THE MATHS, MADE CLEAR
How it works
The model compares your estimated probability with the break-even probability in the price. A positive difference produces a bankroll fraction; a zero or negative edge produces no positive Kelly stake.
Full Kelly fraction = (b × p − q) ÷ b, where b = decimal odds − 1, p = estimated win probability and q = 1 − p.
Worked examples
Positive edge
At 2.10 with a 52% estimate, Full Kelly is 8.36% of bankroll. Half Kelly is 4.18% and Quarter Kelly is 2.09%.
No positive stake
At 2.00 with a 40% estimate, the raw Kelly value is negative. The suggested mathematical stake is therefore zero.
Limitations and interpretation
Kelly maximises theoretical logarithmic bankroll growth only when the probability estimate and price are reliable. Estimation error, limits, correlation and variance can make the result dangerously aggressive.