Let a be the value that Max can currently get at least.
We are now computing the min_value at some node n.
When we explore 𝑛’s children, if we find that the value of 𝑛will never be better than 𝑎(for agent Max), then we can stop considering 𝑛’s other children.
Properties of alpha-beta pruning
The pruning has no effect on minimax value for the root.
Good child ordering improves effectiveness of pruning.
Complexity of perfect ordering: O(bm/2), meaning that you may look twice as deep as your opponent.
Full search of many games (e.g. Chess, Go) is still hopeless.