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Math Help - odds of having a flop in poker with at least 10 or higher

  1. #1
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    odds of having a flop in poker with at least 10 or higher

    I was wondering how often low flops (flops with all cards less than 9) happen. Or we could do the opposite, odds of having a flop in poker with at least an A, K, Q, J, or 10. I was wondering how to do this properly. Let's say the hand I'm holding is random (negligable) so the amount of cards in the deck is to be 52. So 3 flop cards out of 52.

    It would help me enormously because if I knew how to do this, I could expand further and figure out other problems.
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  2. #2
    Member HappyJoe's Avatar
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    Do you know binomial coefficients? The number C(n,k) determines the number of ways you can choose k elements among n elements, where order doesn't matter. It is usually written \binom{n}{k}.

    There are 8*4 = 32 cards less than (or equal to) 9. You can choose 3 such cards in C(32,3) ways.

    Among all 52 cards, you can choose 3 cards in C(52,3) ways, hence the probability of flopping cards all less than or equal to 9 is C(32,3)/C(52,3), which is approximately 22,44%.
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