Frequency of 7-card Lowball Poker Hands
See also: Lowball (poker)In some variants of poker a player uses the best five-card low hand selected from seven cards. In most variants of lowball, the ace is counted as the lowest card and straights and flushes don't count against a low hand, so the lowest hand is the five-high hand A-2-3-4-5, also called a wheel. The probability is calculated based on, the total number of 7-card combinations.
The table does not extend to include five-card hands with at least one pair. Its "Total" represents 95.4% of the time that a player can select a 5-card low hand without any pair.
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Hand Frequency Probability Cumulative Odds 5-high 781,824 0.584% 0.584% 170.12 : 1 6-high 3,151,360 2.36% 2.94% 41.45 : 1 7-high 7,426,560 5.55% 8.49% 17.01 : 1 8-high 13,171,200 9.85% 18.3% 9.16 : 1 9-high 19,174,400 14.3% 32.7% 5.98 : 1 10-high 23,675,904 17.7% 50.4% 4.65 : 1 Jack-high 24,837,120 18.6% 68.9% 4.39 : 1 Queen-high 21,457,920 16.0% 85.0% 5.23 : 1 King-high 13,939,200 10.4% 95.4% 8.60 : 1 Total 127,615,488 95.4% 95.4% 0.05 : 1
(The frequencies given are exact; the probabilities and odds are approximate.)
If aces are not low, simply rotate the hand descriptions so that 6-high replaces 5-high for the best hand and ace-high replaces king-high as the worst hand.
Read more about this topic: Poker Probability
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