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Why is minimax invariant to monotonic rescaling of the evaluation?

  • A.It applies the evaluation only at terminal positions
  • B.It compares values rather than combining them arithmetically
  • C.It uses only the sign of the evaluation function
  • D.It normalises the values before backing them up

Answer: B

Every backup in minimax is a maximum or a minimum, which depends only on the ordering of the values, so any order preserving transformation gives the same move. Expectimax averages and so depends on the magnitudes. Signs, normalisation and terminal application are not the reason. Identifying an invariance is practically useful, because it says which aspects of a heuristic need tuning and which are free.

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