TOOL · KELLY CALCULATOR

Kelly Calculator

The Kelly fraction f* gives the betting fraction that maximises long-run wealth growth. Both models below compute instantly — remember F-Star's default discipline: quarter-Kelly, give up a little to survive the long run.

BINARY KELLY · f* = (b·p − q) / b

Binary Kelly

Win probability p (0–1)Odds b (net win / stake)

Optimal fraction f*

20.0%

f*	GROWTH RETAINED (VS FULL KELLY)	LONG-RUN SURVIVAL (APPROX.)
20.0%Full f*	100.0%	~50%
10.0%Half ½f*	75.0%	~90%
5.0%Quarter ¼f* (F-Star default)	43.8%	>99%

CONTINUOUS KELLY · f* = (μ − r) / (γ·σ²)

Continuous-time Kelly

Expected annual return μ (e.g. 0.25)Annual volatility σ (e.g. 0.70)Risk-free rate r (e.g. 0.02)Risk aversion γ (1=full / 2=half / 4=quarter)

Optimal fraction f* · γ=4

11.7%

full f* = 46.9%

f*	GROWTH RETAINED (VS FULL KELLY)	LONG-RUN SURVIVAL (APPROX.)
46.9%Full f*	100.0%	~50%
23.5%Half ½f*	75.0%	~90%
11.7%Quarter ¼f* (F-Star default)	43.8%	>99%

Results are for education only, not investment advice; inputs are your own estimates and real market parameters are uncertain — which is exactly why fractional Kelly exists.