Evaluation functions of Minimax algorithm
An example for Expectimax (root node is a Max node):



(image from CSE AI Faculty / Dan Klein, Stuart Russell, Andrew Moore)

changing the evaluation function changes the action taken.

For Minimax, since $f_1(s_i) \ge f_1(s_j) \implies f_2(s_i) \ge f_2(s_j)$, the best node (action taken) doesn't change (Minimax is insensitive to monotonic transformations):