Optimal Stopping Quant Interview Intuition
Intuition for simple optimal stopping questions in quant interviews, including rerolls, thresholds, continuation value, and value of information.
Candidates seeing reroll, threshold, and choose-or-continue game prompts.
Compare stop versus continue
Optimal stopping questions ask whether the current value is better than the value of continuing. The central move is comparing what you have now to the expected value of the next opportunity.
Thresholds come from comparison
A threshold rule appears when values above a cutoff should be kept and values below it should be rerolled or continued. The cutoff is usually the continuation value, not a random guess.
Value of information
Continuing can be valuable because it gives another chance or more information. It can also be costly if it consumes time, money, or opportunities. State the cost and benefit of continuing before calculating.
Concrete example
If you roll a fair die and may reroll once, the value of rerolling is 3.5. Keep the first roll if it is 4, 5, or 6, and reroll if it is 1, 2, or 3. The threshold comes from comparing the observed roll to continuation value.
Connect to interviews
Interviewers often care more about the threshold logic than a memorized closed form. Explain what state you are in, what continuing is worth, and why the rule changes if the payoff or number of chances changes.
Common mistakes
Candidates sometimes use the average outcome as a threshold without checking whether continuation has the same value in that state. Recompute the continuation value whenever the rules change.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.