Market Making Interview Questions: 10 Worked Examples 2026

What a Market Making Interview Question Tests

"Make me a market" is the question that separates trading interviews from every other kind of technical interview. The interviewer names something uncertain, such as the sum of three dice or the number of primes below 1,000, and asks for a bid and an ask. Then they trade against you, reveal information, or push you on size, and watch what you do next.

The expected value is usually the easy part. What gets scored is whether your width reflects your uncertainty, whether you move your price for the right reasons, and whether you notice when the person opposite you knows more than you do. Candidate reports describe versions of this game at options market makers such as Optiver, IMC, SIG and Maven, and at proprietary trading firms more widely.

This guide works through 10 questions in the order the ideas build on each other. The maths in every answer is checked; the quoting choices are our judgement, and we say so where it matters. For a wider set of trader questions, see our quant trader interview questions.

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How the Game Works

The format varies by firm and interviewer, but the core loop is consistent across candidate reports.

You are asked for a two-way price: a bid (the price you will buy at) and an ask, also called an offer (the price you will sell at). Many interviewers also want a size, for example "6.5 at 7.5, 10 up", meaning you will trade up to 10 lots either way. The interviewer can buy at your ask, sell at your bid, or do nothing. Sometimes they then reveal part of the answer, and you quote again.

Four things are being watched throughout:

• Fair value. Is the midpoint of your market close to the expected value, given what you know?
• Width. Does the gap between bid and ask scale with how uncertain the outcome is, and with how much the counterparty might know?
• Updating. When a trade or a reveal happens, do you move for a reason you can state, or out of nerves?
• Consistency. If you quote several related markets, can the interviewer trade them against each other for a free profit?

Speed matters too. You are expected to do the arithmetic out loud and commit to a price within a few seconds, which is why the mental maths prep in our quant mental math questions guide pays off here as well.

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Warm-Up Markets

1. Sum of three dice

"I roll three fair dice. I'll pay you the sum in pounds. Make me a market."

Answer. Each die has mean 3.5 and variance 35/12, so the sum has mean 10.5 and variance 3 × 35/12 = 8.75. The standard deviation is about 2.96.

A reasonable opening market is 9.5 at 11.5. That centres on fair value and has a width of 2, roughly two-thirds of a standard deviation. There is no single correct width. What the interviewer wants to hear is that you picked it on purpose: wide enough that a few unlucky trades will not hurt, tight enough that someone would actually trade with you.

Before you quote, ask one question: has anyone seen the dice? It costs nothing, and it changes everything that follows.

2. Three dice, revealed one at a time

"Same game, but I'll show you the dice one by one. The first die is a 6."

Answer. Fair value is now 6 plus the expected sum of two dice, so 6 + 7 = 13. The remaining uncertainty is two dice rather than three, so the standard deviation falls to the square root of 70/12, about 2.42. A market of 12 at 14 keeps a similar width relative to the risk left.

"The second die is a 1." Fair value is 6 + 1 + 3.5 = 10.5, with one die left and a standard deviation of about 1.71. Tighten to 10 at 11.

The point of the exercise is the pattern. Every reveal should move your midpoint to the new expected value and pull your width in, because there is less left to be wrong about. Candidates who move the midpoint but keep the same width, or who tighten without being able to say why, lose marks here.

3. Lifted five times

"You quoted 9.5 at 11.5 on three dice. I buy five lots at 11.5. What now?"

Answer. It depends entirely on the answer to the question from Example 1.

If nobody has seen the dice, the trades carry no information about the outcome. You have sold five lots at 11.5 against a fair value of 10.5, an expected profit of £5. Your fair value should not move at all. You might still adjust your quotes because you are now short and carrying risk, which is the next example.

If the interviewer has seen the dice, five buys in a row is strong evidence the sum is high, and you should raise your market sharply. Saying both halves of this out loud is the answer the interviewer is looking for.

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Inventory and Risk

4. Skewing a position

"We're playing the sum of two dice. You've been quoting 6.5 at 7.5 and I've bought 10 lots from you four times. You're short 40. Quote me again."

Answer. Fair value is still 7. The sum of two dice has a standard deviation of about 2.42, so a 40-lot short position has a P&L standard deviation of roughly 40 × 2.42 ≈ £97. That is a lot of risk to hold on one roll.

The standard response is to skew rather than widen. Move both sides up, to something like 7 at 8. Your bid is now at fair value, which makes it more likely someone sells to you and brings your position back towards flat. Your ask is higher, which makes further buying less likely.

Be clear about the trade-off. A bid at fair value earns nothing, so you are giving up expected profit in exchange for less risk. Interviewers often follow up with "why not just widen?" A good answer: widening protects you but also discourages the trades that would reduce your position, whereas skewing invites them.

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When the Other Side Knows More

5. The interviewer has seen the card

"I've drawn a card from a standard deck and looked at it. I'll pay you its rank, ace = 1 up to king = 13. Make me a market."

Answer. Fair value on a random card is 7, but that is irrelevant here. The interviewer only trades when it is good for them: they buy when the rank is above your ask and sell when it is below your bid. Every trade you get loses you money on average.

The honest answer is that you cannot make money quoting against someone who knows the outcome, so you either decline or quote 1 at 13, a market no one can profit from. Say so directly. Interviewers use this question to see whether you recognise adverse selection, the risk of trading with a better-informed counterparty.

A common follow-up is "you must quote a market 2 wide." By symmetry the least-bad choice is 6 at 8. The interviewer buys whenever the rank is 9 to 13 and sells whenever it is 1 to 5, and your expected loss per game is (1 + 2 + 3 + 4 + 5 + 5 + 4 + 3 + 2 + 1) / 13 = 30/13, about £2.31.

6. Some of the flow is informed

"A fair coin is flipped. If it's heads, the contract pays £100; if tails, nothing. A fraction of the people trading with you have seen the coin. The rest buy or sell at random, 50/50. Where should you quote?"

Answer. This is a small version of the model in Glosten and Milgrom (1985), and it gives a clean formula for why spreads exist.

Call the informed fraction μ. Informed traders buy when the coin is heads and sell when it is tails. Uninformed traders buy or sell with probability 1/2 each, whatever the coin shows. You want your ask to equal the expected value of the contract given that someone has just bought from you:

• If heads, a buy happens with probability μ + (1 − μ)/2.
• If tails, a buy happens with probability (1 − μ)/2.

Those two probabilities add up to 1, so the expected value given a buy is 100 × (μ + (1 − μ)/2) = 50 × (1 + μ). By symmetry the bid is 50 × (1 − μ).

With 20% informed flow, the break-even market is 40 at 60. With 50%, it is 25 at 75. The spread is set by how much the counterparty knows, not by how uncertain the coin is. That is the idea behind much of real-world market making, and our bid-ask spread explainer covers the other parts of the spread.

7. How wide is wide enough?

"I shuffle a deck and I'll pay you the number of red cards in the top 10. I've peeked at the top card only. Make me a market."

Answer. With no information, the expected number of red cards in 10 is 10 × 26/52 = 5.

Now work out what the peek is worth. If the top card is red, the expected count is 1 + 9 × 25/51 ≈ 5.41. If it is black, it is 9 × 26/51 ≈ 4.59. The interviewer's information moves fair value by about 0.41 in either direction.

So a market of 4.5 at 5.5 is safe even against someone who uses that information perfectly. If the top card is red, buying from you at 5.5 is worth 5.41, a loss for them. If black, selling to you at 4.5 is worth 4.59, also a loss. Any tighter than roughly 4.6 at 5.4 and they can pick you off.

This is the most useful habit the market making game teaches: size your width to what the other side could know, not to a rule of thumb.

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Structure and Estimation

8. Three related markets

"Make me markets on die A, die B, and the sum A + B."

Answer. A sensible set is 3 at 4 on each die and 6.5 at 7.5 on the sum. The check that matters is whether the interviewer can trade them against each other for a free profit.

Suppose instead you quoted the sum at 8.5 at 9. The interviewer sells you the sum at your bid of 8.5, then buys die A and die B from you at your asks of 4 each, paying 8. They collect 0.5 and their positions cancel, whatever the dice show. The rule: your bid on the sum must not exceed the sum of your asks on the parts, and your ask on the sum must not fall below the sum of your bids.

Interviewers who ask several markets in a row are often checking this, even if they never say so.

9. A capped St Petersburg payoff

"I flip a coin until the first head. If that takes n flips, I pay you 2ⁿ pounds, capped at £1,024. Make me a market."

Answer. The probability that the first head comes on flip n is 1/2ⁿ. For n from 1 to 10, each outcome contributes (1/2ⁿ) × 2ⁿ = 1 to the expected value, which gives 10. Every longer sequence pays the cap of £1,024, and those have total probability 1/1,024, adding another 1. The expected value is £11.

The trap is the shape of the distribution. Half the time you pay out £2, and three-quarters of the time £4 or less. But the variance is large: the expected square of the payoff is (2 + 4 + ... + 1,024) + 1,024 = 3,070, so the variance is 3,070 − 121 = 2,949 and the standard deviation is about £54.

A market such as 8 at 14 is centred correctly, but the right conversation is about size. With a standard deviation roughly five times the fair value, you should offer far fewer lots here than on a dice game with the same expected value. The uncapped version is the St Petersburg paradox, where the expected value is infinite; candidates who mention the cap and why it matters tend to impress.

10. An estimation market

"Make me a market on the number of prime numbers below 1,000."

Answer. Nobody expects you to know this. They want to see you build an estimate and set a width that honestly reflects how unsure you are.

One route: the prime number theorem says primes near n have density about 1/ln n. With ln 1,000 ≈ 6.9, that suggests around 1,000 / 6.9 ≈ 145. You may also remember that there are 25 primes below 100, which is a sign that small numbers are richer in primes than the simple formula suggests. The simple approximation is known to run low, so centre above it.

A market of 140 at 190 is defensible. The true answer is 168. (The refined approximation 1,000 / (ln 1,000 − 1) gives about 169.)

Estimation markets are where width matters most, because you cannot compute a variance. A wide market you can explain beats a tight market you guessed. If the interviewer trades against you, ask yourself whether they are likely to know the answer. For a fact like this one, assume they do.

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How to Practise

Market making games reward reps with another person far more than reading. Take turns with a friend: one person picks a quantity, the other quotes, and the first person trades. Keep a note of every time you moved your price and why. After 20 or 30 rounds, most people find their widths get more consistent and their updates more deliberate.

Alongside the games:

• Arithmetic speed. Expected values have to come out in seconds. Our free mental math trainer and 80 in 8 simulator build that pace.
• Probability depth. The reveals and conditional updates in Examples 2 and 7 are straight conditional expectation. Our probability interview questions cover the underlying toolkit.
• Options intuition. At options market makers, later rounds often move from dice to option prices, so the Greeks need to be intuitive. See our options market making guide.

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Where This Advice Goes Wrong

The widths in this guide are our choices, not firm rules. Some interviewers push hard for tight markets from the first quote and treat a wide opening as timidity, while others reward caution. If an interviewer tells you your market is too wide, tighten it and explain what risk you are now taking on. That is usually the conversation they want.

Conventions also differ. Some firms quote in lots, some in pounds of risk. Some want the size stated; some never mention it. And a few games are deliberately adversarial in ways a dice example cannot capture, such as an interviewer who trades only on one side to see whether you panic. The principles above still apply, but expect the details to change between firms and between interviewers at the same firm.

Finally, these games are one part of the process. Firm-specific guides such as our IMC Trading interview and Maven Securities interview pages describe where the game sits alongside the online assessment and other rounds.

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Recruiting Notes

This guide is based on published models, standard probability and candidate reports of trading interviews. It does not describe any one firm's official scoring, and formats change between hiring cycles. Nothing here guarantees a particular question, format or outcome.

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Frequently Asked Questions

What does "make me a market" mean in a trading interview?

It means quote a bid, the price you would buy at, and an ask, the price you would sell at, on some uncertain quantity. The interviewer can then trade against either side. They are watching your fair value, the width of your market, and how you react when trades or new information arrive.

How wide should my market be?

Wide enough to cover your uncertainty and the chance that the other side knows more than you, and no wider. For a pure chance game, a width of around half to one standard deviation of the payoff is a reasonable starting point. Against a partly informed counterparty, the width should cover what their information is worth, as in Example 7.

Should I move my price when the interviewer trades with me?

Only if the trade could carry information. If nobody has seen the outcome, a trade tells you nothing about fair value, though it can change your inventory and so your skew. If the interviewer might know the answer, repeated trades on one side are evidence and you should move.

Which firms use market making games in interviews?

Candidate reports describe them most often at options market makers and proprietary trading firms, including Optiver, IMC, SIG and Maven Securities. Formats differ, and not every role or round includes one. Our firm interview guides describe where the game appears in each process.

Do I need to know options theory for a market making interview?

For the dice and card games, no. For trader roles at options market makers, later rounds often ask about the Greeks and how option prices respond to volatility, so it helps to have an intuitive grasp of delta, gamma and vega before the final rounds.

How do I practise market making games on my own?

It is much easier with a partner who trades against you, but you can practise the maths alone. Pick a random payoff, compute its mean and standard deviation, and write down a market before checking. Then drill conditional updates: reveal one part of the outcome and requote. Pair that with daily timed arithmetic so the numbers come quickly under pressure.