Kelly criterion explained

The Kelly criterion dates from 1956 and was devised by John L. Kelly, a researcher at Bell Labs. It answers the question of how much you should stake when you have an edge. Too little wastes growth; too much leads to large swings and, in the extreme, to losing everything.

The formula

Share of bankroll = (b × p − q) / b

• p = your probability of winning
• q = 1 − p, the probability of losing
• b = odds − 1, the net profit per euro

If the result is zero or negative, the bet has no value, and Kelly says: do not bet.

Why hardly anyone stakes full Kelly

The formula assumes that p is exactly right. In practice, your own probability is only an estimate, and usually an overly optimistic one. If you overestimate p, Kelly stakes too much, and that is considerably more harmful than staking too little. In addition, the bankroll swings wildly with full Kelly: drawdowns of half are not unusual.

That is why many people use a fraction:

• Half Kelly: 5 per cent instead of 10 per cent in the example. About three quarters of the growth with considerably smaller swings.
• Quarter Kelly: 2.5 per cent. Calmer still, and more forgiving of estimation errors.

A cap is often added as well, for example at most 3 per cent per bet, whatever the formula says.

Kelly with several bets at once

If several bets are running at the same time, for example on one matchday, you should not simply add up the Kelly shares without thinking about the total. Ten bets at 5 per cent each mean 50 per cent of the bankroll at risk. Here, a cap per day or per matchday is usually applied.

Conclusion

Kelly is a sensible framework for relating stake to edge. But the number it produces is only as good as your own probability. If you cannot measure that reliably, you are better served with small fixed stakes.