[BruceZ]

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Hello everyone!
I wonder what the exact probability is that the board pairs (or make quads) when flopped a set.
My home made calculation is:
Number of outs for pairing any of the flopped cards: 3+3+1= 7 outs.

(7/48)+(7/47)=29.47695034%

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7/47 + (40/47)*(7/46) = 27.8445883%

There are 47 cards remaining after the flop, not 48, and the 7/46 on the river applies only if you miss on the turn, hence the 40/47. This is just for pairing a flop card.


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I think that would be correct. I’m less sure about my calculation that a runner runner pair will come though. Does anyone know if this is correct:

I make the calculation: (4/48)x(3/47)x10= 5.31%


29.47695034+5.31=34.7869%

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(4/47)*(3/46)*10 = 5.5504163%

27.8445883% + 5.5504163% = 33.3950046%

You can do this all in one step like this:

7/47 + (40/47)*(10/46) = 33.3950046% same as above.

That is, you pick up an extra 3 outs if you miss on the turn, so you have 10 outs on the river.