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.
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Researchers hope the technology will further our understanding of the brain, but lawmakers may not be ready for the ethical challenges.
- Researchers at the Yale School of Medicine successfully restored some functions to pig brains that had been dead for hours.
- They hope the technology will advance our understanding of the brain, potentially developing new treatments for debilitating diseases and disorders.
- The research raises many ethical questions and puts to the test our current understanding of death.
The image of an undead brain coming back to live again is the stuff of science fiction. Not just any science fiction, specifically B-grade sci fi. What instantly springs to mind is the black-and-white horrors of films like Fiend Without a Face. Bad acting. Plastic monstrosities. Visible strings. And a spinal cord that, for some reason, is also a tentacle?
But like any good science fiction, it's only a matter of time before some manner of it seeps into our reality. This week's Nature published the findings of researchers who managed to restore function to pigs' brains that were clinically dead. At least, what we once thought of as dead.
What's dead may never die, it seems
The researchers did not hail from House Greyjoy — "What is dead may never die" — but came largely from the Yale School of Medicine. They connected 32 pig brains to a system called BrainEx. BrainEx is an artificial perfusion system — that is, a system that takes over the functions normally regulated by the organ. The pigs had been killed four hours earlier at a U.S. Department of Agriculture slaughterhouse; their brains completely removed from the skulls.
BrainEx pumped an experiment solution into the brain that essentially mimic blood flow. It brought oxygen and nutrients to the tissues, giving brain cells the resources to begin many normal functions. The cells began consuming and metabolizing sugars. The brains' immune systems kicked in. Neuron samples could carry an electrical signal. Some brain cells even responded to drugs.
The researchers have managed to keep some brains alive for up to 36 hours, and currently do not know if BrainEx can have sustained the brains longer. "It is conceivable we are just preventing the inevitable, and the brain won't be able to recover," said Nenad Sestan, Yale neuroscientist and the lead researcher.
As a control, other brains received either a fake solution or no solution at all. None revived brain activity and deteriorated as normal.
The researchers hope the technology can enhance our ability to study the brain and its cellular functions. One of the main avenues of such studies would be brain disorders and diseases. This could point the way to developing new of treatments for the likes of brain injuries, Alzheimer's, Huntington's, and neurodegenerative conditions.
"This is an extraordinary and very promising breakthrough for neuroscience. It immediately offers a much better model for studying the human brain, which is extraordinarily important, given the vast amount of human suffering from diseases of the mind [and] brain," Nita Farahany, the bioethicists at the Duke University School of Law who wrote the study's commentary, told National Geographic.
An ethical gray matter
Before anyone gets an Island of Dr. Moreau vibe, it's worth noting that the brains did not approach neural activity anywhere near consciousness.
The BrainEx solution contained chemicals that prevented neurons from firing. To be extra cautious, the researchers also monitored the brains for any such activity and were prepared to administer an anesthetic should they have seen signs of consciousness.
Even so, the research signals a massive debate to come regarding medical ethics and our definition of death.
Most countries define death, clinically speaking, as the irreversible loss of brain or circulatory function. This definition was already at odds with some folk- and value-centric understandings, but where do we go if it becomes possible to reverse clinical death with artificial perfusion?
"This is wild," Jonathan Moreno, a bioethicist at the University of Pennsylvania, told the New York Times. "If ever there was an issue that merited big public deliberation on the ethics of science and medicine, this is one."
One possible consequence involves organ donations. Some European countries require emergency responders to use a process that preserves organs when they cannot resuscitate a person. They continue to pump blood throughout the body, but use a "thoracic aortic occlusion balloon" to prevent that blood from reaching the brain.
The system is already controversial because it raises concerns about what caused the patient's death. But what happens when brain death becomes readily reversible? Stuart Younger, a bioethicist at Case Western Reserve University, told Nature that if BrainEx were to become widely available, it could shrink the pool of eligible donors.
"There's a potential conflict here between the interests of potential donors — who might not even be donors — and people who are waiting for organs," he said.
It will be a while before such experiments go anywhere near human subjects. A more immediate ethical question relates to how such experiments harm animal subjects.
Ethical review boards evaluate research protocols and can reject any that causes undue pain, suffering, or distress. Since dead animals feel no pain, suffer no trauma, they are typically approved as subjects. But how do such boards make a judgement regarding the suffering of a "cellularly active" brain? The distress of a partially alive brain?
The dilemma is unprecedented.
Setting new boundaries
Another science fiction story that comes to mind when discussing this story is, of course, Frankenstein. As Farahany told National Geographic: "It is definitely has [sic] a good science-fiction element to it, and it is restoring cellular function where we previously thought impossible. But to have Frankenstein, you need some degree of consciousness, some 'there' there. [The researchers] did not recover any form of consciousness in this study, and it is still unclear if we ever could. But we are one step closer to that possibility."
She's right. The researchers undertook their research for the betterment of humanity, and we may one day reap some unimaginable medical benefits from it. The ethical questions, however, remain as unsettling as the stories they remind us of.
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