Jamming transitions and avalanches in the game of Dots-and-Boxes

TL;DR

This paper models the game of Dots-and-Boxes using statistical physics, identifying a jamming transition that signals the start of the end-game and predicting avalanche distributions through differential equations.

Contribution

It introduces a novel statistical physics approach to analyze Dots-and-Boxes, characterizing the jamming transition and deriving equations to predict game dynamics.

Findings

Identification of a jamming transition in Dots-and-Boxes

Derivation of differential equations for game state prediction

Prediction of avalanche distributions in the end-game

Abstract

We study the game of Dots-and-Boxes from a statistical point of view. The early game can be treated as a case of Random Sequential Adsorption, with a jamming transition that marks the beginning of the end-game. We derive set of differential equations to make predictions about the state of the lattice at the transition, and thus about the distribution of avalanches in the end-game.