Three-Card Flip Expected Value

This quant interview question is about expected value in a small, structured setting where information is revealed step by step. It lives at the intersection of probability, stopping rules, and optimal decision-making, a common theme in serious quant prep for trading and research interviews. Because the label is unknown but the spacing is known, you're forced to reason about relative information instead of concrete numbers, which is exactly the kind of abstraction top trading firms care about.

It trains conditional expectation, Bayesian-style updating, and thinking in terms of states rather than outcomes. You must keep track of what each observation rules out, how that reshapes the distribution of what remains, and how this feeds into your next decision. It also builds comfort with dynamic programming and backward reasoning inside a tiny but non-trivial state space.

This matters for quant interviews because market-making, options trading, and algorithmic execution all involve sequential decisions under uncertainty with partial information. Interviewers want to see that your quant prep goes beyond static probability puzzles to real decision processes where each quote, trade, or signal changes what you should do next. Performing well on this kind of problem signals readiness for live trading environments, where expected value, information, and timing must be balanced in real time.

What it tests

This problem class is governed by the principle of sequential decision-making under uncertainty, where each action both reveals new information and eliminates possibilities. The core structure is that each revealed outcome updates your knowledge about the remaining options, allowing you to condition your next move on the reduced set of possibilities. The optimal strategy is to compare the expected value of continuing (given the information revealed so far) to the value of stopping now, always choosing the action with the higher expected payout. This is a dynamic programming perspective: at each stage, you maximize expected value by considering all future optimal actions, not just the immediate gain. The pattern holds because, with each reveal, the probability distribution over the remaining unknowns becomes sharper, allowing more informed choices.