The One-Syllable War

What actually happened

John Kelly's 1956 paper connected information theory to bet sizing: wager to maximize the growth rate of wealth and you can't be beaten in the long run. Shannon championed it; Thorp used it in casinos and markets; it became the quiet sizing rule of a generation of quants.

Paul Samuelson's objection was real: maximizing growth rate is not the same as maximizing your utility, and the 'long run' can be longer than your life. After years of arguing, he published 'Why we should not make mean log of wealth big though years to act are long' (Journal of Banking & Finance, 1979), every word one syllable, to be sure, as he put it, that the point could not be missed.

Both sides were right about different questions, which is why the fight never ended.

The longer arc

Kelly never saw his formula become a cult. A Texan who flew combat missions in the Pacific during World War II before joining Bell Labs, he worked on speech synthesis and information theory alongside Shannon and died suddenly of a stroke on a Manhattan sidewalk in 1965, at 41, nine years after publishing the paper and long before Thorp or Wall Street had made it famous. He never lived to defend it against Samuelson.

The fight outlived him by decades. Samuelson, who had won the second Nobel Memorial Prize in economics in 1970, kept sparring with Kelly-criterion advocates through the 1970s, and his one-syllable paper was less a joke than a provocation aimed at economists he thought were being seduced by an elegant formula with hidden assumptions about risk tolerance and time horizon. Practitioners mostly kept using it anyway, usually at a fraction of the full Kelly stake, precisely to blunt the wild swings both sides agreed the pure formula produces. Warren Buffett and Bill Gross have both cited Kelly-style thinking in describing how they size positions.