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 simulating every path. The core tools are linearity of expectation, conditioning, recursion, and fair-price thinking. In trading interviews, the answer often becomes a bid, ask, or bet size.
Concrete example
For the expected sum of three fair dice, do not enumerate 216 rolls. Each die has expectation 3.5, so the sum has expectation 10.5. Linearity works even when variables are dependent, which is why it is so valuable in interview problems.
How to practice
Separate direct expectation problems from stopping-time problems. Direct problems often fall to linearity. Stopping questions usually need a state equation. For each answer, ask what price would make the game fair and what edge would justify taking the other side.
Common mistakes
Candidates over-enumerate, forget that expectation is not the most likely outcome, or fail to define the stopping condition. If the game can end early, condition on the next event before writing a long sum.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.