Expected Value Interview Questions
A quant interview guide to expected value problems, linearity, stopping rules, betting games, and fair prices.
Candidates preparing for expected value and betting questions in quant interviews.
What expected value questions test
Expected value questions test whether you can value uncertainty without walking every path. The core tools are linearity of expectation, conditioning, state recursion, and fair-price thinking. In trading interviews the answer rarely stays a number - it becomes a bid, an ask, or a bet size one follow-up later, and that follow-up is usually where the scoring actually happens.
Concrete example
For the expected sum of three fair dice, do not enumerate 216 outcomes. Each die has expectation 3.5, so the sum is 3 x 3.5 = 10.5. Linearity is doing the work, and because it holds even for dependent variables it also handles questions that look far harder. Ask instead for the expected number of distinct faces showing on those three dice: define an indicator for each of the six faces appearing at least once, each with probability 1 - (5/6)^3 = 91/216, so the answer is 6 x 91/216 = 91/36, about 2.53. Those six indicators are heavily dependent, and linearity does not care.
How to practice
Separate direct expectation problems from stopping problems, because they need different machinery. Direct problems usually fall to linearity plus indicator variables. Stopping problems need a state equation, and the fair-coin waiting time - 2 flips to the first head, 1/p in general - is the template that most harder ones extend by adding states. For every answer you produce, add the two trading follow-ups yourself: what price makes this game fair, and what edge would justify taking the other side of it.
Common mistakes
Candidates over-enumerate where a single line of linearity would do, confuse the expectation with the most likely outcome (a fair die has expectation 3.5, a value it can never actually show), or fail to define the stopping condition, which turns a two-line recurrence into an infinite sum. The trading-specific version is stopping at "positive EV" without mentioning variance or size at all - that answers the arithmetic question and skips the decision the interviewer was really asking about.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.