The central idea
The Kelly criterion converts an estimated probability and an available price into a theoretical fraction of bankroll. Fractional Kelly scales that result.
f* = (bp − q) ÷ b
Worked example
At decimal odds of 2.10 with an estimated 52% chance, Full Kelly is about 8.36% of bankroll. Half Kelly is 4.18%. If the estimate falls below break-even, the formula produces no positive stake.
Limits of the calculation
Kelly is extremely sensitive to probability error and can produce aggressive stakes. Fractional Kelly reduces the fraction but cannot repair an inaccurate estimate.