Guide · market making
Market making interview questions
19 problems · 7 min read · updated 2026-09-07
The market-making round is where trading interviews are decided. It starts innocently — "make me a market on the sum of two dice" — and escalates: the interviewer trades against you, tells you they know something, changes the odds, offers you a game. What they are watching is not the arithmetic. It is whether you update your quote when the flow tells you something, whether you size a bet by its edge rather than your confidence, and whether you can say why a game is worth what it is worth.
This guide covers the whole ladder. Optiver, SIG, IMC, Flow Traders, Jane Street and Citadel Securities all draw from it.
Fair value and quoting
Every market-making question begins with a fair value, and the first trap is the loaded-die version: the interviewer changes the distribution and watches whether you re-derive or recite. Then they ask for a bid and an ask, and the width of your spread is the first thing you defend.
An interviewer asks you to make a market on the sum of two fair six-sided dice. Before you quote a bid and an ask, you need the fair value. What is it?
Answer: 7 · Worked solution →
A die is loaded so that it shows 6 with probability 1/2; the other five faces are equally likely. You must quote a fair value for one roll. What is it?
Answer: 4.5 · Worked solution →
A betting market quotes decimal odds of 4.0 on an outcome (total payout per $1 staked). Ignoring any bookmaker margin, what probability of the outcome does this quote imply, in percent?
Answer: 25 · Worked solution →
EUR/USD trades at 1.10 and USD/JPY at 150. Ignoring transaction costs, what should the EUR/JPY cross rate be so that no triangular arbitrage exists?
Answer: 165 · Worked solution →
You are a market maker and have accumulated a long position of 5,000 shares that you want to reduce. Fair value is unchanged. Relative to your previous quotes, in which direction do you move your bid and ask — up or down?
Adverse selection and where the edge comes from
A trade is information. When someone lifts your offer, the asset is more likely to be worth more than you thought — so the breakeven ask sits above the unconditional fair value. Bookmaker margins, the roulette edge and the Dutch book are the same idea from the other side of the counter.
A binary asset settles at 100 or 0, each with probability 1/2. Of the traders who arrive, 20% are informed (they know the outcome and trade in its direction) and 80% are noise traders who buy or sell with probability 1/2 each. A single trader arrives and buys from you at your ask. To break even in expectation against this flow, what is the lowest ask you can quote?
Answer: 60 · Worked solution →
A sportsbook quotes both sides of an evenly-matched game at American odds of −110 (stake 100). Implied probability of a −110 quote is 110/210. By how much do the two implied probabilities exceed 100%? Give the overround in percent.
Answer: 4.76 · Worked solution →
European roulette has 37 pockets (0–36). A $1 bet on a single number pays 35-to-1. What is the house edge — the casino’s expected profit per dollar staked — in percent?
Answer: 2.7 · Worked solution →
Bookmaker A offers decimal odds of 2.2 on team X winning; bookmaker B offers decimal odds of 2.2 on team X not winning (decimal odds = total payout per 100, split so that your payout is the same either way. What is your guaranteed profit, in dollars?
Answer: 10 · Worked solution →
Betting and sizing
Given an edge, how much do you bet? Kelly is the reference answer and the interviewer will test whether you know its assumptions. The martingale and St. Petersburg questions test the opposite instinct — recognising a "system" that manufactures no edge at all.
A repeatable bet wins with probability 40%. A win pays 2-to-1 (win 1 staked); a loss costs the stake. What fraction of your bankroll should you stake per bet to maximise long-run growth (the Kelly fraction), in percent?
Answer: 10 · Worked solution →
You can repeatedly make an even-money bet (win or lose the amount staked) that you win with probability 60%. What fraction of your bankroll should you bet each time to maximize long-run growth?
Answer: 0.2 · Worked solution →
On a fair even-money coin flip you play the classic martingale: bet $1, and after every loss double the stake until the first win, then stop. Ignoring any table or bankroll limit, how many dollars does every completed run of this system win?
Answer: 1 · Worked solution →
A pot starts at $2 and doubles after every heads; the game ends at the first tails and pays the pot. In dollars, what is the expected payout of this game?
Games, auctions and optimal stopping
The interviewer offers you a game and asks what you would pay to play. Backward induction values the re-roll game; a small dynamic programme values the red–black deck; iterated dominance solves the two-thirds game; bid shading is the first-price auction. These are the questions that separate offers from rejections at Jane Street.
You roll a fair die and are paid its face value in dollars, but you may re-roll up to two times, keeping only the final roll. Playing optimally, what is this game worth?
Answer: 4.67 · Worked solution →
Cards from a shuffled standard 52-card deck are revealed one at a time. Your running total gains 1 for every black card. You may stop whenever you like and collect the running total (you may also stop immediately at $0). Playing optimally, what is this game worth?
Answer: 2.62 · Worked solution →
Everyone in a large group simultaneously picks a number from 0 to 100. The winner is whoever is closest to two-thirds of the group average. If every player is perfectly rational and knows everyone else is too, what number does game theory say everyone picks?
Answer: 0 · Worked solution →
Two bidders compete in a sealed-bid first-price auction. Each privately values the item as an independent uniform draw on [0, 1], and the higher bid wins and pays its own bid. In the symmetric equilibrium each bidder bids half their value. Your value is 0.8 — what do you bid?
Answer: 0.4 · Worked solution →
Two envelopes hold money, one exactly twice the other. You pick one, open it, and see 50 or 125 — always switch!” The same argument applies before opening ANY envelope, implying you should switch forever. Where exactly does the argument break?
Estimation
Fermi questions are market making without a market: state assumptions, keep units honest, land within an order of magnitude, and be willing to revise when the interviewer pushes on one input.
Estimate: how many piano tuners work in Chicago? There is no “right” number — the interviewer is grading the structure of your estimate, the reasonableness of each input, and whether the final answer is the right order of magnitude.
How to approach these in the interview
Quote, then defend, then update. The sequence interviewers want: a fair value with reasoning, a spread with a reason for its width, and a visible update when they trade against you. Refusing to move your quote after being lifted three times is the single most common way to fail this round.
Separate edge from confidence. Kelly sizes by edge over odds, not by how sure you feel. Say the formula, then say what it assumes (known probabilities, repeated bets, log utility) — the assumptions are the follow-up question.
Value games by backward induction. Start from the last decision and work backwards. It is the same technique for the re-roll game, the card game and the auction, and naming it buys credibility.
Keep the bankroll in the picture. Every "system" that seems to create money — doubling after losses, the St. Petersburg pot — dies at a finite bankroll. Bringing that up unprompted is what a market maker sounds like.
Frequently asked
What does "make me a market" mean in an interview?
Quote a bid (the price you will buy at) and an ask (the price you will sell at) on some quantity — the sum of two dice, the number of windows in Chicago, the outcome of a coin game. The interviewer then trades against you and watches whether you update your prices as their trades reveal information.
How wide should my spread be?
Wide enough to cover adverse selection (informed traders picking you off) plus a margin, narrow enough that uninformed flow still trades with you. In interviews, quote a spread you can justify from the variance of the underlying and be ready to widen it when the interviewer starts winning.
Which firms ask market-making questions?
Optiver, SIG (Susquehanna), IMC, Flow Traders, Jane Street, Citadel Securities, DRW, Akuna and Five Rings all use them, typically from the first technical round onward. Research firms rarely do.
Is the Kelly criterion actually used on desks?
As a ceiling, not a target. Most desks size well below full Kelly because probabilities are estimated, not known. Saying this in an interview is the difference between a textbook answer and a trader’s answer.
Practise these with answer checking and spaced review
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