Gardner’s Minichess Variant is Solved

Abstract

A 5 × 5 board is the smallest board on which one can set up all types 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 9 × 10¹⁸ legal positions and is comparable in this respect with checkers. We weakly solve this game: we prove its game-theoretic value and give a strategy to draw against best play for White and Black sides. Our approach requires surprisingly little 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.