Home▸Set-Piece Strategy▸Penalty Mixed-Strategy Game: Minimax Probabilities for Kicker and Keeper — 2D

🥅 Penalty Mixed-Strategy Game: Minimax Probabilities for Kicker and Keeper — 2D

A 2x2 zero-sum penalty game with illustrative payoffs: closed-form minimax mix p* = (d-c)/(a-b-c+d), a payoff-envelope graph, a learning keeper and a Monte Carlo check against a brute-force grid.

Set-Piece Strategy2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

⚙ Under the hood

A 2x2 zero-sum penalty game with illustrative payoffs: closed-form minimax mix p* = (d-c)/(a-b-c+d), a payoff-envelope graph, a learning keeper and a Monte Carlo check against a brute-force grid.

Game TheoryMixed StrategyMinimaxFootballProbability

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install