Poker News

Before you look at your hand, what are the odds that the board will qualify for low? The first column in the table shows all the possible patterns, from all five cards higher (H) than eight to all five lower than nine (L).

The second column shows the number of possible boards with five high cards, four high cards and one low card, etc. The numbers come from the formula, C(20,H)*C(32,L).

To qualify for low, there must be three or more unduplicated ranks from ace through eight. The pattern, H-H-L-L-L, cannot have a duplicated low rank. The pattern, H-L-L-L-L, cannot have more than one rank duplicated. The pattern, L-L-L-L-L, cannot have four of a kind or a full house on the tableau: it could have three of a kind, two pairs, or one pair, and still qualify for low. We examined the fine-structure numbers and eliminated those boards that had too many duplicated ranks. The third column shows the number of boards for each pattern that qualify for low.

Dividing 1,561,728 by 2,598,960, obtains 0.6009, the probability that the board will qualify for low. So that’s your answer, 60 percent of Omaha/8 deals will have a low; 40 percent won’t.

Hakim asked how looking at his hand could change the cards on the table. Looking at your hand won’t change the five cards on the table, of course, those cards were set when the dealer cut the deck; knowing your cards only changes what we can predict about the five cards on the table.

If his hand were four low cards, then his chance that the board will qualify for low would be smaller, and vice versa. These results validate the old advice to play starting hands that could go either way: not only because you might win both ways, but also because you still might have a chance to win high when the tableau doesn’t qualify for low. While Omaha/8 is biased toward the low, these results show that 40 percent of the time no one can possibly have a low, no matter what cards they hold.

Hakim told me that until he saw these results one of his favorite hands was 5-4-3-2. If an ace were to hit the table and if the board qualified for low, then he considered it quite playable because it was so unlikely to be counterfeited. He was no longer so sanguine about that hand: not only would he probably need an ace, he also would have less than a 60 percent chance that the board would qualify for low. He said he intended to wait for hands more like A-K-3-2 from then on.

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