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STORY · Seventy Years of Kelly2026.06.18· 6 min read

The Half-Line Formula at Bell Labs

In 1956 a 32-year-old physicist and former pilot wrote half a line on a note pad, translating Shannon's information theory into wealth growth — and never used the formula himself.

Robert B.

In 1956, in a quiet Bell Labs corridor at Murray Hill, New Jersey, the 32-year-old John L. Kelly Jr. pushed a 'gambler with an inside wire' thought experiment to its limit and wrote half a line: f* = (b·p − q)/b. It translated his colleague Shannon's information theory into something more practical — one more bit of information, one more unit of wealth growth.

What the formula really says

Channel capacity = long-run wealth growth rate. Information converts one-for-one into return.

Literally it reads 'what fraction of capital to bet', but what it truly says is: size your bet in proportion to your information edge, and scale it with your wealth — winning enlarges the next bet automatically, losing shrinks it. Together these make it native to compounding, and the growth-optimal strategy over the long run.

1956
Paper published
A New Interpretation of Information Rate
41
Died young
Stroke, 1965, on a Manhattan sidewalk
0
Times he used it to invest

When he died, not a single financial institution used the formula. But five years earlier, Shannon had handed a copy to the 28-year-old Thorp — the journey was only beginning. F-Star's lib/kelly-formulas.ts turns that half line into code running on-chain.