*find the value of the root*with a bounded-depth search.

1. Assuming that leaf values are finite but unbounded, is pruning (as in alpha–beta) ever possible in a max tree? Give an example, or explain why not.

2. Is pruning ever possible in an expectimax tree under the same conditions? Give an example, or explain why not.

3. If leaf values are constrained to be in the range $[0,1]$, is pruning ever possible in a max tree? Give an example, or explain why not.

4. If leaf values are constrained to be in the range $[0,1]$, is pruning ever possible in an expectimax tree? Give an example (qualitatively different from your example in (e), if any), or explain why not.

5. If leaf values are constrained to be nonnegative, is pruning ever possible in a max tree? Give an example, or explain why not.

6. If leaf values are constrained to be nonnegative, is pruning ever possible in an expectimax tree? Give an example, or explain why not.

7. Consider the outcomes of a chance node in an expectimax tree. Which of the following evaluation orders is most likely to yield pruning opportunities: (i) Lowest probability first; (ii) Highest probability first; (iii) Doesn’t make any difference?

In the following, a “max” tree consists only of max nodes, whereas an
“expectimax” tree consists of a max node at the root with alternating
layers of chance and max nodes. At chance nodes, all outcome
probabilities are nonzero. The goal is to *find the value of the
root* with a bounded-depth search.

1. Assuming that leaf values are finite but unbounded, is pruning (as
in alpha–beta) ever possible in a max tree? Give an example, or
explain why not.

2. Is pruning ever possible in an expectimax tree under the same
conditions? Give an example, or explain why not.

3. If leaf values are constrained to be in the range $[0,1]$, is
pruning ever possible in a max tree? Give an example, or explain
why not.

4. If leaf values are constrained to be in the range $[0,1]$, is
pruning ever possible in an expectimax tree? Give an example
(qualitatively different from your example in (e), if any), or
explain why not.

5. If leaf values are constrained to be nonnegative, is pruning ever
possible in a max tree? Give an example, or explain why not.

6. If leaf values are constrained to be nonnegative, is pruning ever
possible in an expectimax tree? Give an example, or explain why not.

7. Consider the outcomes of a chance node in an expectimax tree. Which
of the following evaluation orders is most likely to yield pruning
opportunities: (i) Lowest probability first; (ii) Highest
probability first; (iii) Doesn’t make any difference?