This is a math question.
osgobo
Red Chipper Posts: 62 ✭✭
You have Ax and you are in a 5 ways pot (this happens a lot where I play). The flop is Axx. What are the odds someone else has an ace assuming a nine handed game where no one folds A2s+ or ATo+ preflop?
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Best Answer

TheGameKat Posts: 3,399 The best way to do it would be to simulate it, but in the absence of that I made an estimate based on the following.
We assume we have Ax and that the dealer flashes and burns an A. The precise calculation depends on whether or not our side card is T+ or not, but since this is just an estimate let's just assume it is.
Removing those 3 cards from the deck and counting combos we find there are 47 combos in the range ATo+,A2s+ and 1176 total combos allowing for this card removal. You can do this manually, but I'd recommend Equilab.
That means the probability of the first of the 8 players having a hand in the specified range is 47/1176 ~ 0.04. Thus the probability they do not have a hand in this range is 0.96. As we go from each player to the next, the probability they do not have a hand in the range changes since we are removing cards. However, this is horrendously complicated to calculate in detail because A9o are outside the range of interest. So I chose to ignore it and just calculated (0.96)**8 ~ 0.72. Thus there's roughly a 70% probability none of the 8 players holds a hand in the specified range.
But let me emphasize again, this is not the solution to the first question you asked. The fact 5 people saw the flop in your first framing introduces a massive selection effect.
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Answers
You don't have to know their ranges all you have to know is how often someone gets dealt A2s+, ATo+ given the constraints.
I don't know how to do it, but I KNOW it can be done. :)
Fair enough, that's a completely different question.
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