When to take the money

What this optimal stopping interview question tests

This is a medium-difficulty dynamic programming puzzle common in quant interviews. It asks you to find the optimal strategy in a sequential decision problem where you must weigh immediate payoff against the option value of continuing.

To solve it, you work backwards from the final round, computing the expected value of accepting or rejecting at each stage. The key insight is recognizing that your decision at any point depends only on the current sample and the optimal expected payoff from future rounds—a classic application of backward induction and the principle of optimality.

• Backward induction and subgame perfection
• Threshold strategies and cutoff values
• Expected value under optimal play
• Recursive structure of multi-stage games