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Kelly was aware that there is one type of favorable bet available to everyone the stock market.
William Poundstone
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William Poundstone
Age: 69
Born: 1955
Born: March 29
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Kelly
Favorable
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Everyone
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Expectation is a statistical fiction, like having 2.5 children.
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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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At a bare minimum, understanding entails being able to detect an internal contradiction: a paradox.
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The assumption that anything true is knowable is the grandfather of paradoxes.
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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.
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Your second ducat, like your second million, is never quite as sweet.
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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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Are there any mythical beasts which aren't simple pastiches of nature? Centaurs, minotaurs, unicorns, griffons, chimeras, sphinxes, manticores, and the like don't speak well for the human imagination. None is as novel as a kangaroo or starfish.
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Samuelson, however, hedged his personal bets - by putting some of his own money in Berkshire Hathaway.
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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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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 and purchasing the one that yields the higher utility, he says. We make do with guesstimates and a vague recollection of what things are “supposed to cost.”
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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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The story of the Kelly system is a story of secrets - or if you prefer, a story of entropy.
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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.
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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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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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A bit is worth 10,000 basis points.
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The ultimate compound return rate is acutely sensitive to fat tails.
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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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