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 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 place on money.

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.

In The Tricky Art of Co-Existing, Sandi Toksvig navigates life's little dilemmas with wit and not-so-common sense. You'll learn the strange history of common courtesy and the one true secret of social success: how to not drive everyone around you crazy.

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