We formalise the game by considering two distinguished players: MAX and MIN. The game tree is a tree such that each node represents a state of the game. Therefore the root note of the tree is the initial state of the game. Each arc of the tree represents a legal move in the game.
The way we analyse the situation is to consider MAX's best interests: MAX plays to maximise his/her chances of a win while MIN plays to minimise MAX's chance of winning.
The notion of lookahead is the idea that, at any state in the game, one of the players can develop the game tree to a limited extent. A lookahead of 3 from the current game state would mean developing the tree to a depth of three levels. The resulting cut-down game tree is termed the lookahead tree. The leaf nodes of the lookahead tree are termed terminal states.
The ``real'' value of a terminal state is unknown since we are not doing exhaustive search. Hence we need to utilise an evaluation function. This function is a numerical assessment of how good the game state (i.e. the state indicated by the terminal node) is for MAX. A positive score indicates a good position for MAX and a negative score a bad position. Non-terminal nodes represent intermediate game states.
The problem for MAX is to play such as to maximise his/her chances. A choice of moves has to be made to reach the most favourable of the current set of terminal nodes. How does MAX choose? An answer lies in the minimax technique.