A Clever Bluff

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.

Missed Opportunities on the River

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.

Low Straight Blockers

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.

Catching Bad versus Catching Good on Fourth Street

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

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.

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

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.

Attacking Third Street Limpers

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.