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%

Fractional Kelly sizes each stake from the estimated edge and the price, then deliberately stakes only a fraction of what the full Kelly formula asks for, to absorb error in the probability estimate.

Inputs used

• Decimal price at lock
• Model probability p for the selection
• This strategy's own live bankroll
• Kelly fraction (25% of full Kelly)

f* = (p × (odds − 1) − (1 − p)) / (odds − 1); stake = 25% × f* × bankroll

Limits and caps, applied in this order

• Bankroll share cap — no single stake may exceed 5% of that strategy's own live bankroll.
• Absolute cap — no single stake may exceed 10× the base stake (€100.00).
• Bankroll cap — a stake can never exceed the money the strategy actually has left.
• Minimum executable stake — below €1.00 the bet is declined and recorded as skipped.
• A zero or negative full-Kelly value declines the bet outright.

Rounding: The stake is rounded to the nearest €0.50 after the Kelly maths. If a cap was actually binding, the rounding is forced downwards, so rounding can never widen exposure beyond a cap.

Bankroll behaviour: Compounds like percentage staking, but the multiplier itself changes bet by bet with the size of the estimated edge.

Sequence behaviour: Each bet is sized independently. There is no ladder, no streak counter and no memory of the previous result beyond the bankroll it left behind.

Reset conditions: Nothing to reset — every bet starts from its own edge and price.

• No €10 floor is applied. A small edge produces a genuinely small stake.
• Kelly is the only one of the four whose stake reacts to the probability estimate, which also makes it the most sensitive to model error — that is precisely why a fraction is used.

Documented against staking logic v2, from a €10.00 base stake. These figures are read from the same module the robot calls when it sizes a live paper bet.

• The probability p is the blended model output recorded at lock time, not a value re-derived later.
• The full-Kelly value, the fraction used, the rounded stake and the minimum applied are all written to a per-bet audit record, so any historical stake can be recomputed.

Risk profile: Moderate. Theoretically the strongest long-run growth per unit of risk, entirely conditional on the probability estimates being roughly honest.

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 €25.00, rounded to the nearest €0.50; on a €400 bankroll it is €10.00.

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