Lab app no. 001 · Game theory for sport
Mixed Strategy Arena
Every penalty kick is a guessing game. Pick a sports duel, read off the mix nobody can beat, then try to beat an AI that learns your habits. Humans are bad at being random, and this shows what it costs.
Payoff matrix
Equilibrium
Value of the game
–
Why the mix works
Geometry
Try a mix
Set up a match
The AI watches your last few choices, predicts your next one and plays the best answer to it. Mix well and it can do no better than the equilibrium.
Advanced
The same seed, choices and settings replay the same match.
Round 1 of 30
Keys: 1–3 choose, Enter next round.
Match over
Stats
Score against the equilibrium
Your points Luck-free value Equilibrium pace
Your mix vs the equilibrium
Predictability
Luck removed
Two simple learning rules play the game against themselves. Neither knows the answer, yet their average play drifts to the equilibrium. Exploitability measures how much a perfect opponent could win from the current average strategies, and it falls toward 0.
Fictitious play
Each side best-responds to the other's whole history so far.
Regret matching
Each side plays actions in proportion to how much it regrets not having played them.
Exploitability over time
Fictitious play Regret matching