Annoying Poker Probability Question.

[durron597]

Ok, say you are trying to figure out a 3 way allin preflop equity calculation. Assume that we've already figured out the ranges of hands, and plugged them all into PokerStove. Hero is the middle stack. I want to find the probability of the shorty winning the main pot, but we win the side pot.

In other words, Pr(Hero wins sidepot | Short Stack wins main pot).

Given our hand and the ranges of hands, we have the following:

Pr(Shortstack wins main pot) = 28.6%
Pr(We win main pot) = 46.4%
Pr(Big stack wins main pot) = 25.0%.

If the short stack is not involved at all in what is entered into PokerStove, we have:
Pr(Hero beats big stack) = 66%
Pr(Big stack beats hero) = 34%.

Assume all chopping is lost in roundoff.

Is there a way to figure out what the above Probability is? If you need a tool like PokerStove (and you me to supply hand ranges), does PokerStove have all the functionality required to solve this problem?

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Ok, say you are trying to figure out a 3 way allin preflop equity calculation. Assume that we've already figured out the ranges of hands, and plugged them all into PokerStove. Hero is the middle stack. I want to find the probability of the shorty winning the main pot, but we win the side pot.

In other words, Pr(Hero wins sidepot | Short Stack wins main pot).

Given our hand and the ranges of hands, we have the following:

Pr(Shortstack wins main pot) = 28.6%
Pr(We win main pot) = 46.4%
Pr(Big stack wins main pot) = 25.0%.

If the short stack is not involved at all in what is entered into PokerStove, we have:
Pr(Hero beats big stack) = 66%
Pr(Big stack beats hero) = 34%.

Assume all chopping is lost in roundoff.

Is there a way to figure out what the above Probability is? If you need a tool like PokerStove (and you me to supply hand ranges), does PokerStove have all the functionality required to solve this problem?

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I'm not sure exactly what you're asking. If it is "What is the probability that I win the sidepot given the short stack wins the main pot?", the answer is equal to the percentage of times your hand beats the big stack in the hand, or 66%.

If you are asking what percentage of total outcomes have you losing the main pot to shorty but winning the sidepot, the answer is P(shorty winning) * P(your hand beats big stack) or .286 * .666 = 19.05%.

Hope this helps.

[SumZero]

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Ok, say you are trying to figure out a 3 way allin preflop equity calculation. Assume that we've already figured out the ranges of hands, and plugged them all into PokerStove. Hero is the middle stack. I want to find the probability of the shorty winning the main pot, but we win the side pot.
In other words, Pr(Hero wins sidepot | Short Stack wins main pot).
Given our hand and the ranges of hands, we have the following:
Pr(Shortstack wins main pot) = 28.6%
Pr(We win main pot) = 46.4%
Pr(Big stack wins main pot) = 25.0%.
If the short stack is not involved at all in what is entered into PokerStove, we have:
Pr(Hero beats big stack) = 66%
Pr(Big stack beats hero) = 34%.
Assume all chopping is lost in roundoff.
Is there a way to figure out what the above Probability is? If you need a tool like PokerStove (and you me to supply hand ranges), does PokerStove have all the functionality required to solve this problem?

[/ QUOTE ]
I'm not sure exactly what you're asking. If it is "What is the probability that I win the sidepot given the short stack wins the main pot?", the answer is equal to the percentage of times your hand beats the big stack in the hand, or 66%.
If you are asking what percentage of total outcomes have you losing the main pot to shorty but winning the sidepot, the answer is P(shorty winning) * P(your hand beats big stack) or .286 * .666 = 19.05%.
Hope this helps.

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The answer you give to the question is wrong. It may be a first order approximation of correct, but it isn't right.

You can partition the possible board cards into those that the short stack loses and those that the short stack wins. Looking only at boards when the short stack loses, you may have better, equal, or worse chances of winning against the other big stack as you'd have across all boards.

Simple contrived example:

Shorty has AK spades. Big stack has AQ clubs. Hero has red QQ. The two A's and three K's not in peoples hands are dead (folded by other players). Now the prob(Hero beats big stack) when shorty wins is ~100% (the only way he can not win when shorty wins is when shorty hits his flush and the board contains JT98 giving both other stacks a tie with the Q-high straight). The prob(hero beats big stack) when shorty loses is a lot, but is more like ~90% (as he loses any board with 3-or-more clubs and no Q-full house).

The probabilities were given by OP based on ranges he assigned to each player and plugged into poker stove. If we take these probabilities of winning as given, then I'm pretty sure my numbers are also correct. Of course, if we know the actual holdings of each player, the probabilities are adjusted, but that is not the situation presented by OP nor is it the situation in an actual game.

[SumZero]

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The probabilities were given by OP based on ranges he assigned to each player and plugged into poker stove. If we take these probabilities of winning as given, then I'm pretty sure my numbers are also correct. Of course, if we know the actual holdings of each player, the probabilities are adjusted, but that is not the situation presented by OP nor is it the situation in an actual game.

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But even in the case where we know hero's cards and the other are ranges you can't just compute the way you did as the majority of the time, for instance, if you win with over cards it means your overcards hit, so now all the pp that may be in one hand or the other are beat simultaneously.

[durron597]

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The probabilities were given by OP based on ranges he assigned to each player and plugged into poker stove. If we take these probabilities of winning as given, then I'm pretty sure my numbers are also correct. Of course, if we know the actual holdings of each player, the probabilities are adjusted, but that is not the situation presented by OP nor is it the situation in an actual game.

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But even in the case where we know hero's cards and the other are ranges you can't just compute the way you did as the majority of the time, for instance, if you win with over cards it means your overcards hit, so now all the pp that may be in one hand or the other are beat simultaneously.

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Yes, this is why I posted the question. I'm getting a non-intuitive answer in an equity calculation and I checked the math three times and that difference Pr(we beat big) <> Pr(we beat big | shorty beats both of us) is the only problem I can see.

If you're interested, the hand ranges I plugged in to get the above numbers are:
Big stack: any two
Shorty: AA-44, AKs-A2s, KQs-K5s, QJs-Q8s, JTs-J9s, AKo-A3o, KQo-K7o, QJo-Q9o, JTo
Hero: AQs

is pokerstove free??? my guess is no.

can i do my own analysis on pokerstove... like my raising pair of 10's questions, i could assume my opponents have A7, K9 and 88 and it could give me the odds that i'm still leading on the flop...... alot of people talk about odds of winning at the showdown, but too much danger/$$$$$ between pre-flop and showdown. need to know where you stand on the flop.

[durron597]

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is pokerstove free??? my guess is no.


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It's free, www.pokerstove.com

[fnord_too]

I have considered writing some code to answer this exact class of question, but I am lazy.