Editing Poker probability (section)

===5-card lowball poker hands===
{{See also|Lowball (poker)}}

Some variants of poker, called [[Lowball (poker)|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 <math display="inline">{52 \choose 5} = 2,598,960</math>, the total number of 5-card combinations.  (The frequencies given are exact; the probabilities and odds are approximate.)

:{| class="wikitable" style="font-size: 95%;"
|-
!Hand        !!   Distinct hands !!            Frequency !! Probability !! Cumulative !! Odds against
|-
|     5-high ||align=right|    1 ||align=right|    1,024 ||     0.0394% ||    0.0394% ||align=right| 2,537.05 : 1
|-
|     6-high ||align=right|    5 ||align=right|    5,120 ||     0.197%  ||    0.236%  ||align=right| 506.61 : 1
|-
|     7-high ||align=right|   15 ||align=right|   15,360 ||     0.591%  ||    0.827%  ||align=right| 168.20 : 1
|-
|     8-high ||align=right|   35 ||align=right|   35,840 ||     1.38%   ||    2.21%   ||align=right| 71.52 : 1
|-
|     9-high ||align=right|   70 ||align=right|   71,680 ||     2.76%   ||    4.96%   ||align=right| 35.26 : 1
|-
|    10-high ||align=right|  126 ||align=right|  129,024 ||     4.96%   ||    9.93%   ||align=right| 19.14 : 1
|-
|  Jack-high ||align=right|  210 ||align=right|  215,040 ||     8.27%   ||   18.2%    ||align=right| 11.09 : 1
|-
| Queen-high ||align=right|  330 ||align=right|  337,920 ||    13.0%    ||   31.2%    ||align=right| 6.69 : 1
|-
|  King-high ||align=right|  495 ||align=right|  506,880 ||    19.5%    ||   50.7%    ||align=right| 4.13 : 1
|-
|'''Total''' ||align=right|1,287 ||align=right|1,317,888 ||    50.7%    ||   50.7%    ||align=right| 0.97 : 1
|}

As can be seen from the table, just over half the time a player gets a hand that has no pairs, threes- or fours-of-a-kind. (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.

Some players do not ignore straights and flushes when computing the low hand in lowball. In this case, the lowest hand is '''A-2-3-4-6''' with at least two suits. Probabilities are adjusted in the above table such that "5-high" is not listed", "6-high" has one distinct hand, and "King-high" having 330 distinct hands, respectively. The Total line also needs adjusting.