text: Monte Carlo Tree Search (MCTS) has improved the performance of game engines in domains such as Go, Hex, and general game playing. MCTS has been shown to outperform classic alpha-beta search in games where good heuristic evaluations are difficult to obtain. In recent years, combining ideas from traditional minimax search in MCTS has been shown to be advantageous in some domains, such as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new way to use heuristic evaluations to guide the MCTS search by storing the two sources of information, estimated win rates and heuristic evaluations, separately. Rather than using the heuristic evaluations to replace the playouts, our technique backs them up implicitly during the MCTS simulations. These minimax values are then used to guide future simulations. We show that using implicit minimax backups leads to stronger play performance in Kalah, Breakthrough, and Lines of Action.
  @cite_19: Monte-Carlo Tree Search is a sampling-based search algorithm that has been successfully applied to a variety of games. Monte-Carlo rollouts allow it to take distant consequences of moves into account, giving it a strategic advantage in many domains over traditional depth-limited minimax search with alpha-beta pruning. However, MCTS builds a highly selective tree and can therefore miss crucial moves and fall into traps in tactical situations. Full-width minimax search does not suffer from this weakness. This paper proposes MCTS-minimax hybrids that employ shallow minimax searches within the MCTS framework. The three proposed approaches use minimax in the selection expansion phase, the rollout phase, and the backpropagation phase of MCTS. Without requiring domain knowledge in the form of evaluation functions, these hybrid algorithms are a first step at combining the strategic strength of MCTS and the tactical strength of minimax. We investigate their effectiveness in the test domains of Connect-4 and Breakthrough.
  @cite_14: 
  @cite_1: Monte-Carlo Tree Search (MCTS) is a successful algorithm used in many state of the art game engines. We propose to improve a MCTS solver when a game has more than two outcomes. It is for example the case in games that can end in draw positions. In this case it improves significantly a MCTS solver to take into account bounds on the possible scores of a node in order to select the nodes to explore. We apply our algorithm to solving Seki in the game of Go and to Connect Four.
summary: One may want to combine minimax backups or searches without using an evaluation function. The prime example is MCTS-Solver @cite_14 , which backpropagates proven wins and losses as extra information in MCTS. When a node is proven to be a win or a loss, it no longer needs to be searched. This domain-independent modification greatly enhances MCTS with negligible overhead. Score-bounded MCTS extends this idea to games with multiple outcomes, leading to @math -style pruning in the tree @cite_1 . One can use shallow-depth minimax searches in the tree to initialize nodes during expansion, enhance the playout, or to help MCTS-Solver in backpropagation @cite_19 .