Strongly Solving $7 \times 6$ Connect-Four on Consumer Grade Hardware

TL;DR

This paper demonstrates that a strong, complete solution for the standard 7x6 Connect-Four game can be computed using symbolic search with binary decision diagrams, producing a large look-up table on consumer hardware.

Contribution

It introduces an efficient symbolic search method that produces a comprehensive look-up table for Connect-Four, previously thought infeasible on consumer hardware.

Findings

Produced an 89.6 GB look-up table in 47 hours on a single CPU core

Enabled fast move determination with alpha-beta search in the solution

Showed feasibility of solving Connect-Four with consumer-grade hardware

Abstract

While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our open source artifact to find the move which achieves the fastest win or slowest loss.