randomized algorithms can be used in solving game trees. there are two main advantages in this type of implementation: speed and practicality. whereas a deterministic version of solving game trees can be done in , the following randomized algorithm has an expected run time of . moreover, it is practical because randomized algorithms are capable of "foiling an enemy", meaning an opponent cannot beat the system of game trees by knowing the algorithm used to solve the game tree because the order of solving is random.