Understanding Poker Decisions Through the Lens of Cumulative Prospect Theory

Bachelor Thesis - Malaika Pohl Khader

Reprository for simulating a Limit Texas Hold'em Poker game for five players under Bayesian Nash Equilibrium (BNE) and Perfect Bayesian Nash Equilibrium (PBE), evaluated with Cumulative Prospect Theory and statistical analysis. The following is an overview of the moodules in the project.

Installation

Clone the repository and install the dependencies:

bash git clone https://github.com/MalaikaPK/Poker-Simulation.git cd Poker-Simulation pip install -r requirements.txt

Requirements

Python 3.12

Project Structure

1. cards.py

The cards.py module provides foundational classes for representing playing cards, decks, and hands. It defines three key components: - Card Class: Represents individual playing cards with a suit (e.g., Spades, Hearts) and rank (e.g., Ace, 2, 3… King). - Deck Class: Constructs and manipulates a 52-card deck, supporting actions like shuffling and dealing. - Hand Class: Represents a players hand, inheriting from the Deck class, and tracks cards drawn from the deck.

This module abstracts the card manipulation logic, providing a clean structure for the game environment.

2. player.py

The player.py module defines the PokerPlayer class and implements decision-making based on Cumulative Prospect Theory (CPT) alongside Bayesian Nash Equilibrium (BNE) and Perfect Bayesian Equilibrium (PBE). The module simulates a poker player’s decision-making, incorporating Monte Carlo simulations to estimate win probabilities, updating beliefs about opponents strategies, and choosing actions based on CPT-weighted expected utility. The belief updating system reflects beliefs based on observed actions and hands, where the priors are drawn from a probability distribution based on previous monte-carlo simulations of hand class probabilities with 10,000,000 iterations, executed from the repository by https://github.com/Sondar4/poker-sim. In order to estimate P(a=raise|H,I), I have used a logistic function to approximate the likelihood that a player would raise given the win rate.

3. poker_cards.py

The poker_cards.py module extends the base card framework to suit poker-specific hand evaluation. It introduces: - PokerCard: A subclass of Card, tailored for poker hands. - PokerHand: A subclass of Hand, which implements the logic for evaluating and comparing poker hands. - PokerDeck: A subclass of Deck, generating PokerCard instances for use in games.

This module handles the rules for determining hand rankings in poker.

4. poker_game.py

The poker_game.py module governs the flow of a single poker game round. It defines the PokerGame class and manages various game elements: - It initialises the game with players and a poker deck. - Deals cards in three stages (Flop, Turn, and River), simulating player decisions (raise or fold). - Tracks game outcomes, including updating player beliefs based on opponent actions, and determining the winner based on the best hand.

This module serves as the core structure for running a poker game in the simulation.

5. poker_simulation.py

The poker_simulation.py module is responsible for executing multiple poker game simulations and collecting results. It runs poker games under BNE and PBE assumptions, comparing player strategies. Furthernore, it initialises diverse players with distinct CPT parameters and aggregates statistics on game outcomes, including total raises, folds, and wins.

This module is key to the experimental framework for testing poker strategies under uncertainty. To run the poker simulation, execute python poker_simulation.py. The simulation will run with the specified settings.

6. chi_square_test.py

The chi_square_test.py module handles the statistical analysis of the poker simulation results. It conducts several tests, including: - Chi-Square Tests: Evaluates the independence of raise/fold distributions across player types and between BNE and PBE. - Statistical Analysis: Runs t-tests, ANOVA, and Tukey HSD tests to examine differences in player behavior. - Visualisations: Generates bar charts and line plots to illustrate raise/fold percentages and win rates for each player type.

This module is crucial for drawing insights from the simulation data and understanding the strategic behavior of players. To run the statistical tests, execute python chi_square_test.py. The simulation will run with the specified settings from the poker_simulation.py module as well as the tests from the chi_square_test.py module.

6. tests.py

This module import the saved CSV files from chi_square_test.py, in order to make the statistical tests and regressions without running the whole simulation each time.

License Information

The following modules are adapted from open-source projects and are licensed under the MIT License:

1. cards.py
   Adapted from Allen Downeys "Think Python".
   License: MIT License
   Copyright (c) 2017 Allen Downey.
   You may freely use, copy, modify, and distribute the software, provided the copyright and license are included in all copies or substantial portions of the software.

   'The MIT License

   Copyright (c) 2017 Allen Downey
   
   Permission is hereby granted, free of charge, to any person obtaining a copy
   of this software (the "Software"), to deal
   in the Software without restriction, including without limitation the rights
   to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   copies of the Software, and to permit persons to whom the Software is
   furnished to do so, subject to the following conditions:
   
   The above copyright notice and this permission notice shall be included in all
   copies or substantial portions of the Software.
   
   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
   AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
   OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
   SOFTWARE.'
   

2. pypokerengine
   The pypokerengine library is also licensed under the MIT License.
   License: MIT License
   Copyright (c) 2017-2025.
   As with cards.py, the software can be freely used, modified, and distributed, provided the copyright and license are included.

Note

This is a cleaned up version of the original repository. The main difference is that this repository exclusively includes the relevant files, whereas the original repository includes the whole process from the beginning, in which my brother in law Jacob Martens had to help me learn Python, to the final result used in this repository.