Monte Carlo tree search (MCTS) is a search paradigm that has been remarkably successful in computer games like Go. It uses Monte Carlo simulation to evaluate the values of nodes in a search tree. The node values are then used to select the actions during subsequent simulations. The performance of MCTS heavily depends on the quality of its default policy, which guides the simulations beyond the search tree. In this paper, we propose an MCTS improvement, called incentive learning, which learns the default policy online. This new default policy learning scheme is based on ideas from combinatorial game theory, and hence is particularly useful when the underlying game is a sum of games. To illustrate the efficiency of incentive learning, we describe a game named Heap-Go and present experimental results on the game.
Triangular Nim, one variant of the game Nim, is a common two-player game in Taiwan and China. In the past, Hsu strongly solved 7 layer Triangular Nim while some of the authors recently strongly solved 8 layer Triangular Nim. The latter required 8 gigabytes in memory and 8878 seconds.Using a retrograde method, this paper strongly solves 9 layer Triangular Nim. In our first version, the program requires four terabytes in memory and takes about 129.21 days aggregately. In our second version, improved by removing some rotated and mirrored positions, the program reduces the memory by a factor of 5.86 and the computation time by a factor of 4.38. Our experiment result also shows that the loss rate is only 5.0%. This is also used to help improve the performance.
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