What Kelly actually tells you to do
The formula maximises long-run growth for known inputs. Estimated probabilities make raw Kelly fragile, so uncertainty belongs in the stake.
On this page
Kelly answers one question precisely: given a known probability and a known price, what fraction of the bankroll maximises the rate the bankroll grows over many repetitions? For a simple bet the answer is the edge divided by the odds against.
Back something at 3.00 that you believe wins 40% of the time. The edge is
0.4 times 3 minus 1, which is 0.2. Divide by the odds against, which is 2, and
Kelly says stake 10%.
The assumption doing all the work
That calculation took your 40% as a fact. It is not a fact, it is an estimate, and the formula has no place to put the uncertainty around it.
This matters because the growth penalty for a mistaken stake is not captured by the headline edge. Overstating the win probability pushes the stake above the true growth optimum and can eventually make expected logarithmic growth negative. The often repeated claim that twice Kelly gives back all growth is a local approximation, not a universal identity for every probability and price.
Why shrinkage is often justified
Near the optimum, a quadratic approximation says staking a fraction c of
Kelly retains roughly 2c - c² of maximum expected log growth. That makes half
Kelly about three quarters in that approximation, not in every real market.
More importantly, Baker and McHale show that parameter uncertainty is a reason
to estimate shrinkage rather than treating the raw probability as known.
Given that every figure here is an estimate with error around it, and given what a bad run does to a bankroll, the fractional version is the one that matches the actual state of knowledge.
What this does not tell you
Kelly maximises expected logarithmic growth under its model. It does not directly minimise drawdown or encode a personal stopping threshold. A person who will stop after a 50% drawdown has a constraint the basic calculation does not model, so the raw Kelly fraction is not a complete staking decision.
Common questions
What is the Kelly criterion?
A formula for the stake fraction that maximises the long-run growth rate of a bankroll, given a known probability and a known price.
Why use fractional Kelly?
Shrinking the raw Kelly stake can improve out-of-sample performance when the win probability is estimated rather than known. An arbitrary half or quarter is a risk choice, not a substitute for modelling the uncertainty.
What happens if you overestimate your edge with full Kelly?
You stake more than the true inputs justify. That can reduce or reverse expected logarithmic growth, but the exact penalty depends on the actual probability and odds.