TL;DR
The Optimal Stopping Dice Game: A canonical quantitative trading interview question at foundation difficulty. Commonly asked at Jane Street, SIG, Optiver, Akuna.
By Valenke Exam Prep Team·Last updated 2026-06-01
foundationExpected Value & Variance
The Optimal Stopping Dice Game
Asked at: Jane Street, SIG, Optiver, Akuna
Problem
You roll a fair six-sided die. After each roll, you can either keep the result (and receive that many dollars) or re-roll. You get at most 3 rolls total (if you haven't stopped, you must keep the third roll). What is your optimal strategy and expected payout?
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