An Enhanced Solver for the Game of Amazons

The game of Amazons is a modern board game with simple rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × 5 board was proven to be a first player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building more powerful endgame databases, including a new type of databases for so-called blocker territories, by improving the rules for computing bounds on complex game positions, by local search to find tighter local bounds, by using ideas from combinatorial game theory to find wins earlier, and by using a df-pn based solver. Using the improved solver, the starting positions for Amazons on the 4 × 5, 5 × 4, 4 × 6, 5 × 6, and 4 × 7 boards were shown to be first player wins, while 6 × 4 is a second player win. The largest proof, for the 5 × 6 board, is presented in detail.