The Kelly criterion tells you the fraction of your bankroll that maximises long-run growth. It is correct mathematics and, nearly always, the wrong tool — because it assumes you know the true probability.
For decimal odds o and true win probability p:
f* = (p · o − 1) / (o − 1)The numerator is your edge per unit staked. The denominator is the amount you win per unit. So the stake is your edge divided by the payout, which is why a small edge produces a small stake.
| True probability (odds 2.00) | Full Kelly | Half Kelly |
|---|---|---|
| 50% | 0% | 0% |
| 52% | 4% | 2% |
| 55% | 10% | 5% |
| 58% | 16% | 8% |
A 3-point edge at even money is a 10% bankroll bet. That is the same edge most people would describe as "slight". Kelly says it is a tenth of everything you have.
Kelly is optimal only if p is exact. If your 55% is really 53%, you are
staking as if the edge were twice what it is; if it is really 50%, you are staking 10% of
bankroll on a zero-edge bet, which is a slow drain with large swings.
Estimation error in p does not produce a small error in f*.
It produces a proportionally large one, because f* is roughly linear in the edge
while the edge itself is a difference of two numbers that are close together.
Half Kelly captures about three quarters of the growth rate with half the volatility. Quarter Kelly is common among people who admit their probabilities are estimates. It is not timidity; it is a correction for the fact that the input is noisy.
If you are not modelling bankroll growth — if you are staking fixed amounts for interest — Kelly is not the right frame at all. The useful part of the idea is the first sentence: stake in proportion to edge, not to confidence. Flat stakes on a negative-expectation bet lose steadily; proportional stakes on a noisy estimate can lose faster than flat ones.
Kelly does not make a losing bettor win. It makes a winning bettor grow faster, and a betting system with an overstated edge lose money at the optimal rate.