Learn about coding a decision-making program.
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Entertainment MiniMax Game Trees
The Minimax Game Tree is used for programming computers to play games in which there are two players taking turns to play moves. In the most basic sense, the minimax tree is just a tree of all possible moves. For instance, take a look at the following minimax tree of all the possible first two moves of Tic-Tac-Toe (the tree has been simplified by removing symmetrical positions).
Notice that unlike other trees like binary trees, 2-3 tres, and heap trees, a node in the minimax game tree can have any number of children, depending on the game situation.
The tree above has three levels, but in programming, the levels of a minimax tree are commonly refered to as plies . At each ply, the opportunity to play (the "turn") switches to the other player. The two different players are usually refered to as Max and Min (this convention will be explained shortly).
With a full minimax tree, the computer could look ahead for each move to determine the best possible move. Of course, as you can see in the example diagram, the tree can get very big with only a few moves, and to look even just five moves ahead can quickly overwhelm a simple computer . Thus, for large games like Chess and Go, computer programs are forced to estimate who is winning or losing by sampling just a small portion of the entire tree. Also, programmers have come up with algorithms such as Alpha-Beta pruning, Negascout, and MTD(f) to try to limit the number of nodes the computer must examine.
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