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Minimax Algorithm: Step-by-Step

Watch the Complete Game Tree Exploration

See how Minimax finds optimal moves through recursive evaluation
Current Position
X

X (MAX) played center.
O (MIN) must choose optimal move.

Algorithm Status

Ready to start Minimax exploration

Step 0 of 15
Algorithm Controls

Minimax Game Tree

Depth 0 - MIN Level
X
MIN Node
?
Depth 1 - MAX Level
Depth 2 - Terminal States

Zero-Sum Utilities

MAX (X)

• +1 if X wins
• 0 if draw
• -1 if X loses

MIN (O)

• -1 if O wins
• 0 if draw
• +1 if O loses

Key: MAX maximizes, MIN minimizes utility!

How Minimax Works

1. Recursive Exploration

Explores all possible game continuations down to terminal states.

2. Utility Propagation

Terminal utilities propagate up through MAX and MIN operations.

3. Optimal Decision

Root value shows best achievable utility with perfect play.