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Maths · the arithmetic behind a price

Maths

Why fractional Kelly is the version people actually use

Halving the Kelly stake retains roughly three quarters of the long-run growth rate while cutting the volatility by about half. Quarter Kelly gives up more growth and is far calmer again.

Growth rate falls off slowly either side of the optimum while volatility falls off quickly below it. That asymmetry is why under-betting is cheap and over-betting is expensive, and why every practical version errs downward.

The trade in numbers Full Kelly at a 55 per cent edge stakes 10 per cent. Half Kelly stakes 5 and keeps about 75 per cent of the growth. Quarter Kelly stakes 2.5 and keeps about half, with drawdowns most people can actually live with.

It does not fix a wrong edge estimate; it only reduces the damage. Half of a fabricated edge is a smaller version of the same mistake, applied with the same false confidence.

That is also the expensive part. The fraction is often chosen to feel comfortable rather than from any property of the bettor's edge, which makes it a psychological control wearing mathematical clothes. That is fine, as long as it is named honestly.

What to do with it. Pick a fraction, write it down, and treat it as fixed. Adjusting it after results is staking by mood with extra steps.

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