Implementation of Sprouts: a graph drawing game

TL;DR

This paper presents the first user-friendly AI implementation of the game Sprouts, overcoming decades of challenges by integrating combinatorial game theory and advanced geometric algorithms to achieve near-perfect play.

Contribution

It introduces a novel AI for Sprouts that combines nimber theory with Delaunay triangulations and force-directed algorithms, enabling strong gameplay up to 11 spots.

Findings

Developed the first AI Sprouts player with strong performance

Achieved near-perfect play on up to 11 spots

Integrated advanced geometric and combinatorial methods

Abstract

Sprouts is a two-player pencil-and-paper game invented by John Conway and Michael Paterson in 1967. In the game, the players take turns in joining dots by curves according to simple rules, until one player cannot make a move. The game of Sprouts is very popular and simple-looking, so it may come as a surprise that there are essentially no AI Sprouts players available. This lack of computer opponents is caused by the fact that the game hides a surprisingly high combinatorial complexity and implementing it involves fascinating programming challenges. We overcome all the implementation barriers and create the first user-friendly Sprouts application with a strong artificial intelligence after more than 50 years of the existence of the game. In particular, we combine results from the theory of nimbers with new methods based on Delaunay triangulations and crossing-preserving force-directed algorithms to develop an AI Sprouts player which plays a perfect game on up to 11 spots.