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SIG

SIG Superday Interview: The Definitive Question Bank

SIG’s quant interview is a probability marathon disguised as a job interview. Founded by professional poker players — including three WSOP bracelet winners — Susquehanna International Group tests candidates through 4–5 stages of escalating expected-value problems, Bayesian reasoning, and real-time market-making games. The process spans 2–6 weeks and culminates in a full-day superday at SIG’s Bala Cynwyd headquarters. For a Princeton MFin candidate with equity volatility research at Millennium and HFT execution experience, your edge lies in connecting probability theory to practical trading intuition — exactly what SIG values most.
The firm explicitly states that “the ability to develop a new idea or approach to a problem is far more valued than pre-existing knowledge of finance.” SIG teaches options theory, Black-Scholes, and Greeks during a 3-month post-hire training program. What they screen for in interviews is raw probabilistic reasoning, decision-making under uncertainty, and — critically — clear communication of your thought process.

How the 4–5 stage gauntlet is structured

Stage 1: Online Assessment (Mettl Platform)

For internships, the “SIG Quantitative Evaluation” consists of 16 questions in 20 minutes — a brutal pace of ~75 seconds per question. For full-time roles, the “SIG Problem Solving Assessment” gives 17 open-ended questions in 60 minutes. Both formats cover conditional probability, Bayes’ theorem, expected value, combinatorics, path-counting, Markov chains, logic puzzles, and rapid mental arithmetic. Candidates report you cannot skip or return to questions, and tab-switching is flagged immediately. A score of 13/16 or higher is considered competitive for advancing. One candidate (Glassdoor, Aug 2025) described it: “17 questions on probability, calculus, and logic, generally increasing in difficulty. I was allowed paper, pen, and a calculator.”

Stage 2: Phone/HR Screen (30–45 minutes)

SIG’s recruiters have above-average mathematical ability — the firm requires recruiters to complete mathematics coursework. The screen splits between behavioral questions (“Why SIG?”, “Why trading?”, “What’s happening in markets?”) and 2–3 probability/EV problems at easy-to-medium difficulty. One frequently reported question: “If the probability of seeing at least one hawk in one hour is 0.8, what’s the probability of seeing at least one in half an hour?” (Answer: assume Poisson process, ≈55.3%).

Stage 3: Technical Interview (60 minutes, video)

Conducted by a senior trader or quantitative researcher, this round features harder probability questions that escalate in difficulty throughout. Topics include Markov chains, complex expected value, conditional probability, and multi-step game theory. One candidate noted: “Questions get harder and harder as the interview progresses.” For Quant Researcher roles, this round also includes machine learning questions, linear algebra, and deep-dives into your research projects.

Stage 4: Take-Home Project (48 hours to 1 week)

Not always included, but frequently reported. Candidates receive a data set of trades to analyze and must develop a trading strategy in any programming language. For QR roles, this is more research-oriented; for QT roles, it’s a strategy simulation. One candidate described: “48 hours to analyze a sequence of trades and develop a strategy.”

Stage 5: The Superday (full day, on-site)

The final round consists of 4–6 sessions rotating through:
  • Technical interview (~60–90 min): The hardest probability questions and brainteasers, often with a head researcher or senior trader
  • Market-making games: Real-time card/dice expected-value games where you quote bid-ask spreads and update beliefs with new information — this is SIG’s signature assessment
  • Group problem-solving: Brain teasers worked through with other candidates; board game sessions evaluating collaborative thinking
  • Project deep-dive: Detailed walkthrough of your research — “What inspired this topic? What specific methods did you use? Looking back, what would you change?”
  • HR/behavioral final: “What would be your edge vs. other traders?” and “How would you handle a big loss?”
Multiple candidates report a “good cop, bad cop” dynamic between a trader and HR member during final rounds. Interviewers deliberately chat about random topics while you work through problems to test composure under distraction.

73 actual math and probability questions from SIG interviews

The questions below are organized by category and drawn from Glassdoor, Wall Street Oasis (255+ SIG entries), QuantNet, 1point3acres (353+ SIG submissions), Blind, GitHub candidate reports, and interview prep databases. Each has been reported by at least one candidate.

Brain teasers and logic puzzles

Q1. Eight Marbles: You have 8 marbles; one weighs less than the others. Using a balance scale with only 2 weighings, find the odd one out. (Split into groups of 3-3-2; weigh the two groups of 3.)
Q2. Five Pirates, 100 Gold Coins: Five pirates ranked 5 to 1; the top pirate proposes a division. If fewer than half agree, he’s killed. How should Pirate 5 allocate? (Keep 98, give 1 coin each to Pirates 1 and 3 — backward induction.)
Q3. Bridge Crossing: Four people cross a bridge (times: 1, 2, 5, 10 minutes), two at a time with one flashlight. Minimum crossing time? (17 minutes: 1+2 cross → 1 returns → 5+10 cross → 2 returns → 1+2 cross.)
Q4. 1000 Lockers: Guards sequentially toggle every kth door. Which doors remain open? (Perfect squares only — they have an odd number of divisors.)
Q5. Cube Interior: A 10×10×10 cube of unit cubes. Remove all cubes with an exterior surface. How many remain? (8³ = 512.)
Q6. Greatest Coin Value Without Making a Dollar: What’s the most money in US coins you can hold without being able to make change for $1? ($1.19: 3 quarters + 4 dimes + 4 pennies.)
Q7. 25 Horses: 25 horses, race 5 at a time (no stopwatch). Minimum races to find the top 3? (7 races.)
Q8. Circle Regions: Cutting a circle with n straight lines creates at most how many regions? (n(n+1)/2 + 1.)
Q9. Game Show Decision: Staying gets $1,000; a correct answer gets $4,000; wrong leaves $250. What minimum probability of correctness makes guessing worthwhile?
Q10. Counting to 60 Game: You and an opponent take turns adding 1–10 to a running total. Whoever is forced to say “60” loses. What’s the winning strategy? (Classic modular arithmetic — ensure you always leave your opponent at a number ≡ 5 mod 11.)

Probability and conditional probability

Q11. Biased Coin in Bag (Bayes’): 99 fair coins + 1 double-headed coin. Pick randomly, flip 7 heads in a row. Probability it’s the double-headed coin? (128/227 ≈ 56.4%.)
Q12. Two Coins Bayes: One double-headed coin, one fair. Pick randomly, flip 6 heads. Probability you chose the biased coin? (64/65 ≈ 98.5%.)
Q13. Hawk Probability (Poisson): P(≥1 hawk in 1 hour) = 0.8. P(≥1 hawk in 30 minutes)? (1 − √0.2 ≈ 55.3%. Key insight: don’t simply halve the probability.)
Q14. Event Probability Over Time: P(event in 1 hour) = 84%. P(event in 30 min)? (1 − √0.16 = 60%.)
Q15. Painted 3×3×3 Cube: All faces painted green, cut into 27 cubes. Pick one randomly, see a green face. Probability it’s an edge cube? (24/54 = 4/9.)
Q16. Obtuse Triangle on Circle: Three random points on a unit circle. Probability they form an obtuse triangle? (3/4.)
Q17. Triangle Containing Center: Three random points on a circle. Probability the triangle contains the center? (1/4.)
Q18. Seating in Age Order: 5 people of different ages sit randomly around a round table. Probability they’re in age order (CW or CCW)? (2/24 = 1/12.)
Q19. Sock Drawer (Bayes’): Rack X: P(red)=0.4; Rack Y: P(red)=0.7. Pick a rack randomly, draw 2 red socks. Probability they came from X? (16/65 ≈ 24.6%.)
Q20. Weighted Coin: P(H)=0.4, flip 5 times. P(≥3 tails)? (≈68.3%.)
Q21. Biased Coin — Rachel Problem: “Rachel flips a biased coin. P(two heads) = 0.16. P(two tails)?” (p=0.4, so P(TT) = 0.6² = 0.36.)
Q22. Correlation Validity: cor(x,y)=0.9, cor(y,z)=0.9, cor(x,z)=0.5. Is this valid? (No — the correlation matrix must be positive semi-definite. Given constraints, cor(x,z) ≥ 0.62.)
Q23. Three Dots on a Square: Place 3 dots randomly on the 4 edges of a square. Probability they lie on distinct edges? (3/4 × 2/4 × … — combinatorial argument.)
Q24. Two Decks: One deck has 52 cards, another 104 cards. Draw 2 from the same deck. If both red, you win. Which deck? (52-card deck: P = 25/51 ≈ 49%; 104-card deck: P = 51/103 ≈ 49.5%. Choose the 104-card deck.)
Q25. 10 Dice Sum: 10 six-sided dice rolled. Probability the sum is divisible by 6?
Q26. HT vs TT Race: Flip coins until you get “HT” or “TT”. Probability “HT” comes first?
Q27. Penney’s Game: Player A picks HHT, Player B picks HTH. Who has the advantage in sequential coin flips? (Player A — HHT beats HTH.)
Q28. Median of 3 Uniforms: Three independent U[0,3] variables. Probability the median falls in [1,2]?
Q29. Submarine/Torpedo Probability: Reported from the Dublin office — conditional probability in a military scenario.
Q30. International Trip Problem: “I had two trips last year, one of which was an international trip in December. What is the probability that both trips were international?”

Expected value problems

Q31. Dice Re-Roll (Classic SIG): Roll a die, get paid face value. You can re-roll once (taking second result). Fair price? (Keep 4,5,6 (avg 5); re-roll 1,2,3 (EV 3.5). Overall EV = $4.25.)
Q32. Three Dice Match: Roll 3 dice. Triple = $10, double = $5, all different = −$2. Expected value? ($1.25.)
Q33. Four Heads Game: $1 to play; flip 4 coins. 4 heads wins $10. Play? (No: EV = $10/16 − $1 = −$0.375.)
Q34. Matching Coins: You and opponent each flip 3 coins. Same # of heads: you lose $2. Different: you win $1. Play? (Yes: EV = +$1/16 per game.)
Q35. Tic-Tac-Toe EV: Toss 3 Tic Tacs on a 3×3 board. Win $20 for a line, lose $1 otherwise. Play? (8 winning arrangements out of C(9,3)=84. EV ≈ +$0.90. Yes, play.)
Q36. Painting Valuation: A painting sells for $X. Probability of real = Y. If real, worth A; if fake, worth B. Expected gain?
Q37. Poker Pot Odds: You and friend bet $10 each. Friend raises to $20. If you fold, lose $10 blind. Minimum win rate to call? (25%.)
Q38. Doubling Bet: $10 bet. At any time, opponent offers to double stakes. Minimum probability to accept? (1/3.)
Q39. Repeating Dice: Roll die; paid face value. If 1–3, roll again (game stops on 4–6). EV? (E = (1/2)(5) + (1/2)(2+E) → E = 7.)
Q40. 12-Sided vs Two 6-Sided: Roll a 12-sided die (paid the result). Can re-roll with two 6-sided (take sum). How much to pay? (Re-roll if ≤6 since E[2d6]=7. EV = $8.25.)
Q41. Coin Ratio Optimization: Flip coins until you decide to stop. Maximize heads/total ratio. Optimal strategy? (Stop immediately if first flip is heads; continue if tails. Expected ratio ≈ 0.77.)
Q42. Vegas Prime Game: Win $x if number is prime, lose $x/2 if composite. Number drawn uniformly from 1–10. Play? Follow-up: What if you can play n times?
Q43. Card Stopping Game: Deck of 2 black, 2 red cards. Black = −$1, red = +$1. Stop anytime. Optimal EV? ($2/3.)
Q44. Red/Black Guessing: 4 marbles (2 red, 2 blue). Predict color before each draw. $1 per correct guess. Optimal EV?
Q45. Horse Race Arbitrage: Horse A wins with odds X, B with Y, C with Z. Find optimal allocation guaranteeing profit regardless of outcome.
Q46. Dice Option: Roll a 4-sided die, paid face value. You can buy an option to re-roll. How much is that option worth? (EV without = 2.5; with option = 3.0; option value = 0.5.)
Q47. Land Expected Value: Calculate the expected value of land under uncertain conditions.
Q48. Random Cake Cutting: Cut a cake with n cuts. Expected number of pieces?

Combinatorics and counting

Q49. Frog Lattice Path: A frog from (0,0) to (4,6), taking 1-unit steps up or right. How many paths? (C(10,4) = 210.)
Q50. Constrained Lattice Path: Same frog (0,0) to (4,6), but cannot take 3 consecutive steps in the same direction. How many paths?
Q51. Balls in a Row: 11 balls — 5 of type A, 6 of type B (same type indistinguishable). How many ways to arrange a row of 6?
Q52. Adjacent People at Round Table: 3 people randomly seated at a table of 8. Probability at least two are adjacent?
Q53. Three Numbers Average: Three numbers from 1–20. Probability one equals the average of the other two?
Q54. Circular Table Combinations: Various “how many arrangements” problems at a circular table.
Q55. Handshakes: 10 people in a room all shake hands. Total handshakes? (C(10,2) = 45.)

Stochastic processes and Markov chains

Q56. Good Day/Bad Day Chain: If today is Good, P(Good tomorrow)=0.6, P(Bad)=0.4. If today is Bad, P(Good)=0.3, P(Bad)=0.7. Starting from Bad, expected days until next Bad? (1.75 days.)
Q57. Two Heads in a Row: Expected flips to get two consecutive heads? (6 flips — set up states: Start, 1H, HH.)
Q58. Three Heads in a Row: Expected flips for 3 consecutive heads? Follow-up: “When is the game likely to end if the winner needs 3 heads in a row?”
Q59. Gambler’s Ruin: Start with $N. Each round: heads win $2, tails lose $1. Stop if bankrupt. Probability of never going bankrupt?
Q60. Ball Replacement Markov: Bag has 2 red, 1 blue. After each draw, 1 blue ball placed back. Expected replacements until all blue?
Q61. Alternating Dice: Dice A and B rolled alternately (A first). Game ends when A rolls 6. P(game ends on A’s roll)? Expected total rolls?
Q62. Martingale Questions: “A lot of coin-dropping questions and also martingale questions” — reported from QR interview, Philadelphia, Nov 2024.

Statistics and estimation

Q63. Best-of-3 vs. Ahead-by-2: Win probability per round = 0.6. Better to play best-of-3 or first-to-lead-by-2? (Ahead-by-2: P = 0.6²/(0.6²+0.4²) = 69.2% vs. best-of-3: 64.8%.)
Q64. Hypothesis Testing — Coin Bias: Design a test to determine whether a coin is biased.
Q65. Normal Approximation: Interview reported as “basic probability questions: normal approximation to binomial, 3 sigma intervals.”
Q66. Free Throw: 70% free throw shooter, shoots twice. P(≥1 make)? (1 − 0.3² = 91%.)
Q67. Tire Demand Estimation: Estimate global demand for tires. (Fermi estimation — vehicle-to-population ratios.)
Q68. Average Salary Privacy: A group wants to determine their average salary without anyone learning individual salaries. Can they? How?
Q69. Expected Chord Length: Two random points on a unit circle. Expected chord length? (4/π.)

Coding questions lean practical, not pure LeetCode

SIG’s coding assessment uses CodeSignal (sometimes Codility/HackerRank) with 3–4 Python problems in 60 minutes at easy-to-medium LeetCode difficulty. The emphasis is on practical simulation problems rather than pure algorithm puzzles. Reported questions include:
Q70. Adjacent Element Check: Single pass checking every three adjacent elements in an array for a condition.
Q71. DP Station Problem: Target value 1000; sort stations, compute f[i] = minimum steps to reach position i (dynamic programming).
Q72. Bouncing Path Simulation: Starting from each point on leftmost column, simulate a ball bouncing toward upper-right corner, flipping direction on wall hits. Track totals and sort.
Q73. Wildcard Digit Matching: Treat each number as a string (max length 10). For number 123, generate wildcard patterns (23, 13, 12*). Group numbers differing by exactly one digit.
Q74. DFS with Bubbles: Connected component elimination (DFS-based), reported Dec 2025.
Q75. Live Code Optimization: Given inefficient code, optimize for time/space complexity and reusability. Must justify data structure choices with Big-O analysis. Interviewer leaves for 30 minutes, returns to discuss follow-ups.
For Quant Researcher roles, coding is tested more seriously — expect Python-heavy problems plus pseudo-coding. For Quant Trader roles, coding is secondary to math (“programming skills being a plus”), though the OA still includes quantitative problems. SIG accepts Python (preferred for quant), C++, C#, and Java.

Finance questions are lighter than you’d expect

SIG’s entry-level interviews do not emphasize deep derivatives theory. No Black-Scholes derivations, no vol surface construction, no advanced Greeks calculations — these are taught post-hire during the 3-month Quantitative Trading Program. What they do test:
  • “What is a market maker?” — basic understanding required
  • “Both time and volatility increase the prices of calls and puts” — candidates expected to know this relationship
  • Probability questions framed in financial context — “expected values, distributions, and calculating probabilities of various trading outcomes and market events” (Glassdoor, Sep 2025)
  • Arbitrage identification — “identifying arbitrage opportunities using two lotteries”
  • Behavioral biases in trading — anchoring, availability bias, confirmation bias, illusory correlation — SIG explicitly tests awareness of these
  • Market-making games are the primary finance assessment — you calculate fair values of dice/card outcomes, quote bid-ask spreads, and update estimates as information is revealed
For a Princeton MFin with Millennium vol research, you’ll likely face deeper follow-ups on your options knowledge during project deep-dives, but the structured interview rounds remain probability-centric.

The market-making game is SIG’s signature test

The superday’s most distinctive element is the real-time market-making game, which multiple candidates describe as the most important assessment. Here’s what to expect:
Cards or dice are dealt face-down. You’re told a contract pays out based on the sum (or some function) of hidden values. You must quote a bid-ask spread, then SIG’s interviewer will trade against you — buying your offer or selling your bid. As cards/dice are progressively revealed, you must update your expected value in real-time and adjust your market. You’re assessed on: mental math speed, ability to update conditional expectations, spread management (not too wide, not too tight), composure when the interviewer deliberately pressures you, and clear articulation of your reasoning.
A second variant involves group games where all superday candidates play simultaneously, making markets on total values while managing risk against each other and AI opponents. One candidate described: “2 phone screens then 5-hour super day where phones were 3 probability problems; super day was all games — mix of one-on-one and group interviews, which were fun.”

What SIG specifically looks for — and how to leverage your background

SIG’s culture descends directly from poker. Co-founder Jeff Yass teaches new hires poker theory, and the firm employs three World Series of Poker bracelet winners. Interviews reward:
  • Process over answers: How you think matters more than getting every question right. Communicate reasoning continuously — don’t go silent while calculating.
  • Intellectual humility: One candidate reported being rejected after “refusing to concede I was wrong” on an approach. Admit mistakes quickly and pivot.
  • Composure under pressure: Interviewers will deliberately distract you during calculations and push questions to the limit of your ability.
  • Competitive gaming experience: Mention poker, chess, bridge, or competitive sports. This resonates deeply with SIG’s culture.
  • Communication clarity: Multiple sources note SIG “doesn’t hire many people who sound like nerds.” Confident, conversational articulation matters.
For your profile specifically: Your equity volatility research at Millennium is a significant asset during the project deep-dive — prepare to explain your methodology, data sources, feature engineering, and results in exhaustive detail. Your HFT execution strategy research demonstrates the real-time decision-making SIG values. During behavioral rounds, frame these experiences through an EV lens: what decisions did you make under uncertainty, and how did you quantify edge? Mention any competitive gaming background. Study the probability questions above until you can solve them under time pressure with clear verbal narration — that combination of speed, accuracy, and communication is what separates candidates who get offers from those who don’t.

Conclusion: preparation priorities for maximum impact

SIG’s interview is 80% probability and expected value, 15% behavioral/cultural fit, and 5% finance knowledge at the entry level. The single highest-impact preparation activity is drilling conditional probability, Bayes’ theorem, and EV calculations under time pressure while narrating your reasoning aloud. Practice market-making games with dice and cards until updating conditional expectations feels automatic. For the OA, target 13+/16 correct and practice gambler’s ruin, path combinatorics, and random walks specifically — these appear disproportionately. The recommended preparation texts are “A Practical Guide to Quantitative Finance Interviews” (the Green Book), “Heard on the Street,” and Sklansky’s “Theory of Poker.” Online, Tradermath and QuantGuide maintain SIG-specific question databases with 59–146 tagged problems. Finally, your Millennium and HFT experience give you a narrative advantage that most candidates lack — prepare a compelling story connecting your research to SIG’s decision-science philosophy.