Alpha-Beta Pruning

Alpha-Beta Pruning applies two optimisations:

• skip rest of MIN children when $\beta \le \alpha$
• skip rest of MAX children when $\beta \le \alpha$

Which are based on two observations of Minimax:

• when some of the children of a MAX node have been evaluated, there is a lower-bound $\alpha$ on how much MAX can get, even if the other children have not been evaluated yet
• when some of the children of a MIN node have been evaluated , there is an upper bound $\beta$ on how much MAX can get, even if the other children have not been evaluated yet