Nash reweighting of Monte Carlo simulations: Tsumego

Monte Carlo simulations are widely accepted as a tool for evaluating positions in games. It can be used inside tree search algorithms, simple Monte Carlo search, Nested Monte Carlo and the famous Monte Carlo Tree Search algorithm which is at the heart of the current revolution in computer games. If one has access to a perfect simulation policy, then there is no need for an estimation of the game value. In any other cases, an evaluation through Monte Carlo simulations is a possible approach. However, games simulations are, in practice, biased. Many papers are devoted to improve Monte Carlo simulation policies by reducing this bias. In this paper, we propose a complementary tool: instead of modifying the simulations, we modify the way they are averaged by adjusting weights. We apply our method to MCTS for Tsumego solving. In particular, we improve Gnugo-MCTS without any online computational overhead.