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The Kelly Criterion: sizing risk to your edge

The classic bankroll formula — what it says, why full Kelly is dangerous, and why disciplined bettors only ever use a fraction of it.

Once you believe you have an edge, a second question follows: how much should you risk? Risk too little and an edge barely compounds; risk too much and a bad run wipes you out. The Kelly Criterion is the textbook answer to that trade-off — a piece of bankroll theory worth understanding, and worth handling with great care.

What the formula says

For a single bet at decimal odds d with your estimated win probability p, Kelly suggests staking the fraction:

f = (p × (d − 1) − (1 − p)) ÷ (d − 1)

The numerator is just your edge in expected-value terms; the denominator is the net price. So Kelly scales your stake to how big the edge is and how long the price pays. Bigger edge, bigger fraction. No edge, no bet — Kelly returns zero or negative, telling you to pass.

Why "full Kelly" is a trap

Two reasons full Kelly is almost never the right setting:

1. It is brutally volatile. Full Kelly maximises long-run growth in theory, but the swings along the way are enormous — drawdowns of half your bankroll are routine. Most people cannot stomach that, and panic is how good strategies die.
2. It assumes your probability is exactly right. It never is. If you overestimate your edge — easy to do — Kelly tells you to overbet, systematically, every time. Overbetting compounds toward ruin even with a genuine edge.

What disciplined bettors actually do

They use fractional Kelly — a quarter or a half of the formula's number. Half-Kelly keeps most of the long-run growth while cutting the volatility dramatically, and it cushions the damage when your edge estimate is too high. The fraction is a margin of safety against your own uncertainty.

The honest framing

Kelly is only ever as good as the edge you feed it: garbage in, garbage out. It is a tool for understanding risk, not a recommendation to stake any particular amount — this article gives you none. Never risk money you cannot afford to lose, and remember that betting is entertainment, never a source of income. Analysis, not advice.