Conditional Expectation Puzzles

Problem Statement#

The Question#

Interview question: You roll a fair six-sided die repeatedly. After each roll, you decide whether to stop and collect the value shown, or roll again. You must eventually stop. What is the optimal stopping strategy, and what is your expected payout under that strategy?

This problem shows up in first-round interviews at Jane Street, Citadel, and IMC, often as a warm-u...