Gardner's Minichess Variant is solved

TL;DR

This paper presents a weak solution to Gardner's Minichess, a 5x5 variant with a vast number of positions, proving its game-theoretic value and providing a strategy to draw, using surprisingly modest computational resources.

Contribution

The paper demonstrates the weak solvability of Gardner's Minichess and offers a human-readable proof and strategy, with a method applicable to larger chess variants or other games.

Findings

Game-theoretic value of Gardner's Minichess is a draw.

Strategy to force a draw against optimal play.

Solution achieved with minimal computational power.

Abstract

A 5x5 board is the smallest board on which one can set up all kind of chess pieces as a start position. We consider Gardner's minichess variant in which all pieces are set as in a standard chessboard (from Rook to King). This game has roughly 9x10^{18} legal positions and is comparable in this respect with checkers. We weakly solve this game, that is we prove its game-theoretic value and give a strategy to draw against best play for White and Black sides. Our approach requires surprisingly small computing power. We give a human readable proof. The way the result is obtained is generic and could be generalized to bigger chess settings or to other games.