O on the board), taking symmetry into account. c.Mark on your tree the evaluations of all the positions at depth 2. d.Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0,and use those values the choose the best starting move. e.Circle the nodes at depth 2 that would not be evaluated if alpha-beta pruning were applied, assuming the nodes are generated in the optimal order for alpha-beta pruning. Figure S6.1 shows the game tree, with the evaluation function values below the terminal nodes and the backed-up values to the right of the non-terminal nodes. The values imply that the best starting move for X is to take the center. The terminal nodes with a bold outline are the ones that do not need to be evaluated, assuming the optimal ordering.
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