The Kelly criterion, derived in plain English
Explain what the Kelly criterion is, how to compute it, and what it tells you about position size.
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Explain what the Kelly criterion is, how to compute it, and what it tells you about position size.
The Kelly criterion, plain English
The Kelly criterion is a position-sizing formula. It answers one question: given my winrate and my average win-to-loss ratio, what fraction of my account should I risk on this trade? It was developed by John Kelly Jr. at Bell Labs in 1956 and has been borrowed by gamblers, traders, and hedge funds ever since. The idea is simple: bet too small and you leave growth on the table; bet too big and a losing streak wipes you out. Kelly tries to find the sweet spot.
Here's the formula. f* = (winrate x b − loss_rate) / b. The 'b' is your payoff ratio — your average win divided by your average loss. The 'loss_rate' is just 1 minus the winrate. Let's plug numbers in. Say you win 50% of the time, and when you win you make twice what you lose (b = 2). Kelly says f* = (0.5 x 2 − 0.5) / 2 = 0.5 / 2 = 0.25. Translation: bet 25% of your bankroll on each trade. On a $500 account, that's $125 of risk per trade.
Notice what the formula actually does. If you have NO edge — say a 50% winrate at b = 1 (you win and lose equal amounts) — Kelly gives you f* = (0.5 − 0.5) / 1 = 0. Bet nothing. If you have a negative edge — a 40% winrate at b = 1 — Kelly returns a negative number. Translation: don't take the trade at all. Kelly is honest in a way most position-sizing rules aren't.
Recap: Kelly = (winrate x payoff_ratio − loss_rate) / payoff_ratio. It tells you the 'optimal' fraction to risk per trade. No edge equals zero. Negative edge equals don't trade. But pure Kelly is too aggressive for real trading — that's the next lesson.
Knowledge check
Answer before moving on.
1. You have a 60% winrate and a payoff ratio b = 1 (average win equals average loss). What does Kelly tell you to risk per trade?
2. What does Kelly return when your edge is exactly zero (winrate equals loss_rate at b = 1)?
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