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.
To add to what Charlie and Jer have mentioned...
There are hands with Jokers that can be "turned into" other hands.
For example, 5, 5, 5, 6, J, can be a full house (J=6) or 4 of a kind (J=5).
Standard poker ordering implies that 4 of a kind is rarer than a full
house and therefore is more valuable (rated as a higher hand).
In evaluating this problem, with the additions of the joker, one needs
to consider if a "higher rated" hand is, in fact, rarer. That is,
with the jokers, is it actually easier to make a "higher rated" rated
than a lower one. This raises the question of reordering the
hands with the addition of wild cards.
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On example of such going on (in a potentially different problem) is
making all dueces wild (rather than adding any jokers). In this
scenario, it is actually more difficult to get a full house than 4 of a
kind.
(I have to double check the math, but I think that is the case.)
And the common reaction is to leave the ordering of the hands in place,
even though it may be harder to get a "lesser" hand.
additional complications
