Applying the Kelly Criterion to a Single Interview Bet

The Kelly criterion converts a stated edge and payoff into a fraction of a bankroll, and interviewers expect a specific dollar figure.

Applying the Kelly criterion to a single interview bet means converting your edge and the payoff odds into a fraction of your stated bankroll, rather than answering with a flat dollar amount or refusing to size the bet at all. Interviewers ask this immediately after an expected value question specifically to see whether you understand that a positive edge does not justify an unlimited stake.

The Kelly fraction is your edge divided by the odds you are being paid, where edge means the probability of winning times the payoff minus the probability of losing, and odds means how many units you win for every unit you risk. In plain terms: multiply your win probability by the payoff multiple, subtract the loss probability, and divide by the payoff multiple again to get the fraction of your bankroll to bet.

For a bet that pays even money, meaning you win one dollar for every dollar risked, the formula simplifies to twice your win probability minus one. A 60 percent chance of winning an even money bet gives a Kelly fraction of 2 times 0.6 minus 1, which is 0.2, or 20 percent of your bankroll.

Suppose the interviewer gives you a bankroll of $1,000 and offers a bet that pays 2 to 1, meaning you win $2 for every $1 risked, with a 45 percent chance of winning. Edge equals 0.45 times 2 minus 0.55, which is 0.9 minus 0.55, or 0.35. Dividing that edge by the payoff of 2 gives a Kelly fraction of 0.175, so the recommended stake is 17.5 percent of $1,000, or $175.

If the interviewer instead lowers the win probability to 35 percent, the edge becomes 0.35 times 2 minus 0.65, which is 0.7 minus 0.65, or 0.05. Dividing by 2 gives a Kelly fraction of 0.025, or just $25 on the same $1,000 bankroll. The point of walking through both cases out loud is to show that a small change in win probability produces a large change in optimal stake, which is exactly the sensitivity a trading desk cares about.