Minimax explores the entire game tree, alternating between maximizing and minimizing players. MAX nodes pick the highest value child; MIN nodes pick the lowest.

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▲ MAX node — selects child with the highest value.

▽ MIN node — selects child with the lowest value.

◆ Leaf node — terminal node with a static heuristic value.

α (alpha) — best value MAX is guaranteed so far. Starts at −∞.

β (beta) — best value MIN is guaranteed so far. Starts at +∞.

When α ≥ β, the remaining subtree cannot affect the final result and is pruned.

Minimax: O(b × d) — stores one path at a time.

Alpha-Beta: O(b × d) — same space, fewer evaluations.