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# Texas hold 'em, flush probability

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Suppose you are playing Texas Hold'em poker and you are dealt the ace of hearts and the ten of hearts. What is the probability that you make a flush with exactly three more hearts on the board by the river?

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When starting with two suited cards, this solution finds the probability a poker player makes a flush with exactly 3 cards of the same suit on the board.

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You have seen the ace and ten of hearts so there are 11 other hearts and 39 non-hearts among the 50 unseen ...

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