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Problem of the Week 1175
Best Full House
You and a few friends are playing stud poker (5 cards dealt, no exchanging of cards) with a standard 52-card deck.
It's your lucky day and God tells you that you are guaranteed to end up with a full house, but only if you correctly choose the best full house.
Which full house should you choose?
This is indeed a mathematical question: Which full house has the highest probability of winning?
Extra credit: Same story, but for the game of 5-card draw poker, where one can exchange any number of cards. If you are promised to end up with a full house, what would be the ideal cards to be dealt and exchanged so as to maximize the probability of winning? [I do not know the answer.]
© Copyright 2014 Stan Wagon. Reproduced with permission.