Stopping a deal to bet the next card is red
Question
A dealer flips cards face up one by one from a shuffled standard deck. At any moment you may say stop, and you win if the next card to be turned is red. With the best possible stopping strategy, what is your highest probability of winning?
Short answer
. Given what has been seen, the next card and the bottom card of the deck are equally likely to be red. So any strategy wins with the same probability as betting on the bottom card, which is red with probability regardless of strategy.
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- Optimisation Problems
- Constrained Optimisation and Lagrange Multipliers
- Sample Spaces, Events, and the Probability Axioms
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