Size the optimal bet.
Optimal bet sizing: f* = W − (1 − W) / R. Most traders use a fraction of full Kelly.
INPUTS
%
Honest probability, not your best month.
Average win ÷ average loss. 1.5 means wins are 1.5× losses on average.
$
For the dollar-equivalent bet sizes.
TRY ONE
RESULT
Full Kelly25.00%
$ at full Kelly$2,500
Half Kelly (50%)12.50%
$ at half$1,250
Quarter Kelly (25%)6.25%
$ at quarter$625
Full Kelly is mathematically optimal for log-wealth but emotionally brutal — expect 50% drawdowns. Most practitioners bet ½ or ¼ Kelly.
HOW IT WORKS
The Kelly criterion solves for the bet size that maximizes long-run geometric growth: f* = W − (1 − W) / R, where W is win rate and R is the win/loss ratio. Bet less and you grow slower than you could; bet more and the variance kills you (negative geometric return even with positive expectancy). The catch: full Kelly is wildly volatile — expected drawdowns to 50% of bankroll happen on the way. Most serious bettors use half or quarter Kelly to trade some growth for sanity. The math is elegant; the practice is humbling.
FAQ
What is the Kelly criterion?
A formula for the bet size that maximizes long-run geometric growth: f* = W − (1 − W) / R, where W is win probability and R is the win/loss ratio.
Why use half- or quarter-Kelly?
Full Kelly is mathematically optimal for log-wealth but unrelentingly volatile — expected drawdowns to 50% of bankroll happen on the path. Fractional Kelly trades some growth for sanity.
Does Kelly apply to trading?
In theory yes, but it assumes you know your win rate and R precisely. Real traders' win rates drift; betting full Kelly on an estimated edge is the textbook way to blow up. Quarter-Kelly is the common practitioner choice.
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