Frequency of 5-card Lowball Poker Hands
See also: Lowball (poker)Some variants of poker, called lowball, use a low hand to determine the winning hand. 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 5-card combinations. (The frequencies given are exact; the probabilities and odds are approximate.)
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Hand Distinct hands Frequency Probability Cumulative Odds 5-high 1 1,024 0.0394% 0.0394% 2,537.05 : 1 6-high 5 5,120 0.197% 0.236% 506.61 : 1 7-high 15 15,360 0.591% 0.827% 168.20 : 1 8-high 35 35,840 1.38% 2.21% 71.52 : 1 9-high 70 71,680 2.76% 4.96% 35.26 : 1 10-high 126 129,024 4.96% 9.93% 19.14 : 1 Jack-high 210 215,040 8.27% 18.2% 11.09 : 1 Queen-high 330 337,920 13.0% 31.2% 6.69 : 1 King-high 495 506,880 19.5% 50.7% 4.13 : 1 Total 1,287 1,317,888 50.7% 50.7% 0.97 : 1
As can be seen from the table, just over half the time a player gets a hand that has no pairs, three- or four-of-a-kinds. (50.7%)
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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