These posts make more sense when read in order. Please click here for the first article in this series to enter the rabbit hole.
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| © John Richard Stephens, 2024. |
If I were to have a monkey flip a coin 50 times and I make a list of whether it came up heads or tails, and then if I have you create a random list of 50 heads and tails, by comparing the two lists it will be easy to tell which is actually random because that one will have sequences of five or more times that heads or tails came up in a row. Normally we wouldn’t put that in a random list because it doesn’t seem random to us, but probability tells us that it is possible to have all 50 flips turn out to be heads. To us, that doesn’t seem random. If we’re watching coin tosses and every one is heads, we’re going to be convinced something funny is going on, when actually it could be chance.
If you spin a roulette wheel and it comes up black 26 times in a row, the chances of that happening is 1 in 136,823,184. One is almost 137 million. That seems astronomical, but it can happen. Actually black did come up 26 times in 1913 at Monte Carlo. Perhaps it’s happened elsewhere, but was attributed to a faulty wheel, when it was actually just probability.
Those of us who are unfamiliar with probability have difficulty telling random patterns from non-random because it’s easy to find patterns in random data. Mathematician George Spencer-Brown wrote that if you have a random series of 101000007 digits of zeros and ones, you should find somewhere in there a grouping of a million consecutive zeros—and not just one group, but ten of these groups.[1]
That’s the problem we have with probability. We tend to think that when something is random, it won’t have patterns. This is wrong. Patterns do appear by coincidence. And coincidences—no matter how striking or rare—do not indicate something isn’t random. Coincidences happen all the time and it’s our nature to try to link them together—to give them meaning. Chance and randomness do play a role in our lives, but we prefer to subscribe meaning or intention to such events. Once you subscribe imagined meaning in something it’s hard to switch back to seeing its randomness. Some people prefer to believe it’s ghosts, extraterrestrials, or a conspiracy.
If your child is walking down the street and is killed by a golf ball, even though there isn’t a golf course for miles around, you’re going to think chances of this happening are a billion to one so someone must have done it on purpose. Well, it still could be completely random. Probability predicts that strange things will happen, even if the chance is one in a billion.
One expert on statistics found that even she has to be cautious when it comes to probabilities. Dutch mathematician Ionica Smeets said, “It’s easy to get confused with probabilities. I’ve learned not to trust my intuition.”[2]
One of the things that distort our intuition is that we’re interested in exceptions, rather than what’s common. If you often cross a particular street at a particular spot and one time you almost get hit by a truck, you’re going to remember that incident. Even though that spot might be safer than other spots, you’ll likely be more cautious there after that.
The same thing happens on a much larger scale with the news media. As they say, if a dog bites a man, that’s probably not news, but if a man bites a dog... The news largely deals with exceptions and extremes. This can make situations and events seem much larger and more dangerous than they are.
When the volcano on Hawaii’s Big Island erupts, people start contacting me to see whether I’m alright. They may see lava moving down the mountainside or even spouts of lava on the news. Of course the volcano can be very dangerous for those nearby. It can shoot lava bombs for thousands of yards (or meters) and the pouring lava—which moves at the rate of about a mile a day—will destroy almost everything in its path. Still, it wouldn’t affect me as I live about a hundred miles away on Maui, the next island over. Not that we can’t have an eruption here, but the last one was about 600 years ago.
Terrorists rely on this effect in order to terrorize people. After the September 11, 2001 attacks on Twin Towers and the Pentagon, people were afraid to fly, opting to drive instead because of this single incident. Over the next five years 5,500 additional people died from driving than in the previous five years. The fear that terrorists were everywhere spread across the entire country. The news of the attack was so shocking and became so personal to people that many of them truly believed that they or their families were about to become the terrorists’ next victims.
Shortly after the attack I was in Morro Bay, California—a rural area on the other side of the country—standing on a small hill photographing a horse in its corral, when a truck pulled up nearby and the driver started yelling at me that he was going to call the police and have me arrested as a terrorist, adding that I couldn’t be out photographing the power lines. Now, this is the type of hysteria the terrorists are trying to create, and the news reporting unintentionally enhances it.
On a smaller scale this effect distorts our perception of risks and probabilities. Many people are afraid to fly, yet, even with terrorist attacks, air travel is much safer than driving. For every 50 billion miles traveled, 750 people die on the roads, while only one person dies from flying.[3] With those odds, everyone should opt for flying. And we drive kids to school to prevent them from being abducted, not realizing it puts them at higher risk of harm. People are afraid of sharks, when mosquitoes kill far more people because of the diseases they spread. Even cows kill more people each year than sharks do. Cigarettes do too.
Vaccinations date back to the 1400s and have saved millions of lives in the past century alone. They protect against the horrible ravages of diseases and help hinder their spread, yet despite the fact that the chance of side effects is slim and the severity of the side effects are usually minor, some people choose to focus on that, rather than the devastating and often fatal diseases they prevent.
Unfortunately we tend to make decisions based on intuition, impressions, and emotions, rather than statistics and scientific facts. We fail to take into account that the news is usually based on anecdotes and not science. Once again, our perceptions of reality are distorted.
I could go on about this for a long time, but I’m short on space and want to move on to other things. Before I do, I feel I should mention a few more common thinking errors related to probability that get people into a lot of trouble.
The first is
While talent does play a role, much of success or failure depends on randomness, like the toss of a coin. Theoretical physicist Leonard Mlodinow, in his book Drunkard’s Walk, explained that “in all aspects of our lives we encounter streaks and other peculiar patterns of success and failure. Sometimes success predominates, sometimes failure. Either way it is important in our own lives to take the long view and understand that streaks and other patterns that don’t appear random can indeed happen by pure chance. It is also important, when assessing others, to recognize that among a large group of people it would be very odd if one of them didn’t experience a long streak of successes or failures.”[4]
The gambler’s fallacy is the mistaken belief that, in a game with a fixed probability, the odds of something happening will increase or decrease based on recent results. In other words, just because a slot machine hasn’t hit the jackpot in the past month doesn’t mean that it’s due to strike. And just because it paid out doesn’t mean it’s not going to strike again for a while.
This error is part of our natural tendency to see meaning in things. We expect the past to influence the future and we search for patterns, but with fixed probabilities, the likelihood of something happening is reset to zero every time. The odds are exactly the same with each play. It’s the same as if every play is on a brand new slot machine, no matter how long you play on it. Probability can explain what a lot of people call jinxing or luck. Good streaks and bad streaks are a feature of chance and only apply to the past. They have absolutely no effect on the future because the odds always remain the same. There’s no way around it without cheating. If it’s a fair game, it’s impossible to beat the system, unless you can count cards. If it’s not a fair game, then you aren’t going to win anyway...that is, unless you’re the one doing the cheating.
When it comes to gambling, the odds are always set slightly in favor of the house. This means that while you might win in the short run, you’re almost always going to lose in the long run. Just stand in a casino and look around. You can easily see who the winner is. It’s the casinos that are raking in the dough. The odds will throw out cookies once in a while. On rare occasions they throw out really big cookies, but it’s still peanuts compared to the casino’s take. But most people don’t really notice. They have their eyes on the prize. They also have a tendency to forget their losses and remember their winnings. This can make them feel like a winner, even when they’re actually losing.
Professional gamblers don’t play against the house, avoiding slots, roulette, dice, and blackjack. They seek out better odds, usually playing games like poker where they can win against less experienced gamblers.
Still, for most people, when black comes up seven times in a row on the roulette wheel, it’s hard not to think that red is due to come up, but that’s the gambler’s fallacy.
What can make gambling, video games, and surfing the internet addictive is the sporadic nature of the rewards. You never know when you’ll get one. And the more time you invest in getting the prize, the harder it is to leave. If the rewards are regular, like your paycheck, it doesn’t become addictive. It’s the uncertainty and the expectations that make each reward more highly prized when they come. This effect is seen in rats and mice, as well as humans. And the rewards can range from money to finding a humorous cat video.
[1] George Spencer-Brown, Probability and Scientific Inference, London: Longmans, Green, & Co., 1957, p. 55.
[2] Manon Bischoff, “Statistics Are Being Abused, but Mathematicians Are Fighting Back”, Scientific American, September 30, 2022, https://www.scientificamerican.com/article/statistics-are-being-abused-but-mathematicians-are-fighting-back/.
[3] Pradeep Mutalik, “When Probability Meets Real Life”, Quanta Magazine, February 8, 2018, www.quantamagazine.org/the-bayesian-probability-puzzle-20180208/.
[4] Leonard Mlodinow, Drunkard’s Walk, New York: Pantheon Books, 2008.
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