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.

This one is pretty easy:

Think of the deck as consisting of 6 aces of which you want 5. Then multiply by 13 ranks.

13*C(6,5)/C(54,5)
or about .00002466395363

-Jer

Posted by Jer on 2004-07-09 15:47:50