A bit is worth 10,000 basis points.

Your second ducat, like your second million, is never quite as sweet.

A bit is worth 10,000 basis points.

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.

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.

"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.

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