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Poker Hands (Posted on 2004-07-09) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Thalamus    
Rating: 3.0000 (1 votes)

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Hints/Tips additional complications | Comment 5 of 11 |
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.
__________________________

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.

  Posted by SilverKnight on 2004-07-09 16:57:41
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