Single Die Re-roll Profit Hack

This quant interview question is about expected value under a simple decision rule with an option to pay for another outcome. It places you in a controlled, discrete setting where you must decide whether to keep what you see or pay to take another chance, and then work out the average payoff of playing perfectly. This kind of setup is very common in quant prep and real interviews because it isolates risk-reward trade-offs in a clean way.

It trains your ability to translate a narrative decision problem into random variables, payoffs, and expectations. You must formalize an optimal strategy, define a threshold rule, and then compute the overall expected value given that rule. In practice, this builds comfort with piecewise expectations, scenario conditioning, and reasoning carefully from first principles.

This matters for quant interviews because top trading firms want candidates who can quickly find and justify optimal decisions under uncertainty. The same mindset shows up in trading, market making, and structuring: you constantly compare immediate gains to the probabilistic value of alternatives that come with costs. Strong performance on such expected value problems signals you can handle more complex optimal stopping and dynamic decision questions that appear in real trading and research work, making this excellent quant interview prep.

What it tests

This class of problems is governed by the principle of optimal stopping under uncertainty with an option to pay for a second chance. The key structure is that, after observing an initial outcome, you compare its value to the expected value of the alternative (here, a re-roll minus its cost). The optimal strategy is to continue (or pay for a re-do) only if the expected gain from doing so exceeds the value of stopping now. This threshold is found by equating the observed value to the net expected value of the alternative, and the solution is built by partitioning the outcome space at this threshold. The underlying reason this works is that maximizing expected value in a two-stage process always reduces to a comparison between the immediate reward and the expected future reward, properly adjusted for costs or penalties.