Medium · Expected Value & Decision Theory · Numerical · ~8 min · #84

Three Consecutive Hidden Cards

Real interview · Optiver

Three face-down cards show $n$ , $n + 1$ and $n + 2$ in random order, and you do not know $n$ . Turn over a card, then either keep it or turn another, with the same choice at the second card. If you reach the third card you must keep it.

Under the optimal strategy, how far above $n$ is your expected payoff?

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Worked solution

Give the problem an honest attempt first, then reveal the full explanation.

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Concepts

Optimal stoppingConditioning on relative information

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