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Betting on Combinations

Like watching high-stakes poker players in those multimillion-dollar tournaments? If you daydream of cleaning the pot like those pros, you’d better be good at math—or, more specifically, at combinations!

It's All About Math

You may think that poker is all about reading other players’ facial expressions, as well as fooling them with yours. The game does involve some of that strategy, but it’s much more about math than many people think. Did you know that successful poker players only play about 20% of their hands? That's because they wait for the “combinations” to lean their way. The number of combinations that a certain hand can come up directly translates to its probability. At the very beginning of a game, you and your opponents have exactly the same likelihoods of obtaining a flush (five cards in the same suit), or a full house (three cards of the same rank plus a matching pair of another rank), etc. But once the cards are dealt—or when some of them are—the numbers of combinations for different hands start changing.

Do you know why a full house is considered stronger than a flush in a five-card stud? That’s because the total number of possible combinations for the two are 3,744 and 5,108, respectively, implying that a full house is rarer than a flush.

See the total number of combinations for different poker hands here: 

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Learn how some of these combinations are calculated by watching the video below.


Now suppose that in a game of five-card poker, the first two cards you get are both aces. You will receive three more cards from the remaining 50 cards. In how many different ways can you get a full house from this point on?

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