How the Kelly criterion is calculated
The Kelly criterion picks the share of the bank that makes the bank grow fastest over a long run of bets. The share depends on two numbers: your win probability p and the decimal odds k.
share of bank = (p × k − 1) / (k − 1)
The numerator p × k − 1 is the expected value of the bet per unit staked. If it is zero or negative, Kelly gives zero: do not bet. For example, with a probability of 55% and odds of 2.00 the expected value is +10% and full Kelly is 10% of the bank.
Which systems the calculator compares
- Full Kelly gives the fastest bank growth, but only if the probability is known exactly. Its drawdowns are deep.
- Half and quarter Kelly are the same stake divided by 2 and by 4. The bank grows more slowly, but an error in the probability estimate costs far less.
- Flat is the same share of the bank on every bet, whatever the probability and odds. The simplest system.
- Stake to win the flat amount sizes the bet so that a win pays the flat amount: the higher the odds, the smaller the stake.
The main Kelly trap
The formula trusts your probability completely. If the estimate is too high by just a few percentage points, full Kelly stakes too much and the bank is lost faster than with flat staking. The line under the table shows what the right share would be with a probability 5 points lower. That is why in practice people use half or quarter Kelly, and without a proven edge they bet flat.
Frequently asked questions
How do I calculate stake size with the Kelly criterion?
Multiply the win probability by the odds, subtract one and divide the result by the odds minus one. That gives the share of the bank; if it is negative, do not bet.
Why use half or quarter Kelly?
Because a probability is always estimated with an error. Fractional Kelly grows the bank more slowly but copes with an overestimate and long losing streaks far better than full Kelly.
What stake size should I use without any calculations?
The conservative option is a flat stake of 1–2% of the bank per bet. It needs no probability estimate and survives long losing streaks.
What does it mean when Kelly shows zero?
Your probability does not give the bet a positive expected value at these odds. Under the Kelly criterion that bet should not be made.
More on the blog
The xG.Football model calculates result, totals and both-teams-to-score probabilities for the day's matches — handy to compare with the odds.
Football predictions →The content of this site is informational and is not an invitation to gamble. Betting carries a risk of losing money and is for adults only (18+). Please play responsibly.