Based on Wikipedia article, probability of making two pairs among seven cards is 23.5%. But this include cases where the two pairs are on the board (e.x. I have AQ and the board is KKJJ5), or one of the pairs is on the boards and the other pair is with one of the cards I have in my hand (e.x. I have AQ and the board is KKQ53). I want to know the probability of making two pairs using only the (unpaired) cards that I have in my hand. For example I have KJ, and the boards is J92K7. In other words if I have two unpaired cards, what are the chances that both of my cards get paired with the board?

  • Have a look at www.pokerology.com/lessons/math-and-probability It shows these sort of stats simply without needing to remember the maths....
    – Dave
    Dec 13, 2015 at 21:32

1 Answer 1


I take it that you are not seeking exactly two-pair probability, but rather "hitting with both cards once each".

In such case, 5 cards of the board must contain two of your cards and any of three other cards.

P = C(3,1)×C(3,1)×C(44,3)

C stands for "Combin".You divide that result by C(50,5) and thats your answer.

Please note, the above calculation will include the boards like KJ222, which overrides your two pair, but I guessed thats what you were asking for.

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