tl;dr What does the Minimax algorithm do when all its options are the same?
Consider this Minimax tree:
(Green means the ends, orange minimize, blue maximize)
(Source: Myself)
Imagine this is the tree for a game (tic-tac-toe, maybe?). What should the computer do? Pick one at random? Pick the one which on average has the best score (the second one)?
Background
I'm making a program to play Quoridor, and I figure that the Minimax algorithm is the best choice (with some pruning of the really bad ones; otherwise, it would be way too big). The problem is, every choice you can make (the beginning ones in particular) have a chance to loose, and every loss has the same value (-1). So how can I pick the best moves, if all the options are the same?