Fractional Kelly betting strategy explained

Kelly needs two inputs: the probability of winning and the net price. It returns the fraction of the bankroll to risk. When the edge is zero or negative, the formula returns zero or less, which correctly means no bet.

f* = ((odds − 1) × p − (1 − p)) ÷ (odds − 1) stake = bankroll × f* × fraction

With a 45% estimate at 2.50 and a €1,000 bankroll: b = 1.50, so f* = (1.50 × 0.45 − 0.55) ÷ 1.50 = 0.0833. Full Kelly would stake €83.33 — over 8% of the bankroll on a single football match. At quarter Kelly the stake is €20.83, which is a risk level a bankroll can survive being wrong about.

Kelly is only optimal if p is exact. Overestimate your edge and full Kelly overstakes dramatically — a two-point error can turn optimal growth into systematic overbetting. Halving the fraction removes most of the variance while retaining most of the growth.

BetBuddy's implementation applies a fraction, rounds to the nearest €0.50 and enforces a €1 minimum executable stake. There is no €10 floor: a marginal edge produces a genuinely small stake, which is the entire point of edge-proportional sizing.

Kelly assumes an honest, reasonably calibrated probability. If your estimates have not been checked against outcomes over a real sample, flat staking is safer and more informative. Calibration is measurable — Brier score and log loss are the standard checks, and BetBuddy publishes both.

Betting carries financial risk and no staking plan removes it. Historical performance does not guarantee future results, and BetBuddy runs in paper mode: stakes are simulated and no bookmaker account is connected.

Full Kelly for a 45% estimate at odds of 2.60 is (0.45 × 1.60 − 0.55) / 1.60 = 10.6% of the bankroll — €106 on €1,000. That is the growth-optimal stake if the 45% estimate is exactly right, and a catastrophic one if it is 5 points optimistic. Quarter Kelly stakes €26.56 instead, giving up a slice of theoretical growth in exchange for a far shallower drawdown profile.

The asymmetry is the point. Overbetting a Kelly fraction hurts more than underbetting it by the same amount, and model probabilities are always estimates, so the honest response is to bet a fraction of what the formula suggests.

stake = bankroll × fraction × ((p × (odds − 1)) − (1 − p)) / (odds − 1)

A Kelly implementation that returns the same number bet after bet is not running Kelly. Because the formula responds to both edge and price, a healthy Kelly ledger shows a wide spread of stakes: small ones on 3% edges at short prices, larger ones where the estimated edge is genuinely big.

BetBuddy removed an old €10 stake floor precisely because it flattened the distribution and made the plan indistinguishable from fixed staking. The engine now uses a €1 minimum, rounds to the nearest €0.50 for executability, and writes the bankroll, model probability, price, raw fraction and final stake into a stake audit record attached to every bet.

• Identical stakes across many bets indicate a floor or a cap, not Kelly.
• A fraction above one half is aggressive for model-driven estimates.
• Estimate error, not the formula, is the dominant risk in Kelly staking.