Why the “Balancing Force of the Universe” Is Baloney: Gambler’s Fallacy
In the summer of 1913, something incredible happened in Monte Carlo. Crowds gathered around a roulette table and could not believe their eyes. the ball had landed on black twenty times in a row. Many players took advantage of the opportunity and immediately put their money on red. But the ball continued to come to rest on black. Even more people flocked to the table to bet on red. It had to change eventually! But it was black yet again—and again and again. It was not until the twenty-seventh spin that the ball eventually landed on red. By that time, the players had bet millions on the table. In a few spins of the wheel, they were bankrupt.
The average IQ of pupils in a big city is 100. To investigate this, you take a random sample of fifty students. The first child tested has an IQ of 150. What will the average IQ of your fifty students be? Most people guess 100. Somehow, they think that the super-smart student will be balanced out—perhaps by a dismal student with an IQ of 50 or by two below-average students with IQs of 75. But with such a small sample, that is very unlikely. We must expect that the remaining forty-nine students will represent the average of the population, so they will each have an average IQ of 100. Forty-nine times 100 plus one IQ of 150 gives us an average of 101 in the sample.
The Monte Carlo example and the IQ experiment show that people believe in the “balancing force of the universe.” This is the gambler’s fallacy. However, with independent events, there is no harmonizing force at work: A ball cannot remember how many times it has landed on black. Despite this, one of my (Rolf Dobelli) friends enters the weekly Mega Millions numbers into a spreadsheet, and then plays those that have appeared the least. All this work is for naught. He is another victim of the gambler’s fallacy.
The following joke illustrates this phenomenon: A mathematician is afraid of flying due to the small risk of a terrorist attack. So, on every flight he takes a bomb with him in his hand luggage. “The probability of having a bomb on the plane is very low,” he reasons, “and the probability of having two bombs on the same plane is virtually zero!”
A coin is flipped three times and lands on heads on each occasion. Suppose someone forces you to spend thousands of dollars of your own money betting on the next toss. Would you bet on heads or tails? If you think like most people, you will choose tails, although heads is just as likely. The gambler’s fallacy leads us to believe that something must change.
A coin is tossed fifty times, and each time it lands on heads. Again, with someone forcing you to bet, do you pick heads or tails? Now that you’ve seen an example or two, you’re wise to the game: You know that it could go either way. But we’ve just come across another pitfall: the classic déformation professionnelle (professional oversight) of mathematicians: Common sense would tell you that heads is the wiser choice, since the coin is obviously loaded.
In chapter 19, we looked at regression to mean. An example: If you are experiencing record cold where you live, it is likely that the temperature will return to normal values over the next few days. If the weather functioned like a casino, there would be a 50 percent chance that the temperature would rise and a 50 percent chance that it would drop. But the weather is not like a casino. Complex feedback mechanisms in the atmosphere ensure that extremes balance themselves out. In other cases, however, extremes intensify. For example, the rich tend to get richer. A stock that shoots up creates its own demand to a certain extent, simply because it stands out so much—a sort of reverse compensation effect.
So, take a closer look at the independent and interdependent events around you. Purely independent events really only exist at the casino, in the lottery, and in theory. In real life, in the financial markets and in business, with the weather and your health, events are often interrelated. What has already happened has an influence on what will happen. As comforting an idea as it is, there is simply no balancing force out there for independent events. “What goes around, comes around” simply does not exist.
* Source: The Art of Thinking Clearly by Rolf Dobelli