Games with large branching factors pose a significant challenge for game tree search algorithms. In this paper, we address this problem with a sampling strategy for Monte Carlo Tree Search (MCTS) algorithms called {em na{i}ve sampling}, based on a variant of the Multi-armed Bandit problem called {em Combinatorial Multi-armed Bandits} (CMAB). We analyze the theoretical properties of several variants of {em na{i}ve sampling}, and empirically compare it against the other existing strategies in the literature for CMABs. We then evaluate these strategies in the context of real-time strategy (RTS) games, a genre of computer games characterized by their very large branching factors. Our results show that as the branching factor grows, {em na{i}ve sampling} outperforms the other sampling strategies.
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