What Kelly actually tells you to do
The formula maximises long-run growth and assumes you know your edge exactly. You do not, which is why full Kelly is the wrong instruction.
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 penalty for overstaking is not symmetric with the reward for getting it right. Staking twice the correct Kelly fraction gives back the entire expected growth advantage. Staking more than twice turns a method with a positive edge into one that trends to zero. Understaking, by contrast, merely grows more slowly.
Which is why almost nobody uses it straight
Half Kelly captures about three quarters of the growth with roughly half the volatility. Quarter Kelly is common among people who have been doing this a while, and the reason is not timidity: it is that their estimate of their own edge has been wrong before.
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 long-run growth and nothing else. It does not minimise drawdown, it does not care how the ride feels, and it assumes you can keep betting forever at the same edge. A person who will stop after a 50% drawdown has a constraint the formula does not model, and for them the optimal stake is smaller than any version of Kelly says.
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 do people use fractional Kelly?
Because the formula assumes the edge is known exactly and it never is. Staking a half or a quarter of the Kelly amount trades a little growth for a large reduction in the damage an overestimated edge does.
What happens if you overestimate your edge with full Kelly?
You overstake, and the penalty is asymmetric. Betting twice the correct Kelly fraction gives back all of the expected growth, and more than twice it turns a winning method into a losing one.