Quant interview playbook: formulas and numbers to know cold

The compact reference behind the desk: the probability and statistics you should recall instantly, the mental-math tricks that buy you speed, the market-making principles interviewers listen for, and the numbers worth memorizing. Free, in your browser.

Probability and statistics to have cold

• Bayes: P(A | B) = P(B | A)·P(A) / P(B). Rare events are dominated by the base rate.
• Expected value of a geometric wait: E = 1/p. Expected rolls to a 6 is 6; flips to the first head is 2.
• Variance of a fair die: 35/12 ≈ 2.92. Variances add for independent variables; standard deviations do not.
• Binomial: mean np, variance np(1−p). For 100 fair flips, mean 50, one standard deviation 5.
• Gambler's ruin (fair): from i toward N, P(reach N) = i/N.
• Kelly criterion: bet fraction (edge / odds); for even money, f = p − q.
• Correlation and variance: Var(X+Y) = Var X + Var Y + 2·Cov(X,Y).

Mental-math tricks

• Difference of squares: a×b = m² − d² when a, b straddle m by d. So 23×17 = 400 − 9 = 391.
• Percentages via 10% and 1%: 7% of 340 = 34 − 3×3.4 = 23.8.
• Eighths as percentages: 1/8 = 12.5%, so 5/8 = 62.5%.
• Squaring numbers ending in 5: 65² = 6×7 then append 25 = 4225.
• Dividing by 5: multiply by 2 and shift the decimal. 840/35 = 1680/70 = 24.

Numbers worth memorizing

• e ≈ 2.718, ln 2 ≈ 0.693, √2 ≈ 1.414, √3 ≈ 1.732.
• 1/e ≈ 0.368: the derangement probability, and the secretary-problem cutoff.
• 68 / 95 / 99.7 for one, two and three standard deviations of a normal.
• Powers of 2: 2^10 ≈ 1,000, 2^20 ≈ 1 million, 2^30 ≈ 1 billion.

Market-making principles

• Quote a level, a width and a size out loud: "17 at 20, five up" is a complete answer.
• The spread is the price of adverse selection. More informed flow means a wider spread.
• An instant, full-size fill is information. Update your fair value toward the side that traded.
• Manage inventory by skewing the mid, not just by widening.
• When you have an edge, act. If someone quotes against your fair value, trade, then ask why they did.

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