Oct 08, 2026 by Offer

Optiver Expected Value Interview Questions 2027: EV Guide

For the Optiver expected value interview question, compute EV as the probability-weighted sum of outcomes, play only if EV is positive — then discuss risk, bankroll, and repeatability. A positive-EV bet at ruinous size is still a pass. Commonly reported by candidates.

What This Question Assesses

Expected value is the lingua franca of trading, so this question tests whether you think in EVs instinctively. The interviewer wants the calculation done cleanly, the decision stated crisply (play if price < EV), and — crucially — the follow-up thinking: a positive-EV game you can play once with your whole bankroll is different from one you can play a thousand times. Stopping at "EV is positive, so play" misses the risk half of the question.

Optiver Expected Value Interview: How to Answer

Step 1 — Enumerate outcomes and probabilities. "For a standard die: faces 1-6, each with probability 1/6. Write down the payoff for each face."
Step 2 — Compute the EV. "EV = Σ pᵢ × payoffᵢ. Show the arithmetic aloud — e.g. (1+2+3+4+5+6)/6 = 3.5 for the face value itself, then apply the game's payoff rule to each face."
Step 3 — Compare with the price. "If the price to play is below the EV, the game has positive expectation — a trader takes positive-EV bets. If above, pass."
Step 4 — Add the risk overlay. "Then I would ask: how many times can I play, and what fraction of my bankroll is at risk? A +EV bet worth 50% of my bankroll played once is a pass — ruin risk dominates. Played many times at small size, the law of large numbers makes it a clear yes."

An example line: "The expected value is 3.5 per roll on face value, so at a price of 3 I would play — but only at a sensible fraction of bankroll, because one play of a high-variance game is gambling while a hundred plays is investing."

Optiver Expected Value Interview: Common Mistakes

Stopping at the EV number. The calculation is the easy half. Interviewers ask "would you play it?" precisely to hear the risk and repeatability discussion.
Ignoring variance. Two games with the same EV can have wildly different risk. Mention variance or worst-case outcomes before committing.
Arithmetic errors under pressure. Slow down for the sum — a wrong EV with confident delivery is worse than a right EV delivered carefully. Narrate the arithmetic.

EV thinking is the single most transferable trading skill — interviewers use these questions to check whether it is reflexive or rehearsed.

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FAQ

What is expected value, precisely? The probability-weighted average of all possible outcomes: EV = Σ pᵢxᵢ. It is the long-run average payoff per play if the game were repeated many times.

Why does the number of plays matter? Because of the law of large numbers: actual results converge to EV over many repetitions. With one play, variance dominates and a positive-EV bet can still lose — so bet sizing and ruin risk decide.

What is a fair price for a game? The price at which EV equals zero net of the entry cost — i.e. price = EV of gross payoffs. Above fair is −EV, below fair is +EV.

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