Re: AA cracked twice in one hand--how bad is this beat?
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Are you sure the possible hands for this board is 46 nCr 5, or 1370754?
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Yes, Cobra is correct about that. Your objections don't apply because we are concerned with ALL possible boards -- thus there are no constraints. You are describing the conditions of the boards in which this rare event occurs, which would therefore affect the answer of the numerator, not the denominator, of Cobra's calculation.
Also, I'm not sure why you guys added the constraint of the board not pairing. The OP's aces would still lose in this case (just to a boat instead of to trips).
Finally, a question a interpretation. Cobra answered the question "What is the chance of getting beat, given the original starting hands?"
It seemed to me that the OP might also have been asking: "What is the chance of my getting aces, someone else getting kings, a third person getting another pair (eights or better?), and then me still losing?" Just another possibility.
HTH,
gm
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