PROJECT TITLE :

An Enhanced Solver for the Game of Amazons

ABSTRACT:

The game of Amazons is a trendy board game with easy rules and nice mathematical properties. It has a high computational complexity. In 2001, the starting position on a 5 × five board was proven to be a initial player win. The enhanced Amazons solver presented here extends previous work in the following five ways: by building a lot of powerful endgame databases, together with a replacement sort of databases for thus-known as blocker territories, by improving the principles for computing bounds on complex game positions, by native search to find tighter native bounds, by using concepts from combinatorial game theory to seek out wins earlier, and by employing a df-pn based mostly solver. Using the improved solver, the beginning positions for Amazons on the 4 × 5, 5 × 4, four × half dozen, 5 × vi, and four × 7 boards were shown to be 1st player wins, while half-dozen × four may be a second player win. The largest proof, for the 5 × half-dozen board, is presented thoroughly.