AA versus AA the only way to win or lose is a flush

What is the chance of a flush?

To me a general answer on how to calculate odds is not a duplicate. I think most or many people on this site would not know how to calculate this situation even with those instructions. I may open a meta.


Running AA vs AA in ProPokerTools gives us an approximate 2.2% probability of winning, presuming it's an all-in preflop situation.

  • I get 2.22 from that link. Don't know why my answer is different.
    – paparazzo
    May 7 '17 at 2:10
  • You're right, I made a mistake. It's 2.2%. May 7 '17 at 2:44
  • I get 2.17 with Equilab
    – paparazzo
    May 7 '17 at 13:03
  • I rounded up, it was 2.17 something. May 7 '17 at 20:48

Using combination

(combin(12,4)*2*36 + combin(12,5)) / combin(48,5) = 0.0217 = 1 / 42

More often than I would have guesed

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