Optimal Stopping with a Ten-Sided Die and a Reset
OtherQuantitative Researcher · Technical ScreenLast updated
Derive optimal stopping thresholds for a fair ten-sided accumulation game, then account for the continuation value of a one-time zero reset.
Now change the rule: the first zero resets your total to zero but allows you to continue; the second zero ends the game with no winnings. How does the optimal strategy change?
Constraints & Assumptions
Rolls are independent, there is no cost per roll or finite horizon, and the objective is expected cash payout. In the variant, a reset does not bank any previous total. The state must include whether the first zero has already occurred.
Clarifying Questions
Can you stop after a reset? Does the first zero reset or preserve the total? Is the objective expected value rather than probability of exceeding a target?
Follow-up questions
- Why is comparing the next roll's average increment alone insufficient after a reset option is introduced? What happens at an exact indifference threshold? How would a per-roll cost alter the Bellman equation?
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