Adversarial Search

Refer to the game tree to answer the following questions:

$1\mathrm{.}1.$ Using minimax, which of the three possible moves should MAX take at the root node?

$1\mathrm{.}2.$ What is the value of MAX at the root?

$1\mathrm{.}3.$ Using minimax with alpha$-$beta pruning, compute the value of alpha and beta at each node. What branches are pruned?

Select the correct option and argue why is correct:

Alpha$-$beta:

Doubles the depth of minimax search, approximately

Is slower than minimax

Is incompatible with minimax

All of the above

None of the above