The game involves no chance: no coin flips, or die rolls.
Perfect information
Each player can see the complete game state.
Game trees
The tree generated by expanding all possible trajectories of the game.
Game score
The score of the first player at the end of the game.
Game theoretic value of a node
The score of the terminal node that will be reached if both players play optimally. Also called the minimax value of the node.
alpha-beta pruning
A method for speeding up the minimax search. Keep two bounds alpha and beta, where alpha is the best the first play can do up to now, and beta is the best the second player can do. At any point when alpha exceeds beta, the remaining children can be pruned.