Kelly Criterion, in plain words
The Kelly criterion is a formula for how much of your bankroll to stake on a bet with an edge. It stakes more when the edge is bigger and nothing when there is no edge. Over a long run, betting the full Kelly amount grows a bankroll faster than any other fixed fraction, if your probabilities are right.
That last condition is the catch. Your chance estimate is never exact, and full Kelly punishes an overestimate hard: bet too much on edges you do not have and the swings get large fast. That is why most serious bettors use a fraction, a half or a quarter, which gives up some growth for much smaller drawdowns.
Kelly also needs a real edge to start with. With no edge, the formula says stake nothing, which is the right answer. Use it to size bets your numbers say are positive, and treat its answer as a ceiling rather than a target.
The idea, drawn
Worked example · illustration
55% to win at −110
- Win chance
- 55%
- Price
- −110
- Full Kelly
- 5.50%
- Quarter Kelly
- 1.38%
- −110 pays b = 0.9091 per dollar staked.
- Kelly = (b x p - (1 - p)) / b = (0.9091 x 0.55 - 0.45) / 0.9091 = 5.50%.
- On a $1,000 bankroll that is $55.00 at full Kelly, $13.75 at a quarter.
If your 55% is really 53%, the full-Kelly stake is far too big. The quarter stake survives the mistake.