# Falling Victim to the "Gambler's Fallacy" Could Really Ruin Your Day

Spin a roulette wheel a million times, and you'll see a fairly even split between black and red. But spin it a few dozen times, and there might be "streaks" of one or the other. The gambler's fallacy leads bettors to believe that they odds are better if they bet against the streak. But the wheel has no memory of previous spins; for each round, leaving aside those pesky green zeroes, the odds for each color are always going to be 50-50.

Last August, my wife and I welcomed our third daughter into the world. It’s wonderful to be the parent of three girls. There is one significant drawback, however: having to field the question, over and over again, from (mostly) well-meaning people: “So are you going to try for a boy now?” There are several solid reasons we are calling it a day in the reproduction department. But if we were interested in having a fourth child, “trying for a boy” would not be the motivation. The idea is preposterous. Having a string of children of one sex does not presage the arrival of a baby of the opposite sex. Each pregnancy brings the same odds of having a boy or a girl, regardless of how previous pregnancies turned out: about 1 in 2.

The inkling that eventually odds come to favor having a baby of the other sex is an application of the “gambler’s fallacy.” This mistake is often explained with the example of coin tosses. Let’s say you flip a fair coin 5 times and it ends up “heads” each time. Many people watching this unbroken string of unlikely flips would bet good money that the sixth flip will bring “tails.” Heads can’t go on forever! What are the chances that there would be *six *heads in a row? Answer: on the sixth flip, there are *even* odds of getting heads or tails, just as there were for the first five flips. You’d be a fool to place a big bet on tails—or on heads, for that matter—for any individual coin toss.

In the long run, with millions or billions of flips, a fair coin will produce increasingly even numbers of heads and tails. The numbers will show something very close to a 50/50 split. That’s the Law of Large Numbers. But when you’re dealing with only a few handfuls of flips, the Law of Small Numbers applies: seemingly unlikely strings of coin flips are not that improbable after all. In our example, there is a probability of 1/64 that six flips of a fair coin will result in heads each time (that’s 1 over 2 to the sixth power). Those odds aren’t great; they come out to about a 1.6% chance. The gambler’s fallacy is to look at those meager odds and conclude there is a 98.4% chance the sixth flip will be tails. But here's the fundamental problem: the probability of the first five flips coming up heads is now 100 percent. They have already happened! The only question is what will happen with the *next* flip, and those odds are, again, 50/50. Here is another way to look at it: any permutation of six coin flips—*all* heads or *all* tails or three heads and three tails or one tails and five heads, e.g.—has a probability of 1/64. So it’s just as likely—and just as unlikely—that six flips of a coin will produce six heads, or three tails and three heads—or any of the other 62 possible permutations.

When we zoom in on a string of one or two dozen flips, then, we are likely to find some series of flips that don’t look so random. Such non-random-seeming strings are to be expected from time to time. And this principle holds outside the realm of coin flips; it applies to purportedly amazing coincidences you might experience in your life. I’ll admit to being very surprised when, ten years after graduation, I ran into a college classmate on my way out of the St. Vitus Cathedral in Prague. “How random is this!” I think we exclaimed. The answer: just as random as any other chance encounter. The chances of our meeting were, no doubt, small. But the chances of meeting any of my other college classmates in any other attraction in a foreign city are equally low—and I have never had any other such encounters. Those didn’t happen; this one did. It might be spooky if my entire Freshman year hallway showed up at the same time at a cafe in Vienna, but stumbling across one fellow in one place at one moment is not, statistically speaking, anything remarkable.

It’s clear how a gambler can suffer from this fallacy: he can lose big money. If you throw all your chips on black in a game of Roulette after the ball has landed on red 10 times in a row because it couldn’t *possibly* wind up there an eleventh time—well, you have a good chance of walking home empty-pocketed. On August 18, 1913, scores of French gamblers left the Monte Carlo casino bereft after falling victim to this mistake: the Roulette ball landed on black 26 times in a row that day; during the run, everybody was betting that the wheel would even itself out and turn to red. But of course the wheel had no memory of its previous spins. Only the irrational bettors thought that previous spins had anything to do with how the next spin would turn out.

A new piece of research shows there are weighty implications of this cognitive bias well beyond the casino floor. In next Friday's Praxis, I will discuss evidence that judges, loan officers and baseball umpires tend to succumb to the gambler's fallacy in their decision making—dramatically expanding the damage the fallacy can cause to innocent bystanders.

*Image credit: Shutterstock.com*

## Befriend your ideological opposite. It’s fun.

Step inside the unlikely friendship of a former ACLU president and an ultra-conservative Supreme Court Justice.

- Former president of the ACLU Nadine Strossen and Supreme Court Justice Antonin Scalia were unlikely friends. They debated each other at events all over the world, and because of that developed a deep and rewarding friendship – despite their immense differences.
- Scalia, a famous conservative, was invited to circles that were not his "home territory", such as the ACLU, to debate his views. Here, Strossen expresses her gratitude and respect for his commitment to the exchange of ideas.
- "It's really sad that people seem to think that if you disagree with somebody on some issues you can't be mutually respectful, you can't enjoy each other's company, you can't learn from each other and grow in yourself," says Strossen.
**The opinions expressed in this video do not necessarily reflect the views of the Charles Koch Foundation, which encourages the expression of diverse viewpoints within a culture of civil discourse and mutual respect.**

## First solar roadway in France turned out to be a 'total disaster'

French newspapers report that the trial hasn't lived up to expectations.

*Image source: Charly Triballeau / AFP / Getty Images*

- The French government initially invested in a rural solar roadway in 2016.
- French newspapers report that the trial hasn't lived up to expectations.
- Solar panel "paved" roadways are proving to be inefficient and too expensive.

## Physicist advances a radical theory of gravity

Erik Verlinde has been compared to Einstein for completely rethinking the nature of gravity.

- The Dutch physicist Erik Verlinde's hypothesis describes gravity as an "emergent" force not fundamental.
- The scientist thinks his ideas describe the universe better than existing models, without resorting to "dark matter".
- While some question his previous papers, Verlinde is reworking his ideas as a full-fledged theory.

## Physicists find new state of matter that can supercharge technology

Scientists make an important discovery for the future of computing.

- Researchers find a new state of matter called "topological superconductivity".
- The state can lead to important advancements in quantum computing.
- Utilizing special particles that emerge during this state can lead to error-free data storage and blazing calculation speed.