  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.
