Example 1 – Penalty Kick: Striker vs. Goalkeeper
Striker chooses: shoot Left or Right.
Goalkeeper chooses: dive Left, stay Centre or dive Right.
Numbers = advantage for the striker (positive = good for striker).
There is a saddle point – a pure equilibrium strategy.
Example 2 – Attacker vs. Defender
Attacker shows: Heads or Tails.
Defender tries to guess: Heads or Tails.
No saddle point – both must randomize to avoid being exploited.
Example 3 – Rock, Paper, Scissors
Classic 3×3 zero-sum game: Scissors beats Paper (+1), loses to Rock (−1), tie (0).
Game value = 0. Optimum: play each strategy with probability 1/3.
Enter: Payoff for Player 1 (row maximizer).
Player 2 (column minimizer) receives the negative value. Positive = good for P1.