Fractional Kelly explained for betting

In one sentence

Fractional Kelly means staking a set fraction, typically a quarter to a half, of what the full Kelly formula recommends, to cut the swings and protect you when your edge is smaller than you think.

How it works

Full Kelly maximises growth only if your probabilities are exactly right. In real betting they never are, and Kelly punishes overestimated edges harshly. Scaling every stake down gives you a buffer against your own model errors.

The trade-off is favourable. Half Kelly keeps about three quarters of the growth rate while cutting the size of the swings in half. Think of it like driving at 50 mph instead of 70: you arrive a bit later but you are far less likely to crash.

The maths

f = k \times f^{*} = k \times \frac{b\,p - q}{b}

f is the fraction of your bank you actually stake.
k is the Kelly fraction you choose, for example 0.5 for half Kelly.
f* is the full Kelly fraction.
b is decimal odds minus 1, p is your win probability and q is 1 − p.

A useful rule of thumb for small edges:

G(k f^{*}) \approx (2k - k^{2})\, G(f^{*})

G is the long-run growth rate of the bank per bet.

In plain English: half Kelly gives roughly 75% of full Kelly's growth, quarter Kelly roughly 44%, and the swings shrink in proportion to k.

Worked betting example

You back away wins on Match Odds at 3.00 and believe each one lands 36% of the time. Bank £1,000. The figures are illustrative and, to keep the sums clean, leave out commission.

Edge per £1: 0.36 × 2 − 0.64 = +£0.08, an 8% edge.
Full Kelly: (2 × 0.36 − 0.64) ÷ 2 = 4%, a £40 stake. Half Kelly is £20, quarter Kelly is £10.
Growth per bet: full 0.00158, half 0.00119 (75% of full), quarter 0.00070 (44% of full).

Now suppose your model is a little optimistic and the true win rate is 34%, an edge of only 2%. Your stakes do not change, because you do not know you are wrong:

Full Kelly growth becomes −0.00078 per bet: the bank shrinks over time despite a real edge.
Half Kelly growth is almost exactly zero.
Quarter Kelly still grows, at about 0.00010 per bet.

We simulated 500 bets 40,000 times for each case. Final bank is the median result; the last column is the chance of falling 40% or more from a previous peak at some point.

True win rate	Staking	Median final bank	Chance of finishing below £1,000	Chance of a 40%+ drawdown
36%	Full Kelly	£2,203	27.5%	99.2%
36%	Half Kelly	£1,813	16.6%	52.4%
36%	Quarter Kelly	£1,417	14.3%	3.7%
34%	Full Kelly	£678	62.9%	99.9%
34%	Half Kelly	£1,001	48.4%	76.9%
34%	Quarter Kelly	£1,051	44.7%	15.8%

When the model is right, full Kelly wins on median bank but almost guarantees a 40% drawdown. When the model is slightly wrong, full Kelly loses money and quarter Kelly still comes out ahead.

Where it's good

Almost any real staking plan built on model probabilities, since estimation error is unavoidable.
New models with limited track record, where quarter Kelly buys time to gather evidence.
Trading banks that must survive to fund future opportunities.

Limitations and pitfalls

Choosing k is a judgement call; there is no formula that picks the perfect fraction without knowing your true edge.
It shrinks the stake but does not fix a model with no edge. Fractional Kelly on a negative edge still loses, just more slowly.
Commission must still be built into b before you scale.
Small fractions on small banks produce stakes below the Betfair minimum, forcing rounding that changes the plan.
It still assumes bets are settled one at a time; overlapping bets need joint sizing.
The 75%-of-growth rule is only an approximation for small edges.

How to build it

Compute full Kelly after 2% commission, multiply by k, and round to a sensible stake.
Test your chosen k with a Monte Carlo simulation (numpy) that deliberately includes an overestimated edge, as in the table above.
Practical tip: many punters settle on a quarter to a half Kelly and only move up after several hundred bets confirm the edge.

Kelly criterion – the full-stake formula this scales down.
Drawdown analysis – measuring the swings fractional Kelly reduces.
Risk of ruin – the danger of overbetting.
Calibration – how far to trust the probabilities you feed in.
Monte Carlo simulation – testing a staking fraction before using it.