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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
A team of archaeologists has discovered 3,200-year-old cheese after analyzing artifacts found in an ancient Egyptian tomb. It could be the oldest known cheese sample in the world.
A team of archaeologists has discovered 3,200-year-old cheese after analyzing artifacts found in an ancient Egyptian tomb. It could be the oldest known cheese sample in the world.
The tomb that held the cheese lies in the desert sands south of Cairo. It was first discovered in the 19th century by treasure hunters, who eventually lost the knowledge of its location, leaving the Saharan sands to once again conceal the tomb.
“Since 1885 the tomb has been covered in sand and no-one knew about it,” Professor Ola el-Aguizy of Cairo University told the BBC. “It is important because this tomb was the lost tomb.”
In 2010, a team of archaeologists rediscovered the tomb, which belonged to Ptahmes, a mayor and military chief of staff of the Egyptian city of Memphis in the 13th century B.C. In the tomb, the team found a jar containing a “solidified whitish mass,” among other artifacts.
“The archaeologists suspected [the mass] was food, according to the conservation method and the position of the finding inside the tomb, but we discovered it was cheese after the first tests,” Enrico Greco, the lead author of the paper and a research assistant at Peking University in Beijing, told the The New York Times.
To find out what the substance was, the team had to develop a novel way to analyze the proteins and identify the peptide markers in the samples. They first dissolved parts of the substance and then used mass spectrometry and chromatography to analyze its proteins.
Despite more than 3,000 years spent in the desert, the researchers were able to identify hundreds of peptides (chains of amino acids) in the sample. They found some that were associated with milk from goat, sheep and, interestingly, the African buffalo, a species not usually kept as a domestic animal in modern Africa, as Gizmodo reports.
Those results suggested that the substance was cheese, specifically one that was probably similar in consistency to chevre but with a “really, really acidy” taste, as Dr. Paul Kindstedt, a professor at the University of Vermont who studies the chemistry and history of cheese, told the The New York Times.
“It would be high in moisture; it would be spreadable,” he said. “It would not last long; it would spoil very quickly.”
The researchers also found traces of the bacterium Brucella melitensis, which causes brucellosis, a debilitating disease that can cause endocarditis, arthritis, chronic fatigue, malaise, muscle pain and other conditions. It’s a disease usually contracted by consuming raw dairy products.
“The most common way to be infected [with Brucella melitensis] is by eating or drinking unpasteurized/raw dairy products. When sheep, goats, cows, or camels are infected, their milk becomes contaminated with the bacteria,” the U.S. Centers for Disease Control wrote on its website. “If the milk from infected animals is not pasteurized, the infection will be transmitted to people who consume the milk and/or cheese products.”
Dr. Kindstedt said one reason the study is significant is for its novel use of proteomic analysis, which is the systematic identification and quantification of the complete complement of proteins (the proteome) of a biological system.
“As I say to my students every year when I get to Egypt, someone has to go ahead and analyze these residues with modern capabilities,” he told the The New York Times. “This is a logical next step and I think you’re going to see a lot more of this.”
'The Great Pyramid of Chee-za'. An artist's interpretation of a very ripe, slightly deadly Egyptian tomb cheese. (Credit: Creative commons/Big Think)
However, Dr. Kindstedt did offer a bit of caution on the conclusions the researchers drew from the findings.
“The authors of this new study did some nice work,” he told Gizmodo in a statement. “But in my view, on multiple grounds (I suspect in their zeal to be “the first”), they inferred considerably beyond what their data is capable of supporting within reasonable certainty, and almost certainly they are not the first to have found solid cheese residues in Egyptian tombs, just the first to apply proteomic analyses (which is worthy achievement on its own).”
As bad as this sounds, a new essay suggests that we live in a surprisingly egalitarian age.
- A new essay depicts 700 years of economic inequality in Europe.
- The only stretch of time more egalitarian than today was the period between 1350 to approximately the year 1700.
- Data suggest that, without intervention, inequality does not decrease on its own.
Economic inequality is a constant topic. No matter the cycle — boom or bust — somebody is making a lot of money, and the question of fairness is never far behind.
A recently published essay in the Journal of Economic Literature by Professor Guido Alfani adds an intriguing perspective to the discussion by showing the evolution of income inequality in Europe over the last several hundred years. As it turns out, we currently live in a comparatively egalitarian epoch.
Seven centuries of economic history
Figure 8 from Guido Alfani, Journal of Economic Literature, 2021.
This graph shows the amount of wealth controlled by the top ten percent in certain parts of Europe over the last seven hundred years. Archival documentation similar to — and often of a similar quality as — modern economic data allows researchers to get a glimpse of what economic conditions were like centuries ago. Sources like property tax records and documents listing the rental value of homes can be used to determine how much a person's estate was worth. (While these methods leave out those without property, the data is not particularly distorted.)
The first part of the line, shown in black, represents work by Prof. Alfani and represents the average inequality level of the Sabaudian State in Northern Italy, The Florentine State, The Kingdom of Naples, and the Republic of Venice. The latter part, in gray, is based on the work of French economist Thomas Piketty and represents an average of inequality in France, the United Kingdom, and Sweden during that time period.
Despite the shift in location, the level of inequality and rate of increase are very similar between the two data sets.
Apocalyptic events cause decreases in inequality
Note that there are two substantial declines in inequality. Both are tied to truly apocalyptic events. The first is the Black Death, the common name for the bubonic plague pandemic in the 14th century, which killed off anywhere between 30 and 50 percent of Europe. The second, at the dawn of the 20th century, was the result of World War I and the many major events in its aftermath.
The 20th century as a whole was a time of tremendous economic change, and the periods not featuring major wars are notable for having large experiments in distributive economic policies, particularly in the countries Piketty considers.
The slight stall in the rise of inequality during the 17th century is the result of the Thirty Years' War, a terrible religious conflict that ravaged Europe and left eight million people dead, and of major plagues that affected South Europe. However, the recurrent outbreaks of the plague after the Black Death no longer had much effect on inequality. This was due to a number of factors, not the least of which was the adaptation of European institutions to handle pandemics without causing such a shift in wealth.
In 2010, the last year covered by the essay, inequality levels were similar to those of 1340, with 66 percent of the wealth of society being held by the top ten percent. Also, inequality levels were continuing to rise, and the trends have not ended since. As Prof. Alfani explained in an email to BigThink:
"During the decade preceding the Covid pandemic, economic inequality has shown a slow tendency towards further inequality growth. The Great Recession that began in 2008 possibly contributed to slow down inequality growth, especially in Europe, but it did not stop it. However, the expectation is that Covid-19 will tend to increase inequality and poverty. This, because it tends to create a relatively greater economic damage to those having unstable occupations, or who need physical strength to work (think of the effects of the so-called "long-Covid," which can prove physically invalidating for a long time). Additionally, and thankfully, Covid is not lethal enough to force major leveling dynamics upon society."
Can only disasters change inequality?
That is the subject of some debate. While inequality can occur in any economy, even one that doesn't grow all that much, some things appear to make it more likely to rise or fall.
Thomas Piketty suggested that the cause of changes in inequality levels is the difference in the rate of return on capital and the overall growth rate of the economy. Since the return on capital is typically higher than the overall growth rate, this means that those who have capital to invest tend to get richer faster than everybody else.
While this does explain a great deal of the graph after 1800, his model fails to explain why inequality fell after the Black Death. Indeed, since the plague destroyed human capital and left material goods alone, we would expect the ratio of wealth over income to increase and for inequality to rise. His model can provide explanations for the decline in inequality in the decades after the pandemic, however- it is possible that the abundance of capital could have lowered returns over a longer time span.
The catastrophe theory put forth by Walter Scheidel suggests that the only force strong enough to wrest economic power from those who have it is a world-shattering event like the Black Death, the fall of the Roman Empire, or World War I. While each event changed the world in a different way, they all had a tremendous leveling effect on society.
But not even this explains everything in the above graph. Pandemics subsequent to the Black Death had little effect on inequality, and inequality continued to fall for decades after World War II ended. Prof. Alfani suggests that we remember the importance of human agency through institutional change. He attributes much of the post-WWII decline in inequality to "the redistributive policies and the development of the welfare states from the 1950s to the early 1970s."
What does this mean for us now?
As Professor Alfani put it in his email:
"[H]istory does not necessarily teach us whether we should consider the current trend toward growth in economic inequality as an undesirable outcome or a problem per se (although I personally believe that there is some ground to argue for that). Nor does it teach us that high inequality is destiny. What it does teach us, is that if we do not act, we have no reason whatsoever to expect that inequality will, one day, decline on its own. History also offers abundant evidence that past trends in inequality have been deeply influenced by our collective decisions, as they shaped the institutional framework across time. So, it is really up to us to decide whether we want to live in a more, or a less unequal society."
Our love-hate relationship with browser tabs drives all of us crazy. There is a solution.
- A new study suggests that tabs can cause people to be flustered as they try to keep track of every website.
- The reason is that tabs are unable to properly organize information.
- The researchers are plugging a browser extension that aims to fix the problem.
A lot of ideas that people had about the internet in the 1990s have fallen by the wayside as technology and our usage patterns evolved. Long gone are things like GeoCities, BowieNet, and the belief that letting anybody post whatever they are thinking whenever they want is a fundamentally good idea with no societal repercussions.
While these ideas have been abandoned and the tools that made them possible often replaced by new and improved ones, not every outdated part of our internet experience is gone. A new study by a team at Carnegie Mellon makes the case that the use of tabs in a web browser is one of these outdated concepts that we would do well to get rid of.
How many tabs do you have open right now?
We didn't always have tabs. Introduced in the early 2000s, tabs are now included on all major web browsers, and most users have had access to them for a little over a decade. They've been pretty much the same since they came out, despite the ever changing nature of the internet. So, in this new study, researchers interviewed and surveyed 113 people on their use of — and feelings toward — the ubiquitous tabs.
Most people use tabs for the short-term storage of information, particularly if it's information that is needed again soon. Some keep tabs that they know they'll never get around to reading. Others used them as a sort of external memory bank. One participant described this action to the researchers:
"It's like a manifestation of everything that's on my mind right now. Or the things that should be on my mind right now... So right now, in this browser window, I have a web project that I'm working on. I don't have time to work on it right now, but I know I need to work on it. So it's sitting there reminding me that I need to work on it."
You suffer from tab overload
Unfortunately, trying to use tabs this way can cause a number of problems. A quarter of the interview subjects reported having caused a computer or browser to crash because they had too many tabs open. Others reported feeling flustered by having so many tabs open — a situation called "tab overload" — or feeling ashamed that they appeared disorganized by having so many tabs up at once. More than half of participants reported having problems like this at least two or three times a week.
However, people can become emotionally invested in the tabs. One participant explained, "[E]ven when I'm not using those tabs, I don't want to close them. Maybe it's because it took efforts [sic] to open those tabs and organize them in that way."
So, we have a tool that inefficiently saves web pages that we might visit again while simultaneously reducing our productivity, increasing our anxiety, and crashing our machines. And yet we feel oddly attached to them.
Either the system is crazy or we are.
Skeema: The anti-tab revolution
The researchers concluded that at least part of the problem is caused by tabs not being an ideal way of organizing the work we now do online. They propose a new model that better compartmentalizes tabs by task and subtask, reflects users' mental models, and helps manage the users' attention on what is important right now rather than what might be important later.
To that end, the team also created Skeema, an extension for Google Chrome, that treats tabs as tasks and offers a variety of ways to organize them. Users of an early version reported having fewer tabs and windows open at one time and were better able to manage the information they contained.
Tabs were an improvement over having multiple windows open at the same time, but they may have outlived their usefulness. While it might take a paradigm shift to fully replace the concept, the study suggests that taking a different approach to tabs might be worth trying.
And now, excuse me, while I close some of the 87 tabs I currently have open.