While studying the fail-soft alpha-beta algorithm I'm struggling to come up with a minimal game tree which, when solved with fail-soft alpha-beta produces a fail-low which is different to the minimax value.
For example. Let the initial alpha and beta values be 2 and 4, respectively. Also let's say that the true minimax value of the root node is -2. Furthermore, let's suppose that the fail-soft alpha beta produces 0 for the root node.
Formally:
true_minimax(root_node) = -2
fail_soft(root_node, 2, 4) = 0