The other day we were playing Texas Hold'Em in a casual not-for-money game.
On one hand, we had four 9s show up in the face up cards on the table. "Wow! What are the chances of that?!" was exclaimed. One at the table even took a picture of it. Its pretty rare, but is it really photo worthy?
Well, lets figure it out. There are 13 different ways you can get 4 of a kind. The fifth card can be any of the remaining cards, so there are 13*48 = 624 different combinations which can yield 4 of a kind showing. The total possible hands that could be showing is the combinatorial problem of choosing 5 cards of 52, which is 52! / (5! * 47!) = 2,598,960.
So, the chances of getting 4 of a kind showing in texas hold'em is 1/4165 or 0.024%.
Not too rare!
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