"Average" isn't so hot at the race track given those steep track takes. "Average" is pretty decent for stocks, something like 6 percent above the inf….

The best paradoxes raise questions about what kinds of contradictions can occur-what species of impossibilities are possible..

A bit is worth 10,000 basis points..

The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy..

There is a deep connection between Bernoulli's dictum and John Kelly's 1956 publication. It turns out that Kelly's prescription can be restated as th….

Expectation is a statistical fiction, like having 2.5 children..

Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway..

Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is..

In real conversations, we are always trying to outguess each other..

The ultimate compound return rate is acutely sensitive to fat tails..

The best strategy is one that offers the highest compound return consistent with no risk of going broke..

Bernoulli's real contribution was to coin a word. The word has been translated into English as "utility". It describes this subjective value people p….

Kelly was aware that there is one type of favorable bet available to everyone; the stock market..

Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estat….

Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy o….

The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its impro….

Shannon's most radical insight was that meaning was irrelevant..

The engine driving the Kelly system is the "law of large numbers." In a 1713 treatise on probability, Swiss mathematician Jakob Bernoulli propounded ….

There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon..

At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox..

People tend to be clueless about prices. Contrary to economic theory, we don't really decide between A and B by consulting our invisible price tags a….