Re: Hypothetical Question
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1) Someone has AA. They will reraise preflop, and we will lose 4BB total calling down.
This will happen 9/221, so 9 * (-4.75) / 221 = -0.19 BB
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9/221 is not correct for two reasons.
Once Hero has been dealt KK at most two people can be dealt AA. Fixing on one player, the probability that he his dealt AA is (4 choose 2) / (50 choose 2). The sum of these probabilities for 9 people is 9 * (4 choose 2) / (50 choose 2) and is close to the right answer but it's wrong because it double counts the times that two players hold AA. The probability that two particular players hold AA is (4 choose ) / (50 choose 4) and multiply this by (9 choose 2), the number of ways to choose 2 players from 9 players. Hence the probability that our Hero ends up against AA is
9 * (4 choose 2) / (50 choose 2) - (9 choose 2) * (4 choose 4) / (50 choose 4) =.0439.
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