Sunday, February 28, 2010

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

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.

Thursday, February 18, 2010

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

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.