Minimax Algorithm Visualizer

The Minimax Algorithm

Minimax is the core algorithm used in two-player zero-sum games like chess, checkers, and tic-tac-toe. It assumes both players play perfectly.

The Two Players

• Max (maximizer): tries to get the highest score possible (e.g., the AI player)
• Min (minimizer): tries to get the lowest score possible (e.g., the opponent)

How It Works

At each node in the game tree:

• If it’s a Max node: choose the maximum of child values
• If it’s a Min node: choose the minimum of child values
• Leaf nodes (terminal states) have fixed values (scores)

2-Level Tree

        [Max]             ← root picks maximum
       /     \
    [Min]   [Min]         ← each picks minimum of its leaves
    /  \    /  \
   v1  v2  v3  v4        ← leaf values (terminal scores)

Max will receive: max(min(v1,v2), min(v3,v4))

3-Level Tree

             [Max]                  ← picks max of Min nodes
           /       \
        [Min]       [Min]           ← each picks min of Max children
        /   \       /   \
     [Max] [Max] [Max] [Max]        ← each picks max of leaves
     / \   / \   / \   / \
    v1 v2 v3 v4 v5 v6 v7 v8

Real-World Use

Minimax powers game AI in:

• Chess engines (with alpha-beta pruning to skip branches)
• Go programs (with Monte Carlo extensions)
• Checkers, Connect Four, Tic-tac-toe solvers

Enter 4 leaf values for a 2-level tree, or 8 leaves for a 3-level tree.