Interactive Game Theory Demonstration
Experience zero-sum games and adversarial decision makingGoal: Maximize Utility
Represents: Our AI
Seeks: +1 (Win)
Goal: Minimize Utility
Represents: Opponent
Seeks: -1 (Our Loss)
MAX (X) always moves first. Click any empty cell!
MAX Player (X) turn - Click any empty cell
Game in progress - utilities determined at end
When: Only at terminal states
Values: +1 (win), 0 (draw), -1 (loss)
Certainty: 100% known
Use: Final game scoring
When: During gameplay
Values: Integer (-8 to +8)
Formula: X_lines - O_lines
Use: Strategic position analysis
When: During gameplay
Values: Decimal (-1.0 to +1.0)
Formula: tanh(lines_diff / 3)
Use: Win likelihood estimation
🎓 Educational Point: Students can see how different evaluation approaches give different numerical ranges but maintain the same relative ordering for decision-making!
Represents the AI we're designing. Always moves first and tries to maximize the game's utility value. In tic-tac-toe, MAX wants to win (+1) and avoid losing (-1).
Represents our intelligent opponent. Responds to MAX's moves and tries to minimize the utility value. MIN wants MAX to lose, giving us -1 utility.
Players alternate moves until reaching a terminal state (win, loss, or draw). This creates a predictable sequence that algorithms can analyze.
Total payoffs always sum to zero. One player's success is exactly balanced by the other's failure. This competitive relationship drives adversarial search.
Understanding MAX vs MIN is fundamental to game-playing AI. Every chess engine, checkers program, or game AI must handle adversarial opponents who actively work against them.
The minimax algorithm builds on these concepts, recursively exploring game trees where MAX levels maximize utility and MIN levels minimize it, finding optimal play for both sides.