We introduce a recursive AlphaZero-style Monte--Carlo tree search algorithm, "RMCTS". The advantage of RMCTS over AlphaZero's MCTS-UCB is speed. In RMCTS, the search tree is explored in a breadth-first manner, so that network inferences naturally occur in large batches. This significantly reduces the GPU latency cost. We find that RMCTS is often more than 40 times faster than MCTS-UCB when searching a single root state, and about 3 times faster when searching a large batch of root states. The recursion in RMCTS is based on computing optimized posterior policies at each game state in the search tree, starting from the leaves and working back up to the root. Here we use the posterior policy explored in "Monte--Carlo tree search as regularized policy optimization" (Grill, et al.) Their posterior policy is the unique policy which maximizes the expected reward given estimated action rewards minus a penalty for diverging from the prior policy. The tree explored by RMCTS is not defined in an adaptive manner, as it is in MCTS-UCB. Instead, the RMCTS tree is defined by following prior network policies at each node. This is a disadvantage, but the speedup advantage is more significant, and in practice we find that RMCTS-trained networks match the quality of MCTS-UCB-trained networks in roughly one-third of the training time. We include timing and quality comparisons of RMCTS vs. MCTS-UCB for three games: Connect-4, Dots-and-Boxes, and Othello.