The likelihoods of being dealt various poker hands are widely published (easily found on the internet). A more difficult problem is: what are the likelihoods of being dealt each poker hand, given a 54 card deck (52 card deck + 2 jokers).

The various hands of interest are:
1 pair
2 pair
3 of a kind
straight
flush
full house
4 of a kind
straight flush
5 of a kind

* Jokers can count as any rank card, in any suit.

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How 'bout:

5k:   78

SF:    588

4k:     9,360

FH:      9,360

F:       11,424

S:       34,164

3k:    233,508

2p:    123,552

1p:     1,437,936

zip:   1,302,540

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Just did it in a little spreadsheet, combinatorics.  You have to figure out that ace-high straights come up more often with jokers.  On hands with no jokers, 5-high to ace-high straights occur uniformly; with one, ace-high strights 1.25 times more likely than others; with two, they're twice.

Posted by bernie on 2004-08-20 00:50:32