Poker Texas Hold'em No Limit

This project is a comprehensive implementation of a Poker Texas Hold'em No Limit game from scratch, including:

• all necessary classes
• a custom hand evaluation system
• hand recognition system
• algorithm that calculates win probabilities using Monte Carlo simulation
• algorithm to evaluate decision effectiveness
• bot that makes optimal mathematical decisions using these algorithms

Implementation

Game is implemented using object-oriented programming with the following classes:

• Player: stores information about chip stack, betting amounts and has methods for acting during the game: fold, check or raise.
• Bot: inherits Player class extending it by new method: decision. This method makes a decision based on mathematical probabilities.
• Deck: stores cards
• Card: represents card
• Pot: stores information about amount of chips and tracks minimum bet allowed.
• Game: controls flow of the game.

Custom Scoring System

To evaluate and compare hand strength, an authorial scoring system was developed. This system uses a combination of addition and specifically chosen multipliers to uniquely evaluate each poker hand. Below are the precise formulas for each possible hand in poker:

Let kickers be represented by $k$, and highest card of the hand as $n$: $$\text{High card} = n \cdot 100000 + k_1 \cdot 1000 + k_2 \cdot 100 + k_3 \cdot 10 + k_4 \cdot 1$$ $$\text{Pair} = \text{pair value} \cdot 100000 + 13 \cdot 100000 + k_1 \cdot 1000 + k_2 \cdot 100 + k_3 \cdot 10$$ $$\text{Two Pair} = \text{pair value}_1 \cdot 100000 + 25 \cdot 100000 + \text{pair value}_2 \cdot 1000 + k_1 \cdot 10$$ $$\text{Three of a kind} = \text{value of the three cards} + 38 \cdot 100000 + k_1 \cdot 100 + k_2 \cdot 10$$ $$\text{Straight} = n \cdot 100000 + 48 \cdot 100000$$ $$\text{Flush} = n \cdot 100000 + 56 \cdot 100000 + k_1 \cdot 10000 + k_2 \cdot 1000 + k_3 \cdot 100 + k_4 \cdot 10$$ $$\text{Full house} = \text{value of the full house} + 82 \cdot 100000 + k_1 \cdot 1000$$ $$\text{Poker} = n \cdot 100000 + 92 \cdot 100000$$

Poker Win Probability Calculator

The calculator utilizes Monte Carlo simulations to estimate probabilities. This method involves running a large number of random simulations to model the possible outcomes of a game. Here's how it works in the context of this poker calculator:

• Random Sampling: The calculator generates random combinations of common cards and opponent hands to simulate different game scenarios.
• Statistical Accuracy: By running thousands or even millions of these simulations, the calculator can approximate the true probability of winning a hand with high accuracy.
• Efficiency: Instead of analyzing every possible combination exhaustively, Monte Carlo simulation allows for quick probability estimation by focusing on a representative sample of possible outcomes.

Calculation modes

Against Known Cards

Function: Calculates the win probability for specific player hands and common cards.

Example: For two players with no common cards, the calculator considers 1,712,304 possible combinations. It samples 50,000 combinations for quick results, achieving 2% margin of error within 5 seconds.

Against Unknown Cards

Function: Evaluates probabilities by inputting two known cards and assuming two unknown cards for the opponent.

Example: In a one-on-one game, the opponent's hand can form 1,225 possible combinations. The calculator uses sampling to estimate probabilities efficiently.

Against Hand Ranges

Function: Assesses hand strength against a range of potential opponent hands using Bill Chen’s scoring method.

Example: Calculate the win probability of a pair of Kings against any hands scored 8 or higher.

Installation

Clone and enter the repository

git clone https://github.com/MarcinKadziolka/poker.git
cd poker

Create virtual environment and activate it

python3 -m venv .venv
source .venv/bin/activate

Install required packages

pip3 install -r requirements.txt

Run the program

python3 poker/poker.py

python3 poker/win_evaluation_gui.py