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 improbability.

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 this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric means of outcomes.

A bit is worth 10,000 basis points.

"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 inflation rate. For a buy-and -hold investor, commissions and taxes are small.

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 a law that has been misunderstood by gamblers (and investors) ever since.

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 improbability.