Even or odd bets offered by a genie
Question
A genie throws a fair six-sided die, and you may bet on whether it lands even or odd. A winning even-bet returns $6 for every $4 staked; a winning odd-bet returns $9 for every $6 staked (returns include the stake, losing bets pay nothing). With optimal play, how much money should you wager?
Short answer
Nothing ($0). Each bet pays times the stake with probability , so every dollar wagered returns only dollars on average, on either side or any mix. Every bet has negative expectation, so the best stake is zero.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Counting and Combinatorics
- Expectation, Mean, and Variance
- Conditional Expectation and Variance Revisited
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