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Far from preventing gambler's ruin, martingale accelerates it.
William Poundstone
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Shannon's most radical insight was that meaning was irrelevant.
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Expectation is a statistical fiction, like having 2.5 children.
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By the mid-1930s, Moe Annenburg was AT&T's fifth largest customer.
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In real conversations, we are always trying to outguess each other.
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The ultimate compound return rate is acutely sensitive to fat tails.
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Your second ducat, like your second million, is never quite as sweet.
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The assumption that anything true is knowable is the grandfather of paradoxes.
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The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.
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Kelly was aware that there is one type of favorable bet available to everyone; the stock market.
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At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.
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To hedge the bets he made every working day, Meriwether kept a set of rosary beads in his briefcase.
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Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
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The best strategy is one that offers the highest compound return consistent with no risk of going broke.
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The problem with winning at blackjack and sports betting is that sooner or later a big guy in a suit tells you to leave.
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Use "entropy" and you can never lose a debate, von Neumann told Shannon - because no one really knows what "entropy" is.
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The best paradoxes raise questions about what kinds of contradictions can occur—what species of impossibilities are possible.
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Samuelson spotted a mistake in Bacheliers work. Bachelier's model had failed to consider that stock prices cannot fall below zero.
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From Adam Smith through John Maynard Keynes, economics had been mostly talk. At Harvard economics was talk. At MIT, Samuelson made it math.
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There were many at Bell Labs and MIT who compared Shannon's insight to Einstein's. Others found that comparison unfair - unfair to Shannon.
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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.
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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 of science.
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For reasons mathematical, psychological, and sociological, it is a good idea to use a money management system that is relatively forgiving of estimation errors.
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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.
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The dealer now theorized that Thorp was memorizing the entire deck. He knew exactly which cards remained in the deck and bet accordingly.
Thorp said it was impossible for any one to do that.
William Poundstone
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At last, in 1611, was made, under the auspices of King James, the famous King James version; and this is the great literary monument of the English language.
Lafcadio Hearn
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