Suppose your deck has more than four suits, or some number other than thirteen cards per suit. What happens to the ranks of poker hands?
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2
4 F F F * B B B * O O O A A A A A A A A A A A A A A A A A
5 F F F F F F F B B B B B O O A A A A A A A A A A A D D D
6 F F F F F F F F F F F B B B B B B A A D D D D D D D D D
7 F F F F F F F F F F F F F F F B C C C C E E D D D D D D
8 F F F F F F F F F F F F F F G G G G G C C C C C E E E D
9 F F F F F F F F F F F F F G G G G G G G G G G C C C C E
10 F F F F F F F F F F F F G G G G G G G G G G G G G G G G
11 F F F F F F F F F F F G G G G G G G G G G G G G G G G G
12 F F F F F F F F F F G G G G G G G G G G G G G G G G G G
13 F F F F F F F F F F G G G G G G G G G G G G G G G G G G
14 F F F F F F F F F G G G G G G G G G G G G G G G G G G G
15 F F F F F F F F F G G G G G G G G G G G G G G G G G G G
16 F F F F F F F F F G G G G G G G G G G G G G G G G G G G
O: the familiar case: straight flush > four of a kind > full house > flush > straight > three of a kind > two pair > one pair.
A: four > full house > straight > flush.
B: four > flush > full house > straight.
C: four > flush > straight > full house.
D: four > straight > full house > flush.
E: four > straight > flush > full house.
F: flush > four > full house > straight.
G: flush > four > straight > full house.
*: surprisingly only two cases where two of the scoring hands are equally rare: with four suits and twelve ranks, flush = full house; with four suits and eight ranks, flush = four.
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I have not looked into the effect of taking away the ace’s ability to be both high and low in a straight.
With more than four suits, five of a kind is a possible hand; I should work in its odds.
And I ought to redo the chart with colored hashlines instead of letters.