You've (Likely) Been Playing The Game Of Life Wrong

In power-law environments, most observations are small events which lull you into false sense of security, but occasionally huge events occur; insurance addresses this by protecting against large rare events, but insurance companies face difficult job of pricing because they must charge enough to cover inevitable catastrophic outliers.

“If you have events with one of these power distributions, what you're seeing most of the time is small events. And this can lull you into a false sense of security, you think you understand how things are going. You know, floods for example, there are a lot of small floods, and then every once in a while, there's a huge one”

At critical points, almost none of the physical details about a system matter to how it behaves; there is universal behavior irrespective of what physical system you're talking about (termed 'universality'), allowing extremely powerful theories to be made without technical details because all systems in a universality class behave the same way.

“At that critical point when all the forces are poised and the system is right on that delicate balance between being organized, highly organized, or being totally disorganized, it turns out that almost none of the physical details about that system matter to how it behaves... called universality, and it's kind of a miracle.”

Not all industries can leverage power-law strategy: restaurants need consistent nightly table fills (can't have one mega-summer evening offset quiet nights); airlines need consistent seat fills (can't pack one mega-flight); these are normal-distribution businesses where average performance matters.

“But not every industry can play this game. Like if you're running a restaurant, you need to fill tables night after night. You can't have one particularly busy summer evening that brings in millions of customers to make up for a bunch of quiet nights. Over a year, the busy nights and quiet ones balance out and you're left with the average. Airlines are similar, an airline needs to fill seats on each flight. You can't squeeze a million passengers onto one plane”

Albert-László Barabási discovered the internet follows a power law: few sites like Yahoo have thousands of times more connections than most others; he hypothesized new sites preferentially link to well-known pages (preferential attachment), and simulations confirm this produces power law matching real internet data.

“In the early 2000s, Albert-László Barabási was studying the internet, and to his surprise, he found that there was no normal webpage with some average number of links. Instead, the distribution followed a power law. A few sites like Yahoo had thousands of times more connections than most of the others”

A forest naturally self-organizes to criticality: if domains become too large, one fire burns them out and restores balance; if no fires occur, forest becomes too thick and becomes ripe for massive fires; this feedback mechanism drives the system toward the critical state without external tuning.

“This sort of system will tune itself to criticality, and you can see it start to happen”

At the critical point, the system is maximally unstable and maximally unpredictable—anything can happen, it's hard to know what's going to happen next, and this seems to be a natural procedure that happens in many different systems in the world.

“where the system is maximally unstable, anything can happen. It's also maximally interesting in a way. It means the system is most unpredictable, most uncertain, it's really hard to know what's gonna happen next, and that seems to be a natural procedure that happens in many different systems in the world”

Ironically, real physical sandpiles do NOT follow power-law avalanche distributions at all, violating Bak's model; Bak responded by saying 'self-organized criticality only applies to the systems it applies to,' showing indifference to whether his model matches actual sandpiles because he was interested in universal mechanisms, not literal sand.

“Now, what's ironic is if you look at real sandpiles, they don't behave like this... And of course, it doesn't follow a power law distribution of avalanches at all. It's totally wrong”

Multiple complex systems (Earth with molten core, oceans, moon) can be accurately modeled by focusing on a single parameter (mass) much like Newton did; similarly, systems that reach criticality show universal behavior regardless of physical details—universality means the specific material details don't matter.

“You could think about the Earth and the Earth going around the Sun. That's a very complex system. You've got the molten core, everything sloshing around, and you've got oceans, and you've even got the moon going around the Earth, which in theory, you know, all should affect the exact motion of the Earth around the Sun. But Newton ignored all of that, all he looked at was just a single parameter, essentially, the mass of the Earth”

At a magnet's critical point (Curie temperature), magnetic domains become self-similar at all scales showing fractal geometry, and the size distribution of domains follows a power law—this demonstrates phase transitions produce scale-free, power-law behavior.

“This is called the critical point and it occurs at a specific temperature called the Curie temperature”

Power law distributions have infinite standard deviation and non-convergent means: when sampling from power-law distributions, the average keeps increasing with more samples rather than stabilizing, because extreme outliers dominate the average.

“In the previous games when you have a normal distribution or even a log normal distribution, you can measure the width of that distribution, its standard deviation. And in a normal distribution, 95% of the data fall within two standard deviations from the mean. But with a power law, like in the St. Petersburg paradox, there is no measurable width, the standard deviation is infinite”

In the St. Petersburg game, two exponentials interact: payout grows exponentially (2^n dollars) while probability of that outcome shrinks exponentially (probability = 1/2^n), and when you combine these and eliminate the exponent n, you get a power law where probability of payout x equals x^-1.

“If you look at the payout x, you can see it grows exponentially with each toss of the coin, x equals two to the n. But if you look at the probability of tossing the coin that many times to get a heads, you can see that this probability shrinks exponentially”

In magnets below the Curie temperature, each atom influences only its immediate neighbors (local influence), but as the critical point approaches, local influences chain together like rumors spreading through crowds, and at the critical point influence becomes effectively infinite—a single spin flip can cascade throughout the entire material.

“See, normally in a magnet below the Curie temperature, each atom influences only its neighbors. If one atom's magnetic moment flips up, then that means that its neighbors are slightly more likely to point up too. But that influence is local, it dies out just a few atoms away”

Per Bak's sandpile model (dropping grains until pile reaches critical angle, then avalanches occur) produces power-law distributed avalanches without special tuning, and the model's behavior closely resembles earthquake power-law distributions, published in top journal because it showed a universal mechanism for generating power laws.

“In 1987, Danish physicist Per Bak and his colleagues considered a simple thought experiment. Take a grain of sand and drop it on a grid, then keep dropping grains on top until at some point the sandpile gets so steep that the grains tumble down onto different squares”

In multiplicative games where random effects multiply, log transformations convert the product of random numbers into sums of logs, which are normally distributed, producing log-normal distributions with heavy right tails and extreme inequality.

“When random effects multiply, if I have a certain wealth and then my wealth goes up by a certain percentage next year because of my investments, and then the year after that, it changes by another random factor, as opposed to adding, I'm multiplying year after year”

Random multiplicative returns alone only produce log-normal distributions, not power laws; to get a power law, some other mechanism must be at play beyond simple multiplicative randomness.

“Though as we saw in the second coin game, totally random multiplicative returns give you a log normal distribution, not a power law. To get a power law, there must be some other mechanism at play”

The asymmetry of log-normal distributions exists because losses are capped at zero (you can lose at most your initial investment) while gains are uncapped and can grow to nearly $14,000 in the game example

“The reason this curve is so asymmetric is because the downside is capped at zero, so at most, you could lose $1, but the upside can keep growing up to nearly $14,000.”

At the Curie temperature (critical point for magnetic materials), a magnet transitions from ordered (aligned magnetic moments) to disordered (random moments), and at exactly this critical temperature, the system exhibits fractal structure with domains of all sizes and no inherent length scale, producing a power law distribution of domain sizes.

“This is called the critical point and it occurs at a specific temperature called the Curie temperature.”

Below the Curie temperature, magnetic moments only influence their immediate neighbors, with influence dying out within a few atomic spacings, but as temperature approaches criticality these local influences chain together like a rumor spreading through a crowd

“normally in a magnet below the Curie temperature, each atom influences only its neighbors. If one atom's magnetic moment flips up, then that means that its neighbors are slightly more likely to point up too. But that influence is local, it dies out just a few atoms away. But as the magnet approaches its critical temperature, those local influences start to chain together. One spin nudges its neighbor and that neighbor nudges the next and so on, like a rumor spreading through a crowd.”

Humans like to think of themselves as special and that through intelligence and free will they might escape the laws of physics and order, but this is probably not the case—power laws and critical systems likely govern human behavior and outcomes just as they govern physical systems.

“Human beings like to think of ourselves as being a bit special, and that maybe somehow because we're intelligent and have free will. We will escape the provenance of the laws of physics in order and organization, but I think that's probably not the case.”

In critical systems, you cannot know beforehand which bet will pay off because the system is maximally unpredictable—your next bet might do nothing, do a little, or change your entire life, making outcome determination impossible despite successful prediction being the goal.

“And the thing is that beforehand you cannot know which bet is going to be because the system is maximally unpredictable. It could be that your next bet does nothing, it could do a little bit, or it could change your entire life.”

Casper Sondergaard was inspired by reading a book with the line 'One idea could transform your entire life' to email Derek at Veritasium about helping research videos; after not hearing back for four weeks, he was nearly discouraged but received an email offering him freelance work as a researcher and producer, which is how he began at Veritasium, exemplifying how a single email can cascade into life-changing opportunity.

“In fact, around three years ago, I was reading this little book, and in the book there was this little line saying something like, 'One idea could transform your entire life.' So right underneath that, I wrote, 'Send an email to Veritasium.' A couple days later, I wrote an email to Derek, saying, 'Hey, Derek, I'm Casper. I study physics and I can help you research videos.'”

Forest fires follow a power law distribution: most fires burn less than 1/4 acre, but occasionally massive fires occur that are 70 times larger than the previous record (1.4 million acres in Yellowstone 1988 vs. 18,000 acre record from 1931), and this power law emerges because forests self-organize to criticality where fires of all sizes become possible from identical causes (lightning strikes).

“3/4 of fires burn less than 1/4 of an acre. The largest fire in the park's recent history occurred in 1931. That burned through 18,000 acres... But the 1988 fire was different... it merged with other small fires to create an enormous complex of megafires that blazed across 1.4 million acres of land... That's 70 times bigger than the previous record.”

The US Forest Service's 1935 '10:00 AM policy' suppressed every fire by 10:00 AM the next day, which made sense naively but was extremely risky because it prevented small fires from burning out, allowing fuel to accumulate until conditions became ripe for massive megafires; modern fire management acknowledges that allowing some small fires to burn reduces the likelihood of catastrophic megafires.

“In 1935, the US Forest Service established the so-called 10:00 AM policy. The plan was to suppress every single fire by 10:00 AM on the day following its initial report. Now, naively, this strategy makes sense. I mean, if you keep all fires under strict control, then none can ever get out of hand. But it turns out this strategy is extremely risky.”

Albert-László Barabási studied the internet and discovered that webpage link distributions don't follow normal distributions but instead follow power laws with exponent around negative 2, with a few sites having thousands of times more connections than most others; he predicted this would occur because new sites preferentially link to well-known pages, and simulations confirmed this preferential attachment mechanism generates power law distributions.

“In the early 2000s, Albert-László Barabási was studying the internet, and to his surprise, he found that there was no normal webpage with some average number of links. Instead, the distribution followed a power law. A few sites like Yahoo had thousands of times more connections than most of the others.”

Per Bak defended his sandpile theory against the criticism that real sandpiles don't follow power laws by claiming 'self-organized criticality only applies to the systems it applies to,' prioritizing the universal mechanism over matching real-world sandpile behavior because he was interested in a universal mechanism for generating power laws rather than sandpile accuracy.

“Now, what's ironic is if you look at real sandpiles, they don't behave like this... it doesn't follow a power law distribution of avalanches at all. It's totally wrong... Per Bak, naturally, gets a chance to reply to the criticism, and he says, I'm pretty close to quoting, he says, 'Self-organized criticality only applies to the systems it applies to.'”

In power-law systems, observing only small events creates a false sense of security; the absence of large events during an observation period does not mean they won't occur, because power-law systems are characterized by the unpredictability of large events despite long stretches of apparent stability.

“If you have events with one of these power distributions, what you're seeing most of the time is small events. And this can lull you into a false sense of security, you think you understand how things are going. You know, floods for example, there are a lot of small floods, and then every once in a while, there's a huge one.”

Pareto discovered that income distribution across Italy, England, France, and Prussia follows a power law, where the number of people earning an income greater than X is proportional to one over X to the power of approximately 1.5, with this same pattern holding across different countries.

“In the late 1800s, Italian engineer Vilfredo Pareto stumbled upon something no one had seen before. See, he suspected there might be a hidden pattern in how much money people make. So he gathered income tax records from Italy, England, France, and other European countries”

The 1988 Yellowstone fire was not caused by special conditions; it merged with other small fires to create megafires covering 1.4 million acres (70x larger than previous record, 50x larger than all fires in previous 15 years combined)—demonstrating that catastrophic events can emerge from typical conditions in critical systems.

“That's 70 times bigger than the previous record, and 50 times the area of all the fires over the previous 15 years combined”

The Earth's tectonic system is in criticality: stresses build up slowly from plate movement, most time only tiny earthquakes occur, but sometimes random movements trigger chain reactions where stress propagates along fault lines potentially spanning 40+ km, releasing enormous energy.

“Every day, the Earth's crust is moving and rearranging itself. Stresses build up slowly as tectonic plates rub against each other. Most of the time, you get a few rocks crumbling, the ground might move just a fraction of a millimeter, but the stresses dissipate in many earthquakes that you wouldn't even feel”

The 1995 Kobe earthquake (January 17) released stress along 40 km of the Nojima fault line, shifted ground by up to 2 meters, released energy equivalent of numerous atomic bombs, destroyed thousands of homes and major infrastructure, killed over 6,000 people, and forced 300,000 from their homes.

“The stress propagated to the next section of the fault and the next. Within seconds, the ruptured cascaded along 40 kilometers of crust, shifting the ground by up to two meters and releasing the energy equivalent of numerous atomic bombs”

In 2018, a forest fire destroyed Paradise, California (deadliest and most destructive in state history), but insurance company Merced Property & Casualty hadn't planned for magnitude of loss; when claims came in, they lacked reserves to pay out and the company went bust.

“In 2018, a forest fire tore through Paradise, California, it became the deadliest and most destructive fire in the state's history, but the insurance company, Merced Property & Casualty, hadn't planned for something that huge, and when the claims came in, they just didn't have the reserves to pay out. So just like that, the company went bust”

Publishing industry shows power-law returns: most titles flop, but in 1997 small UK publisher Bloomsbury took chance on Harry Potter, which made Bloomsbury a globally recognized brand—one outlier success disproportionately affected the firm's destiny.

“Book publishers operate in a similar fashion, most titles flop, but in 1997, a small independent UK publisher called Bloomsbury took a chance on a story about a boy wizard. The boy's name, of course, was Harry Potter, and now Bloomsbury is a globally recognized brand”

Private equity firm Horsley Bridge invested in 7,000 startups (1985-2014): over half lost money, but top 6% yielded 10x+ returns and generated 60% of total profit—demonstrating that power-law venture capital returns require accepting that most investments will fail.

“Between 1985 and 2014, private equity firm Horsley Bridge invested in 7,000 different startups and over half of their investments actually lost money, but the top 6% more than 10xed in value and generated 60% of the firm's overall profit”

Most empirical data on human heights, IQ, and apple sizes clusters around an average value following a normal distribution, but many phenomena in nature follow power laws instead, where extreme values are far more common than normal distribution would predict.

“if you go out in the world and start measuring things like human height, IQ, or the size of apples on a tree. You will find that for each of these things, most of the data clusters around some average value”

Normal distributions describe phenomena where random additive effects combine (like human height), creating a bell curve centered on an average with predictable, bounded variation, whereas power laws describe phenomena where outcomes span multiple orders of magnitude with disproportionately large extreme events.

“Most of the data clusters around some average value... you will find that it follows a power law... some things in life are not like this.”

Per Bak's sandpile paper was published in a top-tier journal because it demonstrated something previously thought impossible: a simple universal mechanism for generating power laws across diverse systems

“That's the really surprising thing, and that's why this little paper with a sandpile was published in the world's top journal because it did something that people just didn't really think was possible.”

In 2018, the Paradise, California forest fire became the deadliest and most destructive in state history, but insurance company Merced Property & Casualty had not planned for something that huge and lacked reserves to pay claims when they came in, causing the company to go bust

“In 2018, a forest fire tore through Paradise, California, it became the deadliest and most destructive fire in the state's history, but the insurance company, Merced Property & Casualty, hadn't planned for something that huge, and when the claims came in, they just didn't have the reserves to pay out. So just like that, the company went bust.”

Two exponential functions 'conspiring together' are a very common mechanism in nature for generating power laws, such as exponential decay in frequency of earthquakes combined with exponential increase in energy released

“You put them together, the exponentials conspire to make a power law. And that's a very common thing in nature, that a lot of times when we see power laws, there are two underlying exponentials that are dancing together to make a power law.”

Purely random multiplicative returns generate log-normal distributions, not power laws, so other mechanisms beyond random multiplication must be at play to produce power law distributions

“Though as we saw in the second coin game, totally random multiplicative returns give you a log normal distribution, not a power law. To get a power law, there must be some other mechanism at play.”

A handful of companies, servers, and data centers hold personal information of millions of people, so when one gets hacked it can ripple across the entire network, exemplifying how one outlier failure affects many

“A handful of companies, servers, and data centers hold the personal information of millions of people, so when one of them gets hacked, it can have ripple effects across the whole network.”

At the critical point, the effective range of influence of one atom on the rest of the system becomes effectively infinite, meaning a single spin flip can cascade throughout the entire material

“And right at the critical point, it becomes effectively infinite. A flip on one side can cascade throughout the entire material.”

Wars follow a power law distribution in fatalities: if you measure war size by number of deaths, you find that wars follow a power law virtually identical to the power law found in stock market crashes, suggesting that war is governed by the same critical-system mechanics as other natural hazards.

“If you look at the number of world wars, and if you make a crude measure of how big is the world war by how many people it kills, which is a bit macabre, but still, you find that, again, it follows a power law virtually identical to the power law you find in stock market crashes.”

Casper (researcher collaborator) sent an email to Veritasium after reading that 'one idea could transform your entire life'; didn't hear back for 4 weeks, was about to give up, then received response offering freelance research position; this became how Casper started at Veritasium.

“In fact, around three years ago, I was reading this little book, and in the book there was this little line saying something like, 'One idea could transform your entire life.' So right underneath that, I wrote, 'Send an email to Veritasium.' A couple days later, I wrote an email to Derek, saying, 'Hey, Derek, I'm Casper. I study physics and I can help you research videos.' I didn't hear back for four weeks, so I was getting pretty sad and just wanted to forget about it and move on, but then a couple days later I got an email back saying, 'Hey, Casper, we can't do an internship right now, but how would you like to research, write, and produce a video as a freelancer?' So I did, and that's how I get started at Veritasium”

In the multiplicative game, if you toss 100 consecutive heads, you would win 1.1^100 or approximately $14,000, though the probability of this outcome is around 1 in 10^30 (less likely than winning the lottery three times in a row)

“If you tossed 100 heads, you'd win 1.1 to the power of 100. That's almost $14,000, although the chance of that happening is around 1 in 10 to the power of 30. You'd be more likely to win the lottery three times in a row.”

The 1935 U.S. Forest Service 10:00 AM policy of suppressing every fire by 10:00 AM on the day after report was strategically flawed because it prevented small fires from burning, allowing fuel to accumulate, which made megafires more likely.

“In 1935, the US Forest Service established the so-called 10:00 AM policy. The plan was to suppress every single fire by 10:00 AM on the day following its initial report. Now, naively, this strategy makes sense. I mean, if you keep all fires under strict control, then none can ever get out of hand. But it turns out this strategy is extremely risky.”

If you stand in a room with Bill Gates or Elon Musk, the average wealth in the room becomes approximately 100 billion dollars because a single outlier dominates the average, illustrating how outliers determine averages in power law systems.

“it's sort of like saying, if you're standing in a room with Bill Gates or Elon Musk, the average wealth in that room is gonna be 100 billion dollars or something (laughs) because the average is dominated by one outlier.”

Industries operating under normal distributions (restaurants, airlines) need consistent average performance night after night or flight after flight; a single exceptionally busy period cannot compensate for quiet periods because capacity and demand are additive, so busier nights and quiet nights balance out over a year to define success by average performance.

“Like if you're running a restaurant, you need to fill tables night after night. You can't have one particularly busy summer evening that brings in millions of customers to make up for a bunch of quiet nights. Over a year, the busy nights and quiet ones balance out and you're left with the average.”

Vilfredo Pareto discovered in the late 1800s that income distribution across multiple countries (Italy, England, France, Prussia) follows a consistent power law with exponent approximately 1.5, meaning each time income doubles, the number of people earning at least that amount drops by a factor of approximately 2.8, and this pattern can be expressed as a single equation applicable across all countries studied.

“In the late 1800s, Italian engineer Vilfredo Pareto stumbled upon something no one had seen before... he gathered income tax records from Italy, England, France, and other European countries... a pattern which still holds in most countries to this day.”

In 1987, Danish physicist Per Bak and colleagues studied sand avalanches by repeatedly dropping grains onto a grid until the pile became steep enough that grains tumble down, examining how often avalanches of different sizes occurred

“In 1987, Danish physicist Per Bak and his colleagues considered a simple thought experiment. Take a grain of sand and drop it on a grid, then keep dropping grains on top until at some point the sandpile gets so steep that the grains tumble down onto different squares...They asked for how often do you see avalanches of a certain size.”

On Netflix, top 6% of shows account for over half of all viewing hours; on YouTube, less than 4% of videos reach 10,000 views but those videos account for over 93% of all views—streaming platforms show extreme power-law content distributions.

“We see a similar pattern play out on streaming platforms. On Netflix, the top 6% of shows account for over half of all viewing hours on the platform. On YouTube, less than 4% of videos ever reach 10,000 views, but those videos account for over 93% of all views”

In the St. Petersburg paradox game (coin flips doubling payout each flip, game ends on heads), the theoretical expected value is infinite because increasingly rare outcomes have payouts large enough that their expected contribution remains $1, creating a power-law distribution where probability of payout X equals 1/X (negative exponent of 1).

“You start out with a dollar and the payout doubles each time you toss the coin and you keep tossing until you get a heads, then the game ends... If it took you to the nth toss to get a heads, you would get two to the n dollars.”

Power laws are intrinsically linked to fractals; systems producing power laws reveal fractal-like structure where the same pattern repeats at smaller and smaller scales, and this self-similarity appears across diverse natural systems including veins on leaves, river networks, blood vessels, and lightning.

“When you zoom in, you keep seeing the same structure repeating at smaller and smaller scales. It's self-similar like a fractal, and that's no coincidence. We see the same fractal-like pattern in the veins on a leaf, river networks, the blood vessels in our lungs, even lightning, and in all of these cases, we can describe the pattern with a power law.”

Insurance is precisely designed to protect against large rare events in power law systems that would otherwise be catastrophic, but insurance companies face the difficult problem of calculating premiums without knowing how much to charge for extreme outlier events

“One response to this is insurance, that insurance is designed precisely to protect you against the large rare events that would otherwise be very bad. But then there's the other side of that picture, which is you are the insurance company that needs to insure people and they have a particularly difficult job because they have to be able to say how much to charge so that they have enough money to pay out when the big bad thing comes along.”