Monte Carlo tree search (MCTS)
Monte Carlo tree search chooses an action by imagining many possible futures, but it spends its limited simulations wisely: it digs deeper into lines that look promising while still occasionally checking neglected ones. Over many iterations it grows a search tree biased toward the parts of the game that matter.
Each iteration runs four phases. Selection descends the existing tree by a tree policy, classically UCT, which adds to each action's mean value an exploration bonus proportional to the square root of the log of the parent's visit count over the action's own count. Expansion adds a new leaf, simulation estimates that leaf's value by a rollout, and backpropagation updates the visit counts and values along the path. AlphaZero replaces random rollouts with a learned value-and-policy network that supplies priors and leaf evaluations.
MCTS is an anytime, model-based planner: it needs a simulator or known dynamics, and it returns a better answer the longer it is allowed to think.
The UCT selection rule: exploit high mean value while exploring rarely visited actions via the bonus term.
Without rollouts or a learned evaluator, MCTS still needs a model to expand nodes; it plans by simulation, so a simulator or known dynamics is non-negotiable.