__function__ MONTE-CARLO-TREE-SEARCH(_state_) __returns__ an action

 tree ← NODE(_state_)

 __while__ TIME\-REMAINING() __do__

   __tree__ ← PLAYOUT(_tree_)

 __return__ the _move_ in ACTIONS(_state_) with highest Q(_state_,_move_)

__function__ PLAYOUT(_tree_) __returns__ _updated tree_

 _node_ ← _tree_

 __while__ _node_ is not terminal and was already in _tree_ __do__

   _move_ ← SELECT(_node_)

   _node_ ← FOLLOW\-LINK(_node_,_move_)

 _outcome_ ← SIMULATION(_node_.STATE)

 UPDATE(_node_,_outcome_)

 __return__ _tree_

__function__ SELECT(_node_) __returns__ _an action_

 __return__ argmax_{m ∈ FEASIBLE\-ACTIONS(_node_)} UCB(RESULT(_node_,_m_))

__function__ UCB(_child_) __returns__ _a number_

&emsp;__return__ _child_.VALUE + C &times;<span class="math">$\sqrt{\frac{\log{_child_.PARENT.N}}{_child_.N}}$</span>

__FIGURE ??__ The Monte Carlo tree search algorithm. A game tree, _tree_, is initialized, and then grows by one node with each call to PLAYOUT. The function SELECT chooses a move that best balances exploitation and exploration according to the UCB formula. FOLLOW-LINK traverses from the current node by making a move; this could be to a previously-seen node, or to a new node that is added to the tree. Once we have added a new node, we exit the __while__ loop and SIMULATION chooses moves (with a randomized policy that is designed to favor good moves but to compute quickly) until the game is over. Then, UPDATE updates all the nodes in the tree from node to the root, recording the fact that the path led to the final __outcome__.