Suppose you have found a bet where you really do have an edge. The price is 3.00, and you are confident the true chance is 40%, not the 33% the price implies. How much should you stake?
Stake too little and you waste the edge. Stake too much and a normal losing run will wipe you out before the edge has time to pay. Somewhere in between is a stake that grows your bankroll faster than any other in the long run. In 1956, a physicist at Bell Labs named John Kelly worked out exactly where that point is. His answer is the Kelly criterion, and it is the idea this company is named after.
The formula
For a simple bet that either wins or loses, the fraction of your bankroll to stake is:
f = (b × p − q) ÷ b
- b is the profit per £1 staked — the decimal odds minus one. At 3.00, b = 2.
- p is your probability of winning.
- q is your probability of losing, which is 1 − p.
The top line, b × p − q, is your edge — how much you expect to make per £1 staked. Dividing by b turns that edge into a stake size.
A worked example
Back to our bet: odds 3.00, so b = 2. You think p = 0.40, so q = 0.60.
f = (2 × 0.40 − 0.60) ÷ 2 = (0.80 − 0.60) ÷ 2 = 0.20 ÷ 2 = 0.10
Kelly says to stake 10% of your bankroll. With £1,000, that is £100.
Now change one thing. Say you think the chance is only 35%: f = (2 × 0.35 − 0.65) ÷ 2 = 0.025, so 2.5%. And if you think it is 33%, the same as the price, f = 0 — no bet. Kelly automatically stakes nothing when you have no edge, and it stakes more the bigger your edge is. That is what makes it useful.
Why it works
Most staking advice is a rule of thumb. Kelly is a proof. If you know your true edge, staking the Kelly fraction gives the highest possible long-term growth rate of your bankroll. Any bigger stake grows more slowly — and at twice Kelly, growth drops to zero. Any smaller stake is safer but slower. There is a peak, and Kelly sits on it.
It also never lets you go bust, because it always stakes a fraction of what you have. Lose and the next stake is smaller; win and it grows. Your bankroll compounds.
The catch
The formula needs p, and you never know p for certain. You have an estimate. If your estimate is too optimistic — and most people’s are — you will stake more than the real Kelly amount, which is the one mistake Kelly punishes hardest. Overbetting is worse than underbetting.
Full Kelly is also wild. Even with a real edge, a 10% stake on a 40% shot will lose six times in a row fairly often. Drawdowns of half your bankroll are normal. Very few people can hold their nerve through that, and a strategy you abandon at the bottom is worse than no strategy at all.
Fractional Kelly: what professionals actually do
The standard fix is to stake a fraction of the Kelly amount — usually a half or a quarter. Half Kelly keeps about three quarters of the growth rate while cutting the size of the swings roughly in half. It also gives you a margin for error if your probabilities are a bit off. Ed Thorp, who used Kelly to beat blackjack and then the stock market, recommended exactly this.
In our example, half Kelly on a £1,000 bankroll is £50; quarter Kelly is £25. Smaller, calmer, and still growing faster than a flat stake with the same edge.
Where Kelly Stake fits
Your model supplies p. The exchange supplies the odds. Kelly Stake does the arithmetic, applies the fraction you have chosen, and checks the result against hard limits before any order goes to the market. The formula is the easy part. Having a p you can trust is the work — which is why the platform is built around backtesting first.
Remember
- Kelly stake = edge ÷ (odds − 1). No edge, no bet.
- Full Kelly maximises growth but is very volatile.
- Overbetting is the expensive mistake. Use half or quarter Kelly.
- The formula is only as good as your probability.