This is a math question.

osgoboosgobo Red Chipper Posts: 37 ✭✭
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?

Thanks

Best Answer

Answers

  • TheGameKatTheGameKat Posts: 2,633 -
    Can't be solved without explicit ranges for all players.
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  • osgoboosgobo Red Chipper Posts: 37 ✭✭
    Of course it can be solved my friend. There are 9 players in the game, we have determined one of those players (me) has an ace. We have determined another one of the aces has been removed from the deck (because it's on the flop). If we know, as per my question, that all 8 of those players will see the flop with A2s+,ATo+ then we of course can determine how often one of those 8 players can get one of those hands given the constraints above.

    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. :-)
  • TheGameKatTheGameKat Posts: 2,633 -
    Presumably what you want to know is: when 4 players plus me (holding Ax) see a flop, what is the probability that one of them holds Ax. To answer this we need to know the density of aces in players' ranges. Thus we need their ranges.
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  • TheGameKatTheGameKat Posts: 2,633 -
    To understand why this is so, consider the following. Your opponents' ranges are such that they only get to the flop with A2s+,ATo+. They fold all other hands. In such a scenario, a 5-way flop wouldn't even be possible. However, whenever you went 3-way with an Axx board, the probability that the other players hold an A is 100%. The ranges matter.
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  • osgoboosgobo Red Chipper Posts: 37 ✭✭
    Let me ask this question another way. Assume you are holding an ace and the dealer has accidentally exposed an ace. With those 2 aces gone from the deck what are the odds of one of the other 8 players being dealt A2s+,ATo+?
  • TheGameKatTheGameKat Posts: 2,633 -
    osgobo wrote: »
    Let me ask this question another way. Assume you are holding an ace and the dealer has accidentally exposed an ace. With those 2 aces gone from the deck what are the odds of one of the other 8 players being dealt A2s+,ATo+?

    Fair enough, that's a completely different question.
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  • osgoboosgobo Red Chipper Posts: 37 ✭✭
    I'm not sure it is a completely different question but lets assume it is. Do you have an answer for it? :-)
  • TheGameKatTheGameKat Posts: 2,633 -
    The probability that none of the 8 players holds ATo,A2s+ is about 70%
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  • osgoboosgobo Red Chipper Posts: 37 ✭✭
    Can you teach/tell me how to figure that out for myself?
    Thanks
  • osgoboosgobo Red Chipper Posts: 37 ✭✭
    Thank you for your help!! This is what I was looking for all along. Sorry for my confusing first question . :-)
  • TheGameKatTheGameKat Posts: 2,633 -
    osgobo wrote: »
    Thank you for your help!! This is what I was looking for all along. Sorry for my confusing first question . :-)

    Welcome.
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