The Do-Over Game: Nash Equilibrium at the Golden Ratio

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The Do-Over Game: Nash Equilibrium at the Golden Ratio

DEV Community·White Oak Intelligence·5 months ago

#qVqA3RRB

#dev #threshold #equilibrium #probability #draw

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In This Article

The Question

Why 0.50 Is Not the Answer

Modeling Your Final Draw Distribution

The Indifference Condition for Nash Equilibrium

Solving for t*: The Golden Ratio Appears

Verifying the Nash Equilibrium

Python Simulation and Win Probability Curve

Business Application: Optimal Stopping in M&A and Hiring

The Question

Two players each draw a single number uniformly at random from the interval . After seeing their own draw, each player independently decides whether to redraw — replacing their current number with a fresh uniform draw from — or to keep what they have. A player who redraws must keep the second draw regardless of its value. After both players have finalized their numbers, the player with the higher number wins. Ties are broken arbitrarily (say, in favor of Player 2).

Both players make their redraw decision simultaneously and independently. Each is trying to maximize their probability of winning.…

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The Do-Over Game: Nash Equilibrium at the Golden Ratio