reduce its size by either limiting the search depth or cutting the branches. In a partial game tree, the depth is reduced artificially by making the internal nodes as leaves. This can be done using a heuristic to estimate their outcome, which of course can lead to suboptimal results. The branching factor can be reduced with alpha-beta pruning, which cuts off nodes that cannot provide a better outcome than the current best result. If we set tighter limits for the pruning (like in PVS), we can improve the running even further. The game tree can include probabilistic elements, which can be accounted by modelling them as chance nodes. Game trees can be used in many classical board games, and they have been studied widely. There are many game-specific improvements that allow, for example, to choose the opening and closing moves from a set of pre-calculated alternatives. Nevertheless, in the middle of the game play where the number of possible situations is much greater, the methods revert back to building game trees to find out the best move for the next round.