Synthesizing human-friendly optimal strategies in board games

Abstract

We present a tool for synthesizing and verifying optimal game playing strategies represented by compact fast-andfrugal trees, i.e., prioritized lists of strategic rules. The purpose of the tool is to create human-friendly optimal strategies for simple board games, e.g. for teaching a human player to play optimally, or to assess the difficulty of a given board game in terms of the length of the generated strategy. The tool supports arbitrary oneor two-player zero-sum games with perfect information specified through the game description language GDL within general game playing. When synthesizing a strategy, the game is initially solved, the solution is turned into a fast-and-frugal tree, and the tree is then minimized. We illustrate the use of the tool to synthesize compact optimal strategies for Tic-tac-toe, Nim, and Sim, which leads us to provide an even shorter optimal strategy for Tic-tactoe than the well-known Simon & Newell strategy. Additionally, we have developed a visual tool enabling users to build and verify manually crafted fast-and-frugal strategies.