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.

(In reply to re: More results and solution by Cory Taylor)

Cory,

 I think if you recount your 2-wild combinations you have 64 of them not 63.  Now your calculation 64*4^3 = 4096 agrees with 256+3840 my total of straights and straight flushes from a 3-card stem.

{Edit: To see that 64 is correct: consider the 3-card sets.

If the lowest of the 3-card-set is (A, 2...T) then there are 4C2 = 6 potential straights for each (60 in total).  If the lowest is J, then there are 3 further potential straights.  If the lowest is Q, then there is 1 more potential straight.  Total 64.}

It is a while since I did this but I will try later to check the 1-wild combinations.

Edited on March 16, 2006, 3:02 am

Posted by goFish on 2006-03-15 19:57:40