Jane Street Data Scientist Interview Questions

Jane Street·Data Scientist·Technical Phone Screen

Jul 2026

Jane Street data scientist interview with a pretty gnarly probability/game theory problem. One question, no fluff, just math and reasoning under pressure.

You roll a fair six-sided die repeatedly, accumulating a running sum. You can stop anytime and collect the current sum, but if the sum ever hits a perfect square (1, 4, 9, 16, ...) you lose everything and get zero. There's no roll limit. What's the optimal stopping strategy, and what's the expected payoff under that strategy starting from zero?

“This one wrecked me for the first few minutes.”

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Jane Street·Data Scientist·Technical Phone Screen

Jul 2026

Jane Street Data Scientist interview with a probability/game theory problem involving optimal dice strategy. The math is clean but the reasoning chain to get there is genuinely tricky, especially under pressure.

Alice rolls a fair 30-sided die and Bob rolls a fair 20-sided die. Whoever shows the higher number wins, with ties going to Bob. Bob can reroll once after seeing his first result, but he never sees Alice's number before deciding, and his second roll is binding. Assuming Bob plays optimally, what is the probability that Alice wins?

“This one took me a while to set up properly.”

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Jane Street·Data Scientist·Technical Phone Screen

Jul 2026

Two pretty intense quant/algo questions for a Data Scientist role at Jane Street. Both required actual derivations and working code, not just hand-waving. The kind of interview where you either know the math or you don't.

You're at position k in a 100-person queue when a second checkout counter opens. Each other customer independently moves to the new queue with probability 1/2, and if you also move, your spot among the movers is uniformly random. Both counters serve at the same rate. Derive your expected wait time for staying vs. switching, and find the threshold k where switching becomes the better choice.
Given an integer n in cents and coin denominations of 1, 5, 10, 25, and 100 cents, count the number of distinct combinations (order doesn't matter) that sum to exactly n. Formalize it, design an algorithm for n up to 10,000, and analyze time and space complexity.

“This one took me a while to set up properly.”

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Jane Street·Data Scientist·Technical Phone Screen

Jun 2026

Phone screen for a Data Scientist role at Jane Street. One question, pure mental math and combinatorial reasoning, no calculator allowed. Felt deceptively simple at first glance.

You have 5 pumpkins. You weigh every possible pair on a scale, giving you 10 readings: 21, 22, 23, 24, 25, 26, 27, 28, 29, and 30 pounds. You don't know which pair produced which reading. What is the total weight of all five pumpkins?

“My first instinct was to try solving for individual weights, which is a dead end without knowing which reading maps to which pair.”

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Jane Street·Data Scientist·Technical Phone Screen

Jun 2026

Jane Street Data Scientist interview with a game theory brain teaser that sounds deceptively simple but turns into a full-on Nash equilibrium derivation under pressure. The interviewer keeps asking 'why' until you've either proved your answer or fallen apart.

Two players each secretly pick an integer from 1 to 100. The larger pick has 10 subtracted from it, then that result is compared to the smaller pick. Whichever value is larger wins. What is the optimal strategy, and can you prove it?
For the number-picking game: when exactly does the player who chose the larger number win, lose, or draw? Work it out as a function of the gap between the two picks.
Prove that no pure (deterministic) strategy is optimal in this game, and derive the lowest number a rational player should ever consider picking.
Among the numbers that survive the dominance elimination, is there one that beats all the others? Describe the win/loss structure within that range and find the optimal mixed strategy.
How does the optimal strategy change if the penalty subtracted from the larger pick is k instead of 10, or if the range goes up to N instead of 100?
If your opponent picks uniformly at random over 1 to 100, what is your best response and what is your expected payoff?

“This one wrecked me a little.”

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Jane Street·Data Scientist·Technical Phone Screen

Jun 2026

Jane Street Data Scientist interview with a game theory problem involving a 21-sided die. The core question was deceptively clean but the optimal strategy took some real work to pin down, especially resisting the urge to just accept anything nonnegative.

Two players take turns rolling a fair 21-sided die (faces labeled -10 through 10). On each turn, the roller can accept the face value as a payment from the opponent, or reject and pass the die. Both play optimally. What is the optimal strategy for each player, and what is the expected payoff to the first player?

“My first instinct was 'accept anything >= 0' and I was pretty confident about it for an embarrassingly long time.”

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Jane Street·Data Scientist·Technical Phone Screen

Jun 2026

Jane Street Data Scientist interview with a multi-part probability and game theory problem centered on a sealed-box pricing scenario. The question escalates from basic expected value through adverse selection and competitive bidding, so it's less a stats quiz and more a test of whether you can reason about incentives under uncertainty. Pretty intense for what I expected to be a standard quant screen.

A box contains a dollar amount drawn uniformly at random from $1 to $100. You can buy it at whatever price you name. What is the highest price you should rationally offer, and what is your expected profit if you buy at that price?
Now the dealer's profit equals the sale price minus the box contents. Is there any price where both parties benefit from trading? What does it mean if a dealer agrees to sell at a price you'd find attractive?
The company adds a $10 bonus to the dealer for every box sold. Now what price should you offer, and why?
The $10 bonus still applies, but now the dealer can open the box before deciding whether to accept your offer. You make a single take-it-or-leave-it offer. When does the dealer accept, what is your expected profit as a function of your offer price, and what offer maximizes your payoff?
Given that the dealer's ability to screen boxes destroys value compared to the no-peek scenario, what should the two parties agree to do instead?
Back to no one seeing inside the box, with the $10 bonus still in play. A second buyer shows up and competes with you for the same box. What happens to the price, and who captures the surplus?
Follow-up: how does your offer in the bonus scenario change if the dealer is risk-averse while you remain risk-neutral?
In the dealer-screens-boxes setting, if you interact with the same dealer repeatedly, can a 'always trade at a fixed price' agreement hold without an enforceable contract? What tempts the dealer to defect?
What happens if the two competing buyers in Part 4 can collude before bidding? How does the dealer's outcome change?

“Straightforward expected value warmup.”

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Jane Street·Data Scientist·Technical Phone Screen

Jun 2026

Jane Street data scientist interview, all probability puzzles, no coding, no case studies. The interviewer just handed me five problems and expected me to think out loud the whole time. Felt more like a math exam than a job interview, which I was not fully prepared for.

You eat pizza on Saturday with probability 0.4 and on Sunday with probability 0.3. No information is given about how the two days relate. What is the range of possible values for the probability of eating pizza at least once over the weekend? Describe a dependence structure that achieves each extreme.
You flip 250 gold coins and 250 silver coins. Gold heads score 3 points, silver heads score 1 point, tails score 0. Given that the total score is exactly 900, which combination of gold heads and silver heads is most likely?
An ant starts at one vertex of a unit cube and moves each second to a uniformly random adjacent vertex. What is the expected number of steps to reach the vertex diagonally opposite the starting point?
You have N shoelaces in a pile with 2N free ends. Repeatedly pick two free ends at random and tie them together until no free ends remain. What is the expected number of closed loops formed?
Two equal-volume buckets, one pure white and one pure red. Pour a quarter bucket of red into white, mix, then pour the same volume of the mixture back into the red bucket and mix again. Which bucket's color changed more?

“I jumped straight to the independence formula and got a number, then the interviewer asked me to slow down and think about what the actual bounds were.”

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Jane Street·Data Scientist·Technical Phone Screen

May 2026

Jane Street Data Scientist interview that leaned heavily into probability theory. The core problem was a two-day rain scenario where you had to derive bounds on union probability without assuming independence, then reason about real-world weather dependence. Solid follow-ups pushed further into three-day extensions and conditional inference.

Given that rain on Saturday has probability p and rain on Sunday has probability q, with no assumption about independence between the two days, what is the full range of possible values for the probability that it rains on at least one of the two days? Show that both endpoints are actually achievable.
If rain events typically last only one day, where in that range does the true probability of at least one rainy day fall? What if rain events typically persist for two or more days?
If you are additionally told that both days are rainy with probability r, what is P(at least one rainy day) exactly, and what values of r are even feasible given p and q?
If the two days were exactly independent, where does P(at least one rainy day) fall within the range you derived? Can it ever touch either endpoint when both p and q are strictly between 0 and 1?
Extend the problem to a three-day weekend where each day has its own marginal rain probability. What is the range of possible values for the probability that it rains on at least one of the three days?
Given only P(A union B), p, and q, what can you infer about P(A intersect B) and about the conditional probability P(B given A)?

“This is where inclusion-exclusion saves you.”

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Jane Street·Data Scientist·Technical Phone Screen

May 2026

Jane Street Data Scientist interview with a heavy probability/statistics focus. The core problem was a multivariate correlation question that required both a proof and a construction, which is pretty typical for quant-adjacent roles there but still caught me off guard with how much rigor they expected.

Given seven random variables on the same probability space, each with mean 0 and variance 1, identically distributed, and with the same pairwise correlation rho for every pair, what is the minimum possible value of rho? You need to prove the lower bound is tight by showing it can't go lower AND constructing a valid joint distribution that actually achieves it.

“This wrecked me for the first few minutes.”

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