Bob Sokol has been known to play
a little poker from time to time.

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Just so everyone agrees before we start...

Poker hands are listed here in descending order of value.




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A royal flush:

is the ace, king, queen, jack, and 10 of the same suit.




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A straight flush:

is any sequence of five cards in the same suit.




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Four of a kind:

is any four cards of the same denomination.




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A full house:

is any three cards of one denomination and any two cards of another.




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A flush:

is any five cards of the same suit.




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A straight:

is any five cards of more than one suit in sequence.




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Three of a kind:

is any three cards of the same denomination, plus any other unmatches.




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Two pairs:

is any two cards of the same denomination, plus two cards of another denomination, plus any fifth card.




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One pair:

is any two cards of the same denomination, plus any three other cards.

What are the chances of dealing five cards from a fresh, shuffled deck and getting:

Please note that I borrowed these calculations from someone else's Master's thesis. I can't add past ten unless I take off my shoes, so please don't e-mail me asking the odds against the joker jumping out of a freshly shuffled deck and spitting cider in your ear...

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