Quotes About Probability

Charlie Ledley—curiously uncertain Charlie Ledley—was odd in his belief that the best way to make money on Wall Street was to seek out whatever it was that Wall Street believed was least likely to happen, and bet on its happening.

The world's not just a stage. It's a casino, and our lives are games of chance. And when people calculate the odds in any life situation, they are often making judgments about similarity—or (strange new word!) representativeness. You

That was the reason the casino bothered to list the wheel's most recent spins: to help gamblers to delude themselves.

There were a great many interesting questions in the world to which the only honest answer was, "It's impossible to know for sure." "What will the price of oil be in ten years?" was such a question. That didn't mean you gave up trying to find an answer; you just couched that answer in probabilistic terms.

The line between gambling and investing is artificial and thin. The soundest investment has the defining trait of a bet (you losing all of your money in hopes of making a bit more), and the wildest speculation has the salient characteristic of an investment (you might get your money back with interest).

Stories people told themselves were biased by the availability of the material used to construct them...what people remember about the past, [Kahneman and Tversky] suggested, is likely to warp their judgement of the future. We often decide that an outcome is extremely unlikely or impossible, because we are unable to imagine any chain of events that could cause it to occur. The defect, often, is in our imagination.

They would learn to evaluate a decision not by its outcomes--whether it turned out to be right or wrong--but by the process that led to it. The job of the decision maker wasn't to be right but to figure out the odds in any decision and play them well.

People treated all remote probabilities as if they were possibilities. To create a theory that would predict what people actually did when faced with uncertainty, you had to "weight" the probabilities, in the way that people did, with emotion. Once you did that, you could explain not only why people bought insurance and lottery tickets. You could even explain the Allais paradox.*

It's one thing to bet on red or black and know that you are betting on red or black. It's another to bet on a form of red and not to know it.

human imagination is a poor tool for judging risk. People are really good at responding to the crisis that just happened, as they naturally imagine that whatever just happened is most likely to happen again. They are less good at imagining a crisis before it happens—and taking action to prevent it.

The options suited the two men's personalities: They never had to be sure of anything. Both were predisposed to feel that people, and by extension markets, were too certain about inherently uncertain things. Both sensed that people, and by extension markets, had difficulty attaching the appropriate probabilities to highly improbable events. Both had trouble generating conviction of their own but no trouble at all reacting to what they viewed as the false conviction of others.

For example, if you want to know the likelihood that the geese loitering near the LaGuardia Airport runway will cause your plane to crash-land in the Hudson River and the event will become the subject of a major motion picture, you go to see the undersecretary or deputy undersecretary for marketing and regulatory programs, which oversees the Animal and Plant Health Inspection Service, which handles the bewildering set of conflicts in America between people and animals.

If the player had broken his neck the night before the NBA draft, for instance, it would be nice to know. But if you had asked Daryl Morey in 2006 to choose between his model and a roomful of basketball scouts, he'd have taken his model.

Even people trained in statistics and probability theory failed to intuit how much more variable a small sample could be than the general population—and that the smaller the sample, the lower the likelihood that it would mirror the broader population.

In making predictions and judgments under uncertainty," they wrote, "people do not appear to follow the calculus of chance or the statistical theory of prediction. Instead, they rely on a limited number of heuristics which sometimes yield reasonable judgments and sometimes lead to severe and systematic error.

The math of the matter changed with the situation, but, broadly speaking, an attempted steal had to succeed about 70 percent of the time before it contributed positively to run totals.

The first SARS outbreak had ended because those infected had been isolated quickly and prevented from infecting others. Those capable of infecting others were easy to identify because they were so obviously ill. There were few, if any, asymptomatic spreaders. The virus had not vanished, however. "It's still out there," said Joe. "It didn't come from outer space. There's a very meaningful probability that it can arise again.

If the first three chips they withdrew from a bag were red, for instance, they put the odds at 3:1 that the bag contained a majority of red chips. The true, Bayesian odds were 27:1. People shifted the odds in the right direction, in other words; they just didn't shift them dramatically enough. Ward Edwards had coined a phrase to describe how human beings responded to new information. They were "conservative Bayesians.

Even the fairest coin, however, given the limitations of its memory and moral sense, cannot be as fair as the gambler expects it to be," they wrote. In an academic journal that line counted as a splendid

But because he has misjudged how large the sample needs to be if it is to stand a good chance of reflecting the entire population, he is at the mercy of luck.

The Decision to Seed Hurricanes," a paper coauthored by Stanford professor Ron Howard. Howard was one of the founders of a new field called decision analysis. Its idea was to force decision makers to assign probabilities to various outcomes: to make explicit the thinking that went into their decisions before they made them.

chose the surgery. People facing a life-and-death decision responded not to the odds but to the way the odds were described to them.

The draft has never been anything but a fucking crapshoot," Billy had taken to saying, "We take fifty guys and we celebrate if two of them make it. In what other business is two for fifty a success? If you did that in the stock market, you'd go broke.

doctors don't think probabilities apply to their patients