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.

[View the solution]

21 February 2014