usually assume that it is the door card that is paired.

On later streets a player can obtain an “exposed pair” and if the exposed pair includes the door card opponents will consider trips as a possible holding. Wired pairs are a less likely and more valuable holding because no one will know the rank and it is possible to make trips without an exposed pair.

Starting cards with sequential ranks such as 3, 4, 5, are said to be “connected.” It is better to hold connected cards because these are much more likely to complete a straight than cards that have “gaps.” If you have 3, 5, 6, you must pick up a 4 to have an open-ended straight-draw. But with 3, 4, 5 you have eight cards available, known as “outs” to improve to an open-ended straight draw that will then give you eight additional outs to complete the straight. Sequential cards can also improve to pairs or even trips later on. For 3, 4, 5 you also have nine outs to improve to pair which would then give you a draw to trips or two pair. All total with sequential cards you have 17 outs to improve to a draw for a powerful high.

Starting cards with large gaps have fewer outs available for improvement. Any three starting cards can make a straight, but a hand such as 2, 8, K needs to pick up a 9, 10, J, Q and nothing else for the remaining four cards to straighten.

The number outs needed to improve a hand depends on the exposed cards in other hands known as the “board.” This is a major difference of Stud games compared to flop games such as Hold’em and Omaha where the cards on the board belong to all players. In Stud games cards on the board in other hands will never be part of your hand. That means in counting outs you have to subtract off the exposed cards that would help your hand but are “dead.” An accurate subtraction often requires memory of exposed cards in previously folded (“mucked”) hands. If none of the outs necessary for your hand to improve are exposed your hand is said to be “live.” The longer your hand remains live the better because as more cards are exposed the fewer cards that remain in the deck are more likely to include the cards you need.

A hand that cannot be beat by any of the other players is referred to as the “nuts.” In split pot games it is possible to have a nut-low and a nut-high. Because of the manner in which cards are exposed it is much easier to know if you have a nut-low. Any player with three exposed high cards cannot have a qualifying low. It is much more difficult to know if you have nut-high because your opponent’s three unexposed cards could all be of the same rank, or suit, or be sequential and complete a powerful high with one or more of the four exposed cards.

In Stud-Eight the cards ranked A, 2, 3, 4, 5, 6 7, 8 are referred to as the “low cards” and 9, 10, J, K, Q, A are the “high cards” . The low versus high distinction is a result of the rules that requires a low hand to “qualify” for the low pot by having no card in it higher than an eight. Notice that the Ace is a special card because it is simultaneously the best low card and the best high card. That dual role makes Aces in split-pot games even more valuable than in high-only games because it is equivalent to having an extra eighth card in your hand. The low cards also have added value because they can simultaneously be part of high and low hands. The high cards present problems because they can only work “one-way.”

The dual nature of the low cards is best seen in the hand A, 2, 3, 4, 5 known as the “bicycle” usually shortened to “wheel.” This is the best possible low hand or “nut-low” and it is guaranteed a share of the low pot because the best another player competing for low could do is have another wheel to split the low pot. At the same time the hand competes for the high pot as a five-high straight. The five-lowest cards are referred to as “wheel cards.” The ideal hand in Stud-Eight would be a “steel wheel” which is A, 2, 3, 4, 5 all in the same suit. This hand is both the nut-low and a 5-high straight flush that would defeat any full house or quads for the high pot.

A hand that is viable for just one-half of the pot is a “one-way hand.” A starting hand of K, K, J is a one-way hand for high because it is impossible for it to ever qualify for low. A hand such as 2, 5, 7 is usually played as a one-way hand for low although it is possible that such a hand could “back in” to a high hand with the right additional cards. The ideal in split pot games is to compete simultaneously for both halves of the pot. Winning the high pot and the low pot is known as a “scoop.” The big money in Stud-Eight comes from scooping. It is usually best to play hands that have a reasonable chance of scooping.

A “kicker” is a card that is not part of a grouping. If you have 9, 9, 7 you have a pair of nines with a seven kicker. In Hold’em kickers are important cards because the use of community cards mean that players often share the same pair and in those cases it is the kicker that decides the winner. In Seven-Card Stud, kickers are less important because two players with the same pair is a rare event. Also some groupings possible in Hold’em, such as shared trips or quads, are impossible in Seven-Card Stud.

However, in Stud-Eight kickers are important cards because they determine the likelihood of scooping. A hand of A, A, 2 (pair of Aces with a 2 kicker) is much more likely to make low than A, A, 9 (pair of Aces with a 9 kicker) and the Aces are a powerful start for high. Even if the kicker won’t make low it can threaten low and put pressure on the other players.

You will not win at poker unless you place bets. Checking and calling is needed in some circumstances but if that is all you do you will lose. Part of the reason for this is that bets have a “fold equity.” When you bet, the other players are forced to make decisions. Folding could be an outcome of that decision and if everyone folds, you win.

Jamming refers to the act of betting or raising with the intention of re-raising if the action returns to you. If you raise each time you have the opportunity you are “jamming” your opponents. Stud-Eight has more jamming than any other form of poker because in many cases it can be done free of risk. If you have a made low and are up against one or more players with three exposed high cards there is no reason not to jam the others if given the opportunity. The most common jamming situation is a made low and a monster high such as a full house or quads jamming a third player with a strong but second-best holding. A person with a straight or flush in these situations can be cleaned out if not careful. This is an important difference between Stud-Eight and Stud-high. If you hold a flush in Stud-high you might check and call down some one you suspect has a full house. In Stud-Eight you are better off getting out of the hand in that situation. Remember that even if your hand holds up you will only win half of the pot. The pot odds are not in your favor.

Freerolling refers to the ability to make risk-free bets while drawing for the entire pot. This concept is explained on the page “Unique Features of Stud-Eight.” It is not unique to Stud-Eight because you will find freeroll possibilities in other poker variants. Consider a Hold’em hand with two players in which one holds 6s, 7s, and the other 6d, 7d. The flop is 3s, 4s, 5c. Both players hold the nut-straight but only player can improve to a flush on the later streets. If the players go “all-in” against each other the player with the 6s, 7s is on a freeroll. She cannot lose because the worse that can happen is that she will split the pot. But, if a third Spade hits she wins the entire pot.

Freeroll situations are rare in Hold’em, more common in Omaha, but routine in Stud-Eight. A player with the best qualifying low after 5 or 6 cards and a lock on half the pot, often has opportunities to back into a high hand and claim the other half. Any small pair could improve to trips, a four-flush could become a flush, or an inside straight-draw could hit. There is nothing a high hand can do to “protect” his holdings.

Bricks are cards that do not improve a hand in anyway. A beautiful looking start such as 2-, 3-, 4-, 5-, that is followed by J-, 9-, K-, has been hit with bricks and needs to be mucked (folded) at the end.