The Texas Holdem Statistical Analysis Project Overview

The goal of the project was simple; to find the most optimum strategy to play \$2 - \$4 limit Texas Holdem. Then design a training program that teaches that strategy. Two programs were designed to analyze the statistical advantage of any hand throughout the game. I designed the programs using php on an apache server. This gave me the ability to change directions designing the overall strategy.

The Texas Holdem Odds Calculator

The odds calculator was design to determine the percentage of advantage of any hand on the pre-flop, flop, turn and river. Every player card and board card (flop, turn and river) could be changed. After ten thousand hands the percentage of advantage of each hand was calculated.

= ( ( hands won / hands total ) - ( 1 / total players ) ) * 100

First, the hands on the river need to be identified that have a positive advantage. These would be known as the 'made hands' that are winning hands. Next, identify the pre-flop hands with a positive percentage of advantage. Then design an optimum strategy based upon percentage of advantage.

Finally, identify the best drawing hands on the flop and turn. Poker is a very complicated game. The math involved in playing poker also includes pot odds, the size of the pot compared to the advantage of your hand. If the pot is large, a hand with a slight advantage is worth betting. Then, there is a concept of implied pot odds. Implied pot odds takes into account of what other players usually play. To make matters worse, the percentage of advantage for the same hand changes with the number of players.

A program was needed that can play a complete \$2 - \$4 limit Texas Holdem game from the deal to the showdown. The amount of players during the game could be changed. The playing strategy during pre-flop, flop, turn the river had to be changed at will. The ability to change to cards dealt to the player and board cards on the flop, turn and river was necessary. Of course, the program had to play thousands of hands to calculate the percentage of advantage.

The Texas Holdem Game Simulator

The final problem to consider was the human variable of opponents. I decided to have the program play all hands on the river (as if no one folds) in order to analyze the percentage of advantage. Both programs we used to determine an overall strategy for both a short-handed game (5 players) and a full table game (10 players). This strategy was based on the playing only hands with a positive percentage of advantage.

After years of analysis, here are the results.

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