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What is the effect of the evaluation function's scale in expectimax?

  • A.Only a positive linear transformation leaves the choice unchanged
  • B.Any monotonic transformation leaves the choice unchanged
  • C.The scale has no effect on the move that is selected
  • D.The function must return probabilities between zero and one

Answer: A

Because expectations are taken, doubling one leaf value and not another changes the averages and hence the move, so only affine rescaling is safe. In pure minimax any order preserving transformation is harmless, since only comparisons are made. That difference is easily overlooked and it means an evaluation function tuned for minimax may misbehave in an expectimax setting. Knowing which transformations a method is invariant to tells you how much freedom the designer really has.

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