Poker Pre-Flop Win Percentage

My idea is to input a combination of two playing cards (52 cards total) and create matirx of every combination. Then I wanted to attach a probablitly of winning with that combo based on how many players (or other combos of two cards that we cannot see) and then output the result of that win percentage based on my original input. I have created a matrix with every card combination and was trying to find an easier way to link the win percentage with every combo instead of typing out all 1326 combination's win percentages. Thank you for your time.

[David Goodmanson]

Hi B^2,

I assume you have a way of calculating the win percentages and just want to fill out the matrix. An upper triangular 52x52 matrix, not including the diagonal, has the 1326 entries you mentioned. However, there are really only three basic categories: pairs, nonpair suited and nonpair nonsuited. So consider a 13x13 matrix of just the card values. Pairs are down the diagonal. Nonpair suited can go in the upper triangle. Nonpair nonsuited can go in the lower triangle. That makes 169 cases all together that can have different probabilities, which if you have to enter these by hand is certainly better than 1326.

To verify that all cases are covered, there are 13 ways to do pairs, and for each pair there are 4x3/2 = 6 ways to do the suits. There are 13x12/2 = 78 ways to do nonpairs, and for each of these there are 4 ways to do suited, and 4x3 = 12 ways to do nonsuited.

13x6 + 78x4 + 78x12 = 1326.

[Roshan Hingnekar]

It is not possible to calculate the exact percentage chance of winning with a hand if one doesn't know the pair of cards in other constestant's hand.

For ex. if you are playing heads up, you hold King pair, the opponent holds Ace pair, the chance of your winning is 3%, while if the opponent has queen pair, you have 96% chance of winning.

So if you want to calculate the chance of your opponent(s) being dealt a better hand, then the probability of your winning it would be complex since the sample space for the flop+turn+river would keep changing.

I would suggest arranging the card pairs (1326) in order of strength and running a random forest machine learning algorithm to select the opponents cards and then calculating the winning percentage over multiple tests.