— GUIDE —

EXPECTED VALUE INTERVIEW QUESTIONS

Expected value is the most reused idea in a trading interview. These questions build from a plain fair value up to the cases where the expectation is the wrong thing to quote.

UPDATED 2026-09-08 · 7 MIN READ · BY THE VARIANCE TEAM

Expected value is the first thing you learn and the last thing you stop using. The interesting questions are the ones where the expectation is correct and still not the answer.

These are original representative questions, not real or leaked firm questions.

Fair value first

  1. You are paid the face value of one roll of a fair die. What is the game worth?

    (1+2+3+4+5+6)/6 = 3.5. Say the number, then say that you would pay less than 3.5 to play and sell above it. Interviewers are listening for whether "fair value" and "price I would trade at" are separate ideas in your head.

  2. A ticket costs $10 and pays $100 with probability 8%. Do you buy?

    Expected payoff is 0.08 × 100 = $8, so at $10 you are paying two dollars for the privilege. No. The useful follow-up you should volunteer: at what price would you buy, and how much size would you take there?

Repeated chances, and knowing when to stop

This family shows up constantly because it separates people who compute from people who reason backwards from the end.

  1. Roll a die. You may keep the value, or reroll once and keep whatever comes up. What is the game worth?

    Reroll whenever the first roll is below the value of a fresh roll, 3.5. So you keep 4, 5, 6 and reroll 1, 2, 3: (1/2)(5) + (1/2)(3.5) = 4.25.

  2. Same game, but you may roll up to three times.

    Work backwards. With two rolls left the game is worth 4.25, so on the first roll you keep only 5 or 6: (1/3)(5.5) + (2/3)(4.25) = 14/3 ≈ 4.67. The method is the answer here, not the number.

  3. You flip a fair coin repeatedly and win $1 for every head before the first tail. What is that worth?

    One dollar. Either sum Σ k(1/2)^(k+1), or note that the expected number of heads before a tail is (1−p)/p = 1 for p = 1/2.

Let linearity do the work

Expectations add whether or not the events are independent. That single fact turns several intimidating questions into one line.

  1. You draw five cards from a standard deck. How many aces do you expect?

    5 × 4/52 = 5/13 ≈ 0.385. The draws are dependent and it does not matter.

  2. Twelve people each throw one hat into a pile and take one back at random. How many get their own hat on average?

    One. Each person has a 1/12 chance, and 12 × 1/12 = 1. The answer is one for any group size, which is the part that makes it a good question.

When expected value is not the answer

The strongest candidates get here on their own. Two bets can share an expectation and be nothing alike.

  1. Bet A wins $1 with certainty. Bet B wins $1,000,000 with probability 0.000001 and nothing otherwise. Same expected value. Are you indifferent?

    Not if you only play once. Talk about variance, bankroll, and how many repetitions you get. A trader who can only express a preference through the mean is missing the job.

  2. You price a contract at 50 and someone immediately buys 500 at your offer without negotiating. Is your expected value still 50?

    No. Condition on the trade. The eagerness is information, and the expected value given that someone wanted that much at that price is worse for you than the unconditional 50. Say the word "adverse selection" and explain how you would re-quote.

Where to go next

Expected value is half of a market-making answer; the other half is turning it into a two-sided quote. That is covered in the market-making guide. For the probability machinery underneath these, see the probability question bank.