Fractional Kelly

Full Kelly maximises long-run growth but is far too violent when the model is imperfect.

We take a fraction (quarter Kelly by default), which keeps most of the growth with a fraction of the swings.

When the edge is zero or negative the formula returns zero and the strategy simply declines the bet.

f* = (p × (odds − 1) − (1 − p)) / (odds − 1); stake = kelly_fraction × f* × bankroll

• p — Model probability of the selection winning
• odds — Decimal price taken
• kelly_fraction — Slice of full Kelly actually staked, e.g. 25%

1. Price 2.10, model probability 0.53 → b = 1.10, f* = (0.53 × 1.10 − 0.47) / 1.10 ≈ 0.10.
2. Quarter Kelly: 0.25 × 0.10 ≈ 2.5% of bankroll.
3. On a €1,000 bankroll that is a €25 stake; on a €400 bankroll it is €10.

If the bet wins: The bankroll rises, and the next Kelly stake rises with it — but only when a genuine edge is present.

If the bet loses: The bankroll falls and stakes shrink. Zero or negative edge returns a zero stake and the bet is declined.

Reset conditions: No ladder to reset. Each bet is sized independently from its own edge and price.

• Situations where the probability estimate is reasonably trustworthy
• Maximising long-run growth per unit of risk
• Portfolios where edge size varies a lot between bets