Discussion
Alpha beta with perfect ordering reduces the effective branching factor to \( \sqrt{b} \). What is it for b = 36?
Answer: D
Taking the square root of the branching factor gives:
\[ \sqrt{36} = 6 \]
so the effective branching factor falls to 6, which means the same effort searches twice the depth. For chess, with about thirty five legal moves, that is the difference between a weak program and a strong one. Halving the exponent is a far larger gain than any constant factor, which is why move ordering receives so much attention.
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