Thread: 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.

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 .

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%.