Practice · Quant prep · Jane Street
Jane Street interview questions
Jane Street publishes more about its interviews than most firms. Read it closely and it tells you what to practise: probability, expected value and making markets, reasoned out loud with someone who will push back.
The process, from Jane Street's own pages
- Rounds. Phone interviews first, then in-person interviews for the final stage. Source
- The final round. A variety of question types: problem solving, probability and statistics, coding in any language you choose, data analysis, and your general interests. All run by quantitative traders. Source
- No finance needed. The firm says it won't test knowledge of finance or economics, and that interviews should feel more like a conversation than a quiz. Source
- Research roles. Quantitative research interviews blend the trading and the engineering interviews, so prepare for both. Source
- Their own study guide. The Probability and Markets guide covers counting, expected value, conditional probability, confidence intervals, making markets and adverse selection. Source
What candidates report
Candidates describe trader rounds built around games: a betting or market-making exercise that starts simple and changes its rules as you go, so the interviewer can see how you update. Several rounds, often with a different trader each time.
What Jane Street is testing
The guide's own list of myths is the best summary. On mental arithmetic, it says the firm will not judge you harshly for being unable to multiply double-digit numbers in five seconds. On advanced mathematics, it says the firm prefers the simple, intuitive answer to one built on esoteric theorems.
What does count is visible in the four tips on the interview page: approach problems methodically, communicate clearly, correct your mistakes, and ask why. In practice that means stating an estimate before you calculate, saying which assumption you are making, and changing your answer cleanly when new information arrives. The last one matters most in the market-making questions, where the point of the exercise is how your quotes move after each trade.
Six practice problems
Written by us to match the types Jane Street is publicly reported to ask. None is a copy of a Jane Street question.
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You roll a fair die and are paid its face value in pounds. After seeing the roll you may pay £1 to roll once more, keeping the second result. What is the game worth to you with best play?
Show the answer
£23/6 ≈ £3.83
A re-roll is worth its expected value, 3.5, less the £1 fee: 2.5. So re-roll a 1 or a 2 and keep anything else. The value is (2/6) × 2.5 + (3 + 4 + 5 + 6)/6 = 5/6 + 3 = 23/6. Deciding by comparing each outcome with the value of the alternative is the whole method, and it scales to any number of re-rolls.
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A box holds either £10 or £30, equally likely. You offer to sell it for £22 to a buyer who knows what is inside and buys only if it holds £30. What is your expected profit per box offered?
Show the answer
−£4
Half the time the buyer walks away and you make nothing. Half the time they buy a £30 box for £22 and you lose £8. Expected profit: −£4, even though £22 is above the box's average value of £20. That is adverse selection: the trades you get are exactly the ones you did not want. The fair value to quote is not the average; it is the average given that someone chose to trade with you.
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Two dice are rolled and you are told the total is 8. What is the probability that at least one of them shows a 6?
Show the answer
2/5
The outcomes that total 8 are (2,6), (3,5), (4,4), (5,3) and (6,2): five of them, equally likely. Two contain a 6. Listing the conditioned outcomes is faster and safer than any formula here.
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Each roll of a die costs £1, including the first. After any roll you may stop and be paid the last roll's face value in pounds. What is your expected profit with the best stopping rule?
Show the answer
£3
Stop at the first roll of t or more. The number of rolls is geometric with success probability (7 − t)/6, so the expected cost is 6/(7 − t), and the payout averages (t + 6)/2. The profit is (t + 6)/2 − 6/(7 − t), which is 2.5, 2.8, 3, 3, 2.5 for t = 1 to 5. Stopping on 3 or better and on 4 or better both give £3.
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You roll a die until a face appears that you have seen before. What is the expected number of rolls?
Show the answer
1223/324 ≈ 3.77
Use E[N] = Σ P(N > k). The first k rolls are all different with probability (6/6)(5/6)…((7 − k)/6). Summing k = 0 to 6: 1 + 1 + 5/6 + 20/36 + 60/216 + 120/1296 + 120/7776 = 1223/324 ≈ 3.77. It is the birthday problem on a six-day year.
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You are asked to make a market on the number of different faces showing when three dice are rolled. Where is fair value?
Show the answer
91/36 ≈ 2.53
Count faces by linearity: a given face is missing with probability (5/6)³ = 125/216, so the expected number present is 6 × (1 − 125/216) = 91/36 ≈ 2.53. A sensible first market is about 2.4 at 2.7, then tighten or skew it as you learn how the other side trades.
Practise under time
How to prepare for Jane Street
Read the Probability and Markets guide end to end, then do its questions without looking at the answers. Practise out loud with a partner who is allowed to interrupt: the skill being tested is thinking clearly while someone asks why. For the final round, keep one programming language fluent enough to write small programs quickly, since the firm lets you choose it.
If you have a Jane Street process coming up, the assessment hour tells you where you stand against that bar and what to fix first. The assessment hour.