Many people believe that money in this country is minted by the U.S. Treasury. Over the years, I have come to a different conclusion.

Why? Everyone I know who gambles at Las Vegas or Atlantic City comes back and answers my question, "How did you do?" with, "Oh, pretty good. I won a few dollars." Yet the casinos are spilling over with money and ablaze with light and spectacles. They are clearly doing well. The only explanation is that money is being fabricated there, in some deep underground mint.

Of course, a more cynical person might offer a different answer. Is it possible that people have a talent for self-delusion when it comes to gambling and the odds of winning, and a poor memory of what they won or lost? History certainly supports the cynics. Six-sided dice, very similar to those in use today, have been found in what is now northern Iraq. They are made of clay, and are almost five thousand years old. People were gambling back then, and certainly well before that. You can bet that, as now, the odds favored the house.

Presumably, ancient gamblers knew that "fair" dice should show each score from one to six about an equal number of times, if you throw them over and over. In fact, that was (and is) the definition of fair dice. If you throw three dice, then you must make a score between three and eighteen. The amazing thing is that no one, a thousand years ago, knew how to calculate the odds of making any particular score. Gambling was partly guesswork and hunches and superstition. It still is, for most people, though experienced gamblers know that the chance of scoring a three with three dice is a lot less than the chance of scoring a ten, and professionals know the exact odds.

The trouble is, statistics, and the calculation of the probabilities that underlie them, are very tricky things. They can fool even smart and well-educated people. Here is an example with implications that go beyond winning or losing money.

Suppose that you have been exposed to the rare disease of Galloping Crut, and the chance that you have it is known to be one in ten thousand. The operation to treat the disease is long and painful (and, of course, expensive). Your doctor suggests that you be tested. However, he points out that the test, like most medical tests, is not perfect. Sometimes it gives a "false positive," saying that you have the Galloping Crut when you don't; and sometimes it gives a "false negative," saying you don't have the disease when actually you do. Tests are usually biased to prefer false positives over false negatives, because it's better to think you have Galloping Crut when you don't, than to forego treatment when you have the disease. Your doctor tells you that the false positive rate is two percent, and the false negative rate is half a percent.

You take the test. The result shows that you are suffering a bad case of Galloping Crut. You say to yourself, two percent false positive, there's a 98 percent chance that I've got the dread disease. You are all ready to grit your teeth and reach for your checkbook, but before you do so, you think a little more.

You argue, if I looked at ten thousand people who had been exposed to the disease, on average only one of them would have caught it, because the chance of infection is one in ten thousand. But if I tested those ten thousand people, the test would say that 200 of them (two percent false positives) had the disease. So the actual chance that I have the Galloping Crut is only one in two hundred and one - less than half a percent, rather than the 98 percent that I at first thought. Before any operation, I will at the very least ask for a repeat of the test.

The worst thing about this example is that a case very like it was presented to a group of physicians and fourth-year medical students. Almost half of them came back with the 98 percent figure as their answer. Less than one in five of them came back with the correct answer, of less than half a percent. Our intuition when it comes to statistics is often highly misleading.

Here's another example. Suppose that every family in the world adopts the same policy toward having a family. They will have children until a boy is born, and then they will stop. Intuition might suggest that this will lead in the next generation to a population in which boys vastly outnumber girls. In fact, provided that the probabilities of having a boy or a girl are equal, the next generation will have equal numbers of boys and girls.

Our lack of intuitive feel for probabilities is not the only problem. No matter what people try to prove with statistics, it can't be done. Statistics cannot be used to establish cause and effect. They can only show that certain things correlate with certain others.

A famous example of this occurred about forty years ago. One of the century's greatest statisticians, Ronald Fisher, was asked if the evidence available at the time showed that cigarette smoking caused lung cancer. There was quite a bit of evidence of problems, even then. However, Fisher answered, absolutely correctly in a mathematical sense, that statistics did not - and could not - prove that smoking caused cancer. All that could be said was that the two things were strongly correlated. That was enough for the tobacco companies. They rushed off to announce, "Famous expert says no proof that smoking causes cancer."

It is often said that you can prove anything with statistics. You can actually prove nothing, but you certainly can mislead. I will end with two of my favorite statistics. Both are perfectly accurate, and each is perfectly misleading.

1) An American has an average of one ovary and one testicle.

2) The average resident of southern Florida is born Hispanic and dies Jewish.

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