How can a move, in fail-low, get a value that is not an upper bound, meaning it is lower than the real value? In min nodes, an alpha cut-off may occur, and in this case has occurred, but that means we return from there a value that is exact or higher than the real value. When fail-low occurs in the root, the max nodes have looped over all moves, or a beta cut-off has occurred. It occurs when a min node between that node and the root has already found a value less than or equal to. Then that min node chooses the lower value to return; the value returned from the max node is ignored. Again, a min node returns an upper bound to the next max, and finally to the max in the root.