Problem of the Week 1102

The Holy Game of Poker

Solution to 1102 by Peter Winkler, Dartmouth

The two hands in question are equally likely. The number of ways to get four of a kind (but not five!) is

representing choosing a denomination -- say, A -- plus four of the six cards AAAAjj and a kicker.

To count full houses that are not also four of a kind, we have patterns AAAKK, AAKKK, and AAKKj, thus

Rob Pratt observes that the number of hands of all types in the 2-joker case is given as a sequence on the On-Line Encyclopedia of Integer Sequences: http://www.research.att.com/~njas/sequences/A053083

[Back to Problem 1102]

© Copyright 2008 Stan Wagon. Reproduced with permission.