Why full Kelly is a trap in practice
The Kelly criterion gives the bet size that grows capital fastest. It also assumes you know your win rate exactly, and you do not.
How this was made: an AI assistant drafted this guide under the operator's direction, and the numbers were checked against the calculators on this site. Nothing here is investment advice.
What Kelly sizing says
In 1956, John L. Kelly Jr. of Bell Labs published a formula for the share of your capital to bet when you know the odds and the probabilities, if you want your capital to grow as fast as possible in the long run. For a bet that wins b times what it risks with probability p, the share is p − (1 − p) ÷ b.
Take a 55% win rate on even-money bets: 0.55 − 0.45 ÷ 1 = 10% of capital per bet. It sounds like a rule you could trade by. It is not, for the reasons below.
The formula is fragile
Everything in it depends on p, and p is an estimate. If the true win rate is 50% and not 55%, the right size is 0, not 10%. A five-point error removes the entire edge.
Betting too much is also worse than betting too little. In this example the growth rate per bet is 0.50% at 10%, 0.38% at 5%, and -0.01% at 20%, twice the Kelly size. At twice Kelly the long-run growth is gone, and you take far more risk to get nothing. The curve is lopsided: a size below Kelly gives up a little growth, and a size above it can lose all of it.
What full Kelly feels like
We simulated the 55% even-money bet with 40,000 runs for each size, each starting at 1.0 and betting a fixed share of the current capital. At full Kelly (10%), 32% of runs fell to half of their starting capital before they doubled it. At half Kelly (5%) the figure was 10%, and at quarter Kelly (2.5%) it was under 1%.
Over 200 bets, with 20,000 runs each, the median run fell 70% from its peak at some point at full Kelly. At half Kelly the median worst fall was 42%, and at quarter Kelly 23%. These are results of the correct formula applied to a perfectly known win rate. Few people would hold a position through a 70% fall.
The inputs are the weak point
Trade results are not independent coin flips. They cluster, they depend on the market regime, and the average win and loss change over time. The win rate has to be estimated from a record, and a short record is noisy. In our own analysis a typical trend rule needed about 34 months of live trades before its result could be told apart from luck: how long it takes to prove a strategy. Until then, the Kelly fraction you compute is a number with a very wide error bar.
How the formula is used sensibly
People who use it tend to treat the result as a ceiling and bet a fraction of it, often half or a quarter, and cap the size by the largest fall they could live with. The sensitivity column in the Kelly calculator shows what the number becomes if your win rate is five points lower than you think. If it falls to zero, you have learned that the edge depends on a decimal you do not know.