Game Theory & Decision

Basic

Break-Even Probability

Win probability needed for a bet to break even.

Formula

p = \frac{L}{L + W}

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Variables

pBreak-even probability

LAmount risked

WAmount to win

Example

Risk $100 to win $150: p = 100/250 = 40%

Did You Know?

If you can win more often than the break-even probability, the bet is profitable in the long run.

game theory break-even betting

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More in Game Theory & Decision

Expected Value

Probability-weighted average outcome of a decision.

Kelly Criterion

Optimal fraction of bankroll to bet for long-run growth.

Expected Utility

Weighted average of the utility of outcomes, not just their cash value.

Payoff Comparison

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Minimax Value

Best worst-case payoff a player can guarantee.

Mixed Strategy (Indifference)

Probability that makes an opponent indifferent between their options.