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 additional complications by SilverKnight)

I have seen reports that with wild cards you cannot order the hands' values by their rarity, in effect because making them more valuable makes them less rare, as the holder will use the wild card more to make more valuable hands.  So it makes no sense to switch the relative values of the hands, as such is a vain effort to keep up with the probabilities.  And my understanding is that when played with wild cards, the standard values are in fact kept, adding, of course, the 5 of a kind, but not adding flush-3-of-a-kind, which would theoretically be possible.

Posted by Charlie on 2004-07-09 20:43:35