SIG (Susquehanna) Interview Prep: Math, Probability, and Poker Thinking

Susquehanna International Group (SIG) is one of the largest market makers in the world, trading options and equities across global markets. Their interview process is rigorous, probabilistic, and — uniquely — deeply informed by poker. Understanding why poker matters to SIG is the key to preparing for the interview.

Why SIG Teaches Poker

SIG famously teaches poker to all new trading hires. This isn't a perk — it's a deliberate pedagogical tool. Poker is a reduced-form version of trading:

• You make decisions under incomplete information
• You size bets based on expected value, not certainty
• You must separate short-term variance from long-term edge
• You face opponents who are also trying to deceive and exploit you

SIG interviews test whether you think this way naturally — or can learn to quickly.

The Interview Process

First Round: Online Aptitude Test

SIG typically begins with a proctored aptitude test. It varies by application cycle but generally includes:

• Numerical reasoning: Series completion, data interpretation, arithmetic
• Abstract reasoning: Pattern recognition, logical sequences
• Mental arithmetic: Speed arithmetic similar to Optiver's format, but typically less extreme

The test serves as a first-pass filter. It's designed to be completable by top candidates without running out of time, but not easily aced without genuine quantitative ability.

Phone Screen: Probability and Math

A 30–60 minute call with a trader or quant. Expect a mix of:

Mental arithmetic:

• 2×2 and 2×3 digit multiplication
• Fraction and percentage conversions
• Powers of 2 up to 2¹² (4,096)

Probability:

• "What's the probability of rolling at least one 6 in four rolls of a fair die?"
• "A bag has 3 red and 5 blue balls. You draw 2 without replacement. What's the probability both are red?"
• "What's the expected number of coin flips to get two consecutive heads?"

Expected value:

• "A die is rolled. If it's a 6, you win $10. Otherwise you lose $1. What's the EV? Would you play?"
• Classic bet-sizing questions

On-Site / Superday

Multiple rounds covering:

A) Deeper probability and statistics

SIG goes deeper than most firms on conditional probability and combinatorics. Sample problems:

• "You draw cards from a shuffled deck without replacement until you get an ace. What's the expected number of cards you draw?"
• "A 6-sided die has faces 1,1,2,2,3,3. A second die has faces 1,2,3,4,5,6. Which die wins more often in head-to-head comparison?"
• Poker hands probability: "What's the probability of a full house in a 5-card hand?"

B) Options and market-making intuition

SIG is primarily an options market maker. Even if you're not applying for an options role, expect:

• Basic options concepts: calls, puts, delta, intrinsic vs. time value
• "A stock is at $50. A call option at $55 expires in 1 month. If the stock goes up or down $5 with equal probability, what's the fair value of the call?"
• "You're making markets on a coin flip. What spread would you quote?"

C) Poker / game theory

This is the distinctive SIG component. Problems might involve:

• Simplified poker hands: "You're holding a pair of aces. Your opponent bets $20 into a $30 pot. Do you call if you estimate you're ahead 60% of the time?"
• Bluffing frequencies: "In a simplified poker game, how often should you bluff to make your opponent indifferent to calling?"
• Nash equilibria in simple 2-player games
• "What's your optimal bet size in a game where you win $2 for heads and lose $1 for tails if you can bet any fraction of your bankroll?"

Core Math to Know

Powers of 2 (memorize these)

n	2ⁿ
8	256
9	512
10	1,024
11	2,048
12	4,096

These appear constantly in combinatorics and probability problems.

Key Probability Facts

Birthday problem approximation: P(no match in n people) ≈ e^(-n²/730)
For n=23: P(match) ≈ 50%. For n=30: P(match) ≈ 70%.

Expected flips until first heads: 2 flips
Expected flips until two consecutive heads: 6 flips (classic SIG-style question)

Geometric distribution: Expected trials until first success = 1/p
So: expected rolls until first 6 = 1/(1/6) = 6 rolls.

Hypergeometric distribution: Drawing without replacement. For drawing k successes from N objects with K successes: P(X = k) = C(K,k) × C(N-K, n-k) / C(N,n)

Options Basics

Call option payoff: max(S − K, 0) at expiry
Put option payoff: max(K − S, 0) at expiry

For a simple 1-period binomial model:

• Stock goes up to Su with probability p, down to Sd with probability (1−p)
• Risk-neutral price of call: (p × max(Su−K, 0) + (1−p) × max(Sd−K, 0)) / (1+r)

For interview purposes: if told equal up/down probabilities and no discounting:

Example: Stock at $100, goes to $110 or $90 with equal probability. Call at $105.

• Up: payoff = $5
• Down: payoff = $0
• Fair value: 0.5 × $5 + 0.5 × $0 = $2.50

Kelly Criterion

SIG interviewers may explicitly ask about optimal bet sizing. Know the Kelly formula:

f* = (bp − q) / b

For a 60/40 coin with even odds (b=1): f* = (1 × 0.6 − 0.4) / 1 = 20%

For a game where you win $2 for heads, lose $1 for tails: b=2, p=0.5, q=0.5.
f* = (2 × 0.5 − 0.5) / 2 = 0.5/2 = 25%

Game Theory Basics

SIG values game-theoretic thinking. Know these concepts:

Nash equilibrium: A strategy profile where no player benefits from unilaterally changing their strategy. In poker, this means finding bluff frequencies that make your opponent indifferent.

Mixed strategies: Sometimes the optimal strategy is randomizing (poker bluffing is a mixed strategy — pure "always bluff" or "never bluff" are exploitable).

Indifference principle: In a Nash equilibrium, the opponent must be indifferent between calling and folding. This sets the optimal bluff frequency.

Example: You're bluffing in a $100 pot, betting $50. Your opponent folds or calls. At what bluff frequency should you be indifferent?

• Opponent calls: you lose $50
• Opponent folds: you win $100
• Opponent's indifference: EV of calling = EV of folding
• p × (−$50) + (1−p) × $100 = 0 → p = 2/3 value bets, 1/3 bluffs (rough approximation)

Preparation Timeline

Weeks 1–2: Arithmetic and probability foundations

• Speed arithmetic to under 5 seconds per 2×2 multiplication
• Memorize powers of 2 through 2¹²
• Practice expected value problems daily
• Bayes' theorem until it's reflex

Weeks 3–4: Combinatorics and options

• Permutations, combinations (C(n,k) and P(n,k))
• Hypergeometric distribution (drawing without replacement)
• Basic binomial option pricing
• Call and put payoff structures

Weeks 5–6: Game theory and poker

• Nash equilibrium in simple 2×2 games
• Mixed strategies and indifference conditions
• Kelly criterion and bet sizing
• If possible: play poker (even microstakes) to build intuition for bet-sizing under uncertainty

Common Mistakes

Confusing "with replacement" and "without replacement." Most card problems are without replacement. This changes the probabilities significantly.

Forgetting to normalize. When conditioning on an event, you must divide by P(event). This is Bayes done wrong in every interview.

Treating all probability as independent. Card draws from the same deck are NOT independent.

Not making markets. If asked for a bid/ask or a bet, give one. A $1/$1,000 spread is better than refusing.

Ignoring the Kelly criterion. SIG really does care about bet sizing. "Bet everything" is wrong. "Bet nothing" is also wrong.

Frequently Asked Questions

What GPA / school does SIG target? SIG targets top quantitative programs — MIT, Caltech, CMU, top state schools (Michigan, Georgia Tech). GPA cutoffs are typically 3.5+ for quant roles. Math and CS degrees are preferred.

Does SIG hire liberal arts majors? Rarely for trading roles. Occasionally for tech or operations. Demonstrate genuine quantitative ability if your degree is non-STEM.

What's the compensation like at SIG? Competitive with other prop trading firms. First-year traders typically earn $150K–$300K+ in total compensation including bonus, with significant upside as you progress.

How does SIG compare to Optiver or Jane Street in difficulty? SIG sits between Optiver (pure speed arithmetic) and Jane Street (deep probabilistic reasoning). SIG requires both speed arithmetic and conceptual probability depth, plus the unique game theory/poker layer.

Practice Resources

• Fermiq daily drill — daily calibration across all question types
• Probability category — expected value, conditional probability, combinations
• Interview prep track — structured 6-week curriculum
• Firm-specific SIG pack — questions targeting SIG's format

The SIG interview rewards candidates who think like poker players: probabilistic, strategic, and comfortable with uncertainty. Build those instincts before you walk in the door.