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.
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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.

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