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June 12th, 2009, 01:15 PM   #1
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Calculating Probablities with Poker hands


There are a number of people that want to 'get better at poker with math' for me, I just like poker and I like math. I am though, having trouble finding resources for people who _Actually_ know math and calculating probablities. There are a number of third grade math probability calculations online but that is not what I am looking for.

I am looking to create a program to calculate 'heads up' pokerhand probabilities. If you already know of a program I would love to know were I can get the source code. If not I just need some help creating the math, then putting it into C++.

Basically I want to be able to create a hand, like AA, and calculate the probability that it will win against a hand like 72.

The rules that need to be considered are easy:

Each player gets two cards, there are 13 cards possible and 4 suits possible making a combination of 52 cards possible in total.
After each card is given to the player, there are five more cards dealt which the players can use. The player with the best 5 hand combination wins.

The ranking go like this:
High card (person with the highest card wins)
Pair (person with the highest pair wins)
Three of a kind (person with the highest three of a kind wins)
Straight (person with five cards in a row wins)
Flush (person with 5 cards with the same suit win)
Full House (Person with one pair and one three of a kind win)
Four of a kind (Person with four of a kind wins)
Straight flush (Person with a straight, and all cards are the same suit win)

Basically that's it.

I was thinking about it for a while and realized that this is going to be math beyond me. Any help would be great, wether that be direct help or direction to a reference.

I was hoping to be able to use this to then put a hand agaisnt a descrite distribution of hands that an opponent could be playing. Basically I'm reading a games theory poker book and the author pulls up stats like "Xcard,Ycard has a .67 expected value against Zcard,tcard with a pot size of 1" and I just want to know how to calculate these myself so that I can further do some games theory calculations that I can handle with my math knowledge.

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June 12th, 2009, 02:52 PM   #2
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Re: Calculating Probablities with Poker hands

I may well be wrong, but I would imagine that calculating these probabilities for any given two hands would be very tedious. And you might well have to do each possible hand separately.

If I were to approach this problem (and I'm by no means an expert programmer) then I would probably take the approach of writing a program that would take two two-card hands as input, randomly generate 100 or 1000 sets of 5 cards and then count the number of times hand A won against hand B to give an estimate for the probability of hand A beating hand B.

Having said that, it is obvious that this problem has been approached before, since often when I have watched poker on TV they will display a percentage chance of winning the hand for each player still in, at every stage of the round. I don't know whether these percentages have been worked out exactly, or just estimated.
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