The sequence of states formed by possible moves is called a game tree ; each level of the tree is called a ply. We call the two players Max (us) and Min (the opponent).
The game tree must be an AND/OR tree. We can make any move we wish; thus, if any move is a winner, we win, and we have an OR node. However, we can win on an opponent's move only if we can win for every possible move of the opponent; thus, the opponent's move is an AND node.
Each node of a game tree represents the problem of winning for Max from the corresponding board position. A winning strategy corresponds to a solution tree .