Online Poker Forum - calculus of probability

Magic-Stick100 · High Card Joined: 21 Oct 2009 Posts: 5

Hey,

i have a question to those people who are fit in calculating.

I need a solution for the following problem:

Player A holds 10 9 of hearts
Player B holds A A (both Aces not Heart)

Player A has now a 23% chance of winning and Player B 77% of winning this pot PREFLOP.

My Question is now: How do I get to this values ? I tried very much, but i don't get it.

Hope someone can help me.

Magic

P.S.: Sorry for my bad english, I'm German Wink

IABoomer · Moderator Joined: 29 Oct 2006 Posts: 7351

I think most of the time preflop equities are generated through enumeration. You simulate the dealing of every possible board, calculate the number of times AA wins vs the number of times Th9h wins and figure your percentages from there. Software like Pokerstove has a table that it does preflop equity lookups from to save time.

You can download that table from here: http://www.pokerstove.com/analysis/preflopeq.php

I don't know that there's a practical way to formulate it.

Magic-Stick100 · High Card Joined: 21 Oct 2009 Posts: 5

Yeah i already know this program, but i need the way how to get to this values, because i'm writing a "skilled labour" on that topic...i tried it really hard to get to this values, but this way to calculate the values i already tried:

i tried to figure out how much boards are possible, that my AA is still winning, and then i divide it to the numbers of all boards...but this is very complicated, too...

adam27x · Posted: Wed Oct 21, 2009 1:31 pm Post subject:

finding the total # of boards should not be too difficult as that should be on the internet somewhere

if you are going to brute force it, let me suggest that counting the number of boards that T9hh wins on will be significantly easier than counting the number of boards that AA wins on.

IABoomer · Moderator Joined: 29 Oct 2006 Posts: 7351

I believe the author of Pokerstove enumerated all possible board combinations through simulation then recorded those results for the table.

You'd have to take the two players' hole cards that you know, then generate 48C5, or roughly 1.7 million boards to evaluate.

Otherwise, it becomes a vicious exercise in thinking about every possible way that one hand could win over the other, calculating the odds of that happening, then combining all the possible outcomes.

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