What is the Kelly Criterion?
Developed by John Kelly at Bell Labs in 1956, the Kelly criterion calculates the optimal bet size to maximize long-term wealth growth. The formula is f* = (bp - q) / b, where b is the odds (payout ratio), p is the probability of winning, and q is the probability of losing. For a coin flip paying 2:1 with 50% win probability, Kelly says bet 25% of your bankroll: (2×0.5 - 0.5) / 2 = 0.25.
Application to Investing
Edward Thorp applied Kelly to blackjack card counting and later to hedge fund management. In stock investing, Kelly determines what percentage of your portfolio to allocate to a given opportunity based on its expected return and risk. However, full Kelly sizing produces extreme volatility. Practitioners typically use 'half Kelly' (50% of the calculated fraction) or 'quarter Kelly' to reduce drawdowns while still capturing most of the growth benefit.
Limitations
Kelly assumes you know the exact probabilities and payoffs, which is true in casino games but not in investing. Overestimating expected returns leads Kelly to recommend dangerously large positions. The formula maximizes long-term growth rate but ignores the path, meaning interim drawdowns can be severe. In practice, using 25-50% of the Kelly fraction provides a margin of safety against estimation errors while still benefiting from the mathematical framework.