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.

A straight flush can contain 0, 1, or 2 jokers
there are 40 that contain 0, 40*C(5,1)=200 that contain 1, and 40*C(5,2)=400 that contain two.

640/C(54,5)=.002023709016

it is easier to work from the bottom of your list upwards because then you know how many to subtract away. For instance when we know how many straights total there are we can now subtract the 640 that are straight flushes.

-Jer

Posted by Jer on 2004-07-09 15:59:10