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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.

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  • Possible duplicate of How do I calculate poker hand probabilities?
    – 3N1GM4
    May 8, 2017 at 21:35
  • Keep in mind that a straight flush will also win for only one hand.
    – user45266
    Oct 15, 2018 at 15:03
  • Wouldn't it be lower since I thought even the probability of each person even being dealt AA is .45%. Just lost AA vs AA so I looked this up.
    – Danny James
    Mar 3 at 21:46

2 Answers 2

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

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  • I get 2.22 from that link. Don't know why my answer is different.
    – paparazzo
    May 7, 2017 at 2:10
  • You're right, I made a mistake. It's 2.2%.
    – Cantalouping
    May 7, 2017 at 2:44
  • I get 2.17 with Equilab
    – paparazzo
    May 7, 2017 at 13:03
  • I rounded up, it was 2.17 something.
    – Cantalouping
    May 7, 2017 at 20:48
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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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  • COULD YOU REPHARSE THIS QUESTION ONE OF THE USERS FLAGGED THE QUWSTION AS CONFUSING
    – Jon ♦
    Mar 9 at 7:53

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