Kelly Criterion: Formula and Application in Gambling and Investing

The Kelly criterion (Kelly bet/strategy) calculates the optimal fraction of a bankroll to wager given the odds and probability.

Formula: f* = (bp - q) / b

Variables:

• f* = optimal fraction of bankroll to bet/invest
• b = decimal odds (net profit per unit staked)
• p = probability of winning
• q = 1 - p (probability of losing)

Developed by John L. Kelly Jr., it maximizes long-term growth rate of capital under repeated bets with known probabilities.