Discussion
What determines how much alpha beta actually prunes?
Answer: A
Examining the best move first establishes a strong bound immediately and allows everything else to be cut, while examining the worst first prunes nothing at all. Perfect ordering gives the square root improvement and random ordering gives roughly the three quarters power. Depth, evaluation quality and move count matter but do not control the pruning. That an algorithm's benefit depends entirely on a heuristic choice made outside it is unusual and it makes move ordering a first class concern.
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