Unraveling Go gaming nature by Ising Hamiltonian and common fate graphs: tactics and statistics

TL;DR

This paper models the complex dynamics of Go using an Ising Hamiltonian approach, revealing insights into strategic patterns and stochastic evolution beyond current AI capabilities.

Contribution

It introduces a novel Ising model framework to analyze Go game dynamics, capturing long-term strategies and pattern formations in a way that surpasses existing AI understanding.

Findings

Model accurately predicts game scores

Identifies formation of strategic patterns

Reveals differences between human and AI tactics

Abstract

Go gaming is a struggle between adversaries, black and white simple stones, and aim to control the most Go board territory for success. Rules are simple but Go game fighting is highly intricate. Stones placement and interaction on board is random-appearance, likewise interaction phenomena among basic elements in physics thermodynamics, chemistry, biology, or social issues. We model the Go game dynamic employing an Ising model energy function, whose interaction coefficients reflect the application of rules and tactics to build long-term strategies. At any step of the game, the energy function of the model assesses the control and strength of a player over the board. A close fit between predictions of the model with actual game's scores is obtained. AlphaGo computer is the current top Go player, but its behavior does not wholly reveal the Go gaming nature. The Ising function allows for precisely model the stochastic evolutions of Go gaming patterns, so, to advance the understanding on Go own-dynamic -beyond the player`s abilities. The analysis of the frequency and combination of tactics shows the formation of patterns in the groups of stones during a game, regarding the turn of each player, or if human or computer adversaries are confronted.