Kelly Criterion: Formula & Application in Gambling & Investing

The Kelly criterion or Kelly bet or Kelly strategy, named after John L. Kelly Jr., is a formula used in gambling and investing that tells what proportion of a bankroll to bet (or invest), given the odds offered.

$$f^* = \frac{bp-q}{b}$$

where:

- \(f^*\) is the optimal proportion (or fraction) of the entire bankroll that should be bet or invested.

- \(b\) is the decimal odds of the event occurring, as implied by the current prices.

- \(p\) is the probability that the event will occur.

- \(q\)=1−\(p\)