Alpha-beta search is easily implemented by adding the &alpha and &beta parameters to a depth-first minimax search. The alpha-beta search simply quits early and returns the current value when the &alpha or &beta threshold is exceeded.
Alpha-beta search performs best if the best moves (for Max) and worst moves (for Min) are considered first; in this case, the search complexity is reduced to O(bd/2) .
For games with high symmetry (e.g. chess), a transposition table ( cf. Closed list) containing values for previously evaluated positions can greatly improve efficiency.