The Kelly Criterion Sizes Your Bets
The Kelly Criterion answers the question every investor, entrepreneur, and gambler must face: given that you should never go all-in, exactly how much should you wager?
"These two intuitions, 'don't go all-in' and 'payoffs determine the relative size of the bet,' summarize a betting strategy known as the Kelly Criterion, named after the mathematician who invented it." Luca Dellanna
Imagine ten friends each shoot a basketball. Before each shot, you decide how much of your $100 to bet on it going in. If you bet everything on one shooter and they miss, you are out. You cannot benefit from any future wins. But if you bet nothing, you gain nothing. The Kelly Criterion navigates this tension with a formula: f = (p(b+1) 1) / b, where f is the fraction of your bankroll to wager, p is the probability of winning, and b is the net fractional odds. The formula ensures you bet more on higher-probability, higher-payoff opportunities and less on speculative ones but it never tells you to bet everything.
The deeper insight is that Kelly-optimal betting maximizes the long-run growth rate of your wealth, not the expected value of any single bet. This distinction matters enormously in non-ergodic systems. A strategy that maximizes expected value can still lead to ruin, because a single catastrophic loss wipes out the compounding engine. Kelly sacrifices some short-term expected return to guarantee you stay in the game.
The principle extends beyond finance. Luca Dellanna applies it to his time as an author and consultant: he allocates effort across multiple projects proportional to their upside, but never commits everything to a single venture for an extended period. The risk of that one project failing or the opportunity cost of missing other bets is too high.
Takeaway: Size every bet so that the worst-case outcome still leaves you able to make the next bet.
See also: Avoid Ruin Above All | The Barbell Strategy Handles Uncertainty | Ergodicity Changes Everything | Hyperbolic Discounting Makes the Future Disappear