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How to calculate poker odds using combinations?

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  • Once you know the combinations, you just divide the number of favorable combination by the number of unfavorable ones. The hard part is calculating the combinations though.
    – David
    Sep 26, 2022 at 19:00
  • This should probably be converted into a community wiki. Sep 21, 2023 at 7:51

1 Answer 1

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I got tired of explaining combination in answers so just making one post.

With multiple cards simple fractions don't work.

Combination is how many ways you can make the combination.
Like 52 take 5 or 52 take 2

In Excel it is combin(n, k)

How many possible hole cards combin(52, 2) = 1326

On the river your opponent can have combin(45, 2) = 990

Odds of a pocket pair
13 rank * combin(4, 2) / 1326 = 1 / 17

Suited
4 * combin(13, 2) / 1326 = 4.25

Above you can do with fraction but from a pair chance to hit quads
quad is 1 way
then 3 cards from 48
combin(48, 3) / combin(50, 5) = 1 / 122.5

trips or better from pair
combin(2, 1) * combin(48, 4) / combin(50, 5) = 1 / 5.4444444444

for more

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