7-Card Poker Hands with Joker

Brian Alspach

31 July 2003


We examine the number of various poker hands for 7-card hands using a deck with a single joker.

All hands under discussion here are assumed to occur in a 53-card deck, where a single joker has been added to a standard 52-card deck. The detailed derivations for the numbers quoted in this file appear in the file Pai Gow Poker Computations in the same directory containing this file. Table 3 in Pai Gow Poker Computations contains the information on the number of 7-card hands classified according to the best 5-card hand they contain, and what kind of hand they are relative to pai gow bonus hands. We merge some of the categories yielding the next table in order to provide the information directly.

Of the 210,964 straight flushes listed below, 26,124 are royal flushes.

hand number
5 aces 1,128
straight flush 210,964
4-of-a-kind 307,472
full house 4,188,528
flush 6,172,088
straight 11,236,028
3-of-a-kind 7,470,676
two-pair 35,553,816
pair 64,221,960
high card 24,780,420


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