I have two players involved (MAX = computer and MIN = player). I am searching the game tree with max_depth set to 3. The leaves are evaluated from the MAX's view (more good formations owns the MIN player, worse score will MAX get.) Then the tree is filled bottom up - from leaves to root. MAX nodes receive MAXIMAL value of their MIN children. MIN nodes receive MINIMAL value of their MAX children.

I understand this thanks to you, but I have problem:

What to do in case of MIN's victory? (in tree, not in real). The fact is the search will not continue deeper because it is not neccessary. The second fact is that this MIN victorious node will become leaf. Value of this leaf must be something really small (-infinity).

Problem: How to avoid this leaf (to prevent player's victory) when such leaf won't be detected because MAX nodes receive only MAXIMAL values of their children and "-infinity" has far from "MAXIMAL"?