Statistical mechanics for Scrabble predicts strategy, entropy and language

TL;DR

This paper applies a maximum entropy model to Scrabble game patterns, revealing insights into strategies, language differences, and entropy, without needing detailed tile information.

Contribution

It introduces a pairwise maximum entropy model that accurately predicts Scrabble graph features and distinguishes languages based on gameplay patterns.

Findings

The model predicts word-length statistics and geometric features accurately.

Entropy correlates more with gameplay strategy than lexicon size.

The approach can classify Scrabble graphs by language efficiently.

Abstract

The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We find the most structureless description that reproduces means and covariances observed in real Scrabble games by adapting a maximum entropy approach to connected graphs. This pairwise model captures the data well, and predicts word-length statistics and geometric features of the Scrabble graphs correctly; in addition, the parameters of this model are interpretable and allow us to understand Scrabble playing strategies. Using this pairwise model, we calculate entropy differences and distinguishability of Scrabble graphs across languages, without having access to the letters on the tiles. Notably, we find that the entropy is predicted better by strategic gameplay -- such as word length on the board -- than lexicon size. Finally, we find that we can use the pairwise model to correctly assign Scrabble graphs to languages, avoiding explicit feature selection and at relatively low computational cost.