Optimal Stopping Puzzles for Quantitative Interview Practice

Summary

This document asks for resources on optimal strategies and expected payoffs in dice, card, and casino games, with an emphasis on puzzles that appear in quantitative interviews. It presents two dice examples as practice problems rather than solving them. In the first, a player repeatedly rolls a fair die, choosing whether to keep the current face value or pay a fee to roll again. In the second, rolls accumulate into a running sum, but repeating a previously seen face ends the game with a loss.

Both examples illustrate sequential decision-making under uncertainty: the player must compare the value of stopping now with the expected value of continuing. The document provides no recommended resources, derivations, numerical solutions, or evidence about optimal policies. Its value is therefore mainly as a framing of interview-style optimal stopping and expected-value problems; readers would need additional material to learn solution techniques or verify strategies.

Key ideas

• The document frames casino-style game puzzles as practice for quantitative interviews.
• A repeated-roll problem asks when to accept a die result versus paying to continue.
• A running-sum game adds a termination risk when a die face repeats.
• Solving either problem requires comparing the expected value of continuing with the payoff from stopping.

Tags

# Resources for "Game Theoretic" Quant Puzzles


# Resources for "Game Theoretic" Quant Puzzles












Could I please have some resources that discuss optimal playing strategies in various dice games / card games / casino games and their optimal expected payoffs? I have been encountering many such questions in quant interviews.

For example, I am looking for resources where I can practice questions of the following type:-

- You repeatedly roll a 6-sided fair die. You may choose to either accept the face value of the current roll, or pay $1 and roll again. You may do this infinitely many times. Find the optimal strategy and the optimal payoff.

- You repeatedly roll a die and track the running sum of the face values. You may choose to stop at any point and walk away with the current running sum, or you may choose to roll again. However, if you roll a number that has already been rolled before, you lose and the game ends. Find the optimal expected payoff and the optimal strategy.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.