Personal Research Notes on Mathematics

Texas Hold’em and Expected Utility Functions – Addendum –

This article will supplement my previous posts with information about Texas Hold'em and expected utility functions. In addition, I will briefly describe my impressions of playing Texas Hold'em.

2025.01.16

Economics

Double-Slit Experiment and Schrödinger Equation

This article derives a solution to the Schrödinger equation for the double-slit experiment, and present the hypothesis that phenomena such as the double-slit experiment are caused by the properties of relativistic space-time.

2025.01.05

Physics

Texas Hold’em and Game Theory

This article outlines how to predict the opponent's hand (hand range) in Texas Hold'em and how to apply game theory. By adding these elements as player functions in the game, it may be possible to create a stronger NPC player.

2024.12.27

Economics

Texas Hold’em Game

A Texas Hold'em game developed by the author. You can specify the strength and character of the opponent player, or make them random.

2024.12.16

Probability

Texas Hold’em and Expected Utility Theory

In order to design the behavior of NPCs in Texas Hold'em, we consider how to make decisions using expected utility theory. At the same time, we consider what factors represent the strength and weakness of players.

2024.12.16

Economics

Texas Hold’em Game (Prototype)

I developed a Texas Hold'em game. The opponents are selected randomly, but in the future I plan to develop a version that uses an algorithm to make rational decisions.

2024.12.13

Probability

Texas Hold’em Winning Probability Calculator

A calculator that uses Monte Carlo simulation to estimate the probability of winning in Texas Hold'em when the hand and some common cards are known.

2024.12.13

Probability

Texas Hold’em Game Design

This article will look at the issues that must be taken into consideration when developing a Texas Hold'em game.

2024.12.10

Probability

Monte Carlo Simulation

This article provides an overview of Monte Carlo simulation. As an application example, it considers how to estimate the probability of winning in Texas Hold'em using Monte Carlo simulation.

2024.12.05

Probability

Texas Hold’em

This article is a simple explanation of the rules of the game Texas Hold'em. It may be used as a subject for explaining probability calculations and Monte Carlo simulations in the future.

2024.11.28

Probability