The Kinetics of Riichi Mahjong: A Stochastic Biochemical Analysis

Project Lead: Julian Benson

Dataset: $N = 1,087,446$ Tenhou Phoenix Room Logs (2025)

Overview

This project investigates the non-linear probability curves of Riichi Mahjong through the lens of Michaelis-Menten enzyme kinetics. By treating a "Tenpai" (ready) hand as a catalytic enzyme and the depleting tile wall as a substrate pool, we derived a Michaelis Constant ($K_m$) of ~64 tiles.

The results mathematically demonstrate that Mahjong is a substrate-limited system, providing a rigorous kinetic explanation for strategic "failure points" in the late game.

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Core Findings

• Conformational Locking: We model the Riichi declaration as a conformational lock, where a player sacrifices structural flexibility for an exponential increase in potential energy (payout).
• The Starvation Threshold: Because a standard game starts with only 70 substrate units (tiles) and has a $K_m$ of 64, the "reaction" operates in a state of starvation from Turn 1.
• Kinetic Failure: Win rates collapse non-linearly. We identify Turn 8 as the critical kinetic threshold after which the board state can no longer support high-efficiency product formation.

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Repository Contents

• Mahjong_Kinetics_Paper.md: The full documentary-style deep dive, covering the evolutionary history of the game, the protein dynamics of the hand, and the thermodynamic implications of the "Rule of 64."
• harvest_data.py: High-performance parser for Tenhou JSON logs.
• analyze_kinetics.py: Regression script using scipy.optimize to calculate $V_{max}$ and $K_m$ from experimental data.
• kinetics_data.csv: The processed dataset ($>1M$ records).

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Quick Start

pip install -r requirements.txt
python analyze_kinetics.py

Read the Full Paper Here