Kelly criterion
Computes the fraction of capital that grows an account fastest, and the half of it most traders use. Use it as a ceiling on position size.
The Kelly criterion answers a precise question: what fraction of capital should be staked on each bet to maximise the long run growth rate? Stake less and the account grows more slowly than it could. Stake more and growth actually falls, because the losses compound against a smaller base. Beyond roughly twice the Kelly fraction the expected growth turns negative even with a genuine edge, which is a striking result worth remembering.
Full Kelly is the mathematically optimal fraction, and almost nobody trades it. The reason is that it is optimal only if your win rate and payoff ratio are exactly right and never change. They are neither. They are estimates from a limited sample, and overestimating your edge by a little means overbetting by a lot. Full Kelly also produces drawdowns that are brutal to live through, commonly cutting an account in half on the way to its long run growth.
Half Kelly is the working compromise. It gives up roughly a quarter of the theoretical growth rate in exchange for a large reduction in the depth of drawdowns, and it is far more forgiving of an edge that turns out to be weaker than you thought. Many professional risk frameworks sit at half Kelly or below. Treat the half Kelly figure as an upper bound and consider whether a quarter of it is more appropriate for a strategy you have not traded for long.
When Kelly comes back negative, the card is telling you that this combination of win rate and payoff has no edge at all. The correct stake is nothing. No sizing rule rescues a negative expectancy, and a negative Kelly is the same message that the risk of ruin card delivers in a different currency.
A caveat about the inputs. Kelly is very sensitive to the payoff ratio, and the payoff ratio computed from a small sample of trades is unstable. If your record holds only a few dozen trades, the fraction shown here carries a wide margin of error. Use it to notice that you are risking five percent when the maths supports one, not to fine tune between 1.8 and 2.1 percent.