Since the dawn of civilization, humans have been obsessed with luck. From ancient gamblers rolling dice made of animal bones to modern-day traders betting on stocks, people have always believed that luck plays a mysterious and unpredictable role in shaping their lives.
But as much as people attribute winning streaks, chance encounters, and life-changing fortune to supernatural forces, the truth is far less magical—but far more fascinating.
At its core, luck is often just math wearing the mask of mystery. It is probability in motion, randomness creating patterns that seem miraculous but are, in fact, inevitable given enough time and chances.
- When someone wins the lottery, it feels like fate—but the reality is, with millions of tickets sold, someone had to win.
- When a casino rakes in billions every year, it’s not because the house is lucky—it’s because the rules of probability ensure that, over time, they will always come out ahead.
- When you randomly bump into an old friend in a massive city, it might feel like destiny, but statistically, given the number of interactions we have in a lifetime, such coincidences are bound to happen.
We may struggle to understand these probabilities because our brains aren’t naturally wired to think in terms of large numbers and randomness. Instead, we seek patterns, stories, and meaning in events that are, at their core, simply mathematical outcomes.
This chapter will break down the mathematical truths behind luck—how probability governs winning streaks, lucky breaks, and coincidences, and how understanding these principles can help us navigate life more wisely.
Because while luck may be unpredictable, it is not unknowable.
Luck Is Just Probability in Action
Imagine standing at the top of a skyscraper and flipping a coin.
If it lands on heads, you win a million dollars.
If it lands on tails, you get nothing.
Now imagine flipping that coin 100 times.
Over those 100 flips, you might notice something strange—sometimes, heads appears multiple times in a row. Maybe even seven or eight times in a row. If this happened in a casino, you might start thinking you’re on a hot streak. If it happened in business, people might call you a genius. If it happened in life, you might believe you’re blessed.
But in reality, it’s just probability playing out in real time.
The more times you flip a coin, the more likely you are to see random streaks of heads or tails—even though, in the long run, the results will always even out to 50/50.
This is why casinos make money.
This is why investors sometimes get lucky with stocks but can’t repeat their success.
This is why people see patterns in random events and believe in lucky streaks, curses, and fate.
But the truth is, luck isn’t a supernatural force—it’s just statistics unfolding in ways our brains struggle to interpret.
The Hidden Math Behind “Miracles”
If you asked someone how lucky they think they are, their answer would likely depend on specific moments in their lives.
A person who won a huge prize in a raffle might consider themselves lucky.
A person who has never won anything might believe luck is never on their side.
But what if luck is simply a matter of exposure?
Let’s take lottery winners as an example.
To an outsider, a person who wins the lottery appears to have won the luckiest ticket in history. But the reality is:
- The odds of winning a large jackpot might be 1 in 300 million.
- However, millions of people buy tickets every week.
- Statistically, someone has to win—the randomness of who it is makes it feel special, but the win itself is inevitable.
This concept extends beyond just gambling.
Think about near-death experiences—a person who survives a plane crash might be called the luckiest person alive. But if enough people travel by plane, and enough crashes occur over time, statistically, some people will survive against all odds.
We call these events miraculous, but in reality, they are probability playing out over a large enough sample size.
This leads to an important question:
Is luck really about fate, or is it just the law of large numbers at work?
The Illusion of Lucky Streaks
Let’s return to our coin flip analogy.
Say you flip a coin ten times in a row. The results might look something like this:
🟡 Heads
🟡 Heads
🔴 Tails
🟡 Heads
🟡 Heads
🟡 Heads
🔴 Tails
🟡 Heads
🔴 Tails
🔴 Tails
At first glance, it looks like a pattern—three heads in a row at one point, a streak of tails at another. But over thousands of flips, the overall results will balance out.
This is exactly how gambling works.
- A blackjack player might hit five wins in a row and believe they’re on a hot streak.
- A basketball player might hit seven three-pointers in a game and feel they’ve entered a zone of luck.
- An entrepreneur might launch three successful businesses and believe they have an unstoppable touch.
But are these people truly lucky, or are they just experiencing the natural streaks that appear in all probability-based events?
The answer is both fascinating and unsettling—we see patterns where none exist.
Our brains are wired to recognize patterns—it’s what helped early humans detect danger, find food, and survive. But when we apply this instinct to random events, we misinterpret normal probability as supernatural luck.
The Science of Coincidences
There are moments in life that feel too strange, too perfectly timed, to be mere chance.
You’re traveling abroad, thousands of miles from home, when suddenly, you run into an old friend on a random street.
You wake up thinking about someone you haven’t spoken to in years—and they text you that same day.
You meet a new coworker and, in casual conversation, discover that you share the same birthday.
These moments feel like proof of something greater—fate, destiny, a cosmic force subtly nudging events into place. They demand explanation. How could something so improbable happen by accident?
But the truth is, coincidences aren’t rare at all.
They are the inevitable result of mathematics, probability, and the sheer number of interactions we experience throughout life. The world isn’t full of miracles—it’s full of probabilities playing out in ways our brains struggle to comprehend.
Why Coincidences Feel So Impossible
One of the main reasons coincidences feel special is because our brains are wired to seek meaning and patterns.
Our ancestors relied on pattern recognition for survival—noticing which plants were safe to eat, which animal tracks meant danger, which clouds signaled an incoming storm. This instinct is so deeply ingrained in us that we see patterns even where none exist.
- A gambler who sees the same numbers pop up repeatedly starts to believe they are due for a win.
- A person who keeps seeing the same sequence of numbers on clocks starts to think the universe is sending them a message.
- A sports fan who wears the same lucky jersey on game day becomes convinced it influences the outcome.
Coincidences exploit this cognitive bias. They feel meaningful, but they are just the laws of probability at work.
And nothing demonstrates this better than the Birthday Paradox.
The Birthday Paradox: Why Coincidences Are More Common Than We Think
Imagine you walk into a room with 22 other people. Someone asks:
“What are the chances that two people in this room share the same birthday?”
Your gut reaction might be low—after all, there are 365 days in a year, so it seems unlikely that just 23 people would contain a matching birthday pair.
But the actual probability? Over 50%.
Increase the group size to 50 people, and the odds jump to a staggering 97%.
By the time you have 60 people in a room, it’s almost guaranteed that at least two of them share a birthday.
Why Does This Happen?
The mistake we make is thinking of the problem as:
“What are the chances that someone in the room shares my birthday?”
That probability is low—only about 6% in a room of 23 people.
But that’s not the question.
Instead, the real question is:
“What are the chances that any two people in the room share a birthday?”
And suddenly, the number of possible birthday comparisons explodes.
With 23 people, there are 253 possible pairs of birthdays to compare.
With 50 people, there are 1,225 birthday pairings—more than enough for at least one match to occur.
This is the power of combinatorics—the math of how things pair up. As the number of people in a group increases, so does the likelihood of a coincidence occurring somewhere.
And this same principle applies to real-life coincidences—the more interactions we have, the more likely it is that something wildly improbable will happen to us eventually.
How Probability Explains the “Impossible”
The Birthday Paradox is just one example of how our brains underestimate probabilities. Many real-world coincidences that feel miraculous are simply the statistical inevitabilities of large numbers in action.
1. Running Into an Old Friend in a Foreign Country
Let’s say you’re walking through the crowded streets of Paris when you suddenly spot an old college roommate from years ago. The odds of running into this specific person in this specific city feel astronomically small.
But here’s what your brain ignores:
- You are visiting a major global city that attracts millions of travelers.
- Your friend, like you, also enjoys travel and likely visits similar places.
- Throughout your lifetime, you will visit many places, increasing the chance of a “random” encounter.
- Your brain forgets all the times you didn’t run into anyone you knew.
Viewed through this lens, running into an old friend isn’t as unlikely as it seems—it’s just probability playing out over time.
2. Thinking About Someone Right Before They Call
You’re going about your day when suddenly, you think about an old friend you haven’t spoken to in a while. Minutes later, your phone rings—and it’s them.
A psychic connection? A hidden force at play?
Not really.
What’s really happening is selection bias—your brain remembers the times when a thought and an event coincide, but forgets all the times it didn’t happen.
Think about how many times you’ve thought about someone and they didn’t call.
You never logged those moments as special.
But the one time it did happen, it stood out so strongly that it felt like fate.
This is the same bias that makes dreams feel prophetic—we only remember the ones that seemed to predict something, while ignoring the thousands of dreams that led to nothing.
The Law of Large Numbers: Why Luck and Coincidences Are Inevitable
The reason these “impossible” coincidences happen isn’t because the universe is bending reality for us—it’s because of large numbers.
In a world of 8 billion people, with trillions of interactions happening every day:
- Even a 1-in-a-million event happens 8,000 times a day somewhere on Earth.
- A “one-in-a-billion” chance still happens eight times a year.
- Over the course of a lifetime, the odds of experiencing at least one wild, once-in-a-lifetime coincidence are almost 100%.
The more people, places, and events you interact with, the more opportunities for a coincidence to occur.
This is why seemingly “miraculous” events happen so often. The world is full of mathematical inevitabilities.
What Coincidences Teach Us About Luck
There’s something unsettling about realizing that luck isn’t magic, fate, or divine intervention—it’s just probability in motion.
When you understand that coincidences are inevitable in a world governed by large numbers, your entire perception of luck begins to shift.
That moment when you randomly run into an old friend, or when you think of someone just before they call, suddenly doesn’t seem like fate anymore. It’s just a mathematical inevitability playing out in real-time.
This realization forces us to redefine luck—not as something that mysteriously chooses certain people, but as something that can be cultivated, encouraged, and engineered.
1️ Luck Isn’t a Supernatural Force—It’s a Numbers Game
For centuries, people have viewed luck as something mystical, a force beyond human understanding.
- The Romans saw it as Fortuna, the unpredictable goddess of fate.
- The Chinese saw it as something that could be balanced and cultivated.
- The Hindus viewed it through the lens of karma, where luck was a direct consequence of past actions.
But when we strip away cultural beliefs and superstitions, what remains is pure mathematics.
Luck is not about whether you’re chosen by the universe. It’s about how often you put yourself in a position where probability can favor you.
Imagine two people:
- Person A stays home most of the time, avoids social situations, and rarely takes risks.
- Person B constantly meets new people, tries different experiences, and takes calculated chances.
Who is more likely to meet someone who offers them an incredible job opportunity?
Who has a greater chance of encountering an unexpected stroke of fortune?
The answer is obvious: Person B has simply increased the number of opportunities where luck could strike.
Luck is not magic. It’s a game of exposure. The more interactions, risks, and experiences you engage in, the more likely you are to encounter life-changing coincidences.
2️ If You Expose Yourself to More Opportunities, You Increase Your Odds of Experiencing “Lucky” Moments
Consider the classic example of successful entrepreneurs.
Many people assume that billionaire success stories—from Steve Jobs to Oprah Winfrey—are the result of once-in-a-lifetime luck. They met the right people, stumbled onto the right ideas, and were in the right place at the right time.
But here’s what’s often overlooked:
- These people didn’t just try once. They kept trying, failing, and exposing themselves to opportunities until one of them worked.
- They talked to thousands of people, increasing their chances of meeting the one person who could change their career.
- They put themselves in environments where success was more likely to happen.
If luck is just a game of probability, then the real key to becoming “lucky” is to increase your sample size.
- Want to find your dream job? Apply to 100 companies instead of 10.
* Want to meet the right person? Expand your social circle instead of waiting for fate to intervene.
* Want to start a successful business? Experiment with multiple ideas instead of betting everything on one.
This is how luck actually works—not as a gift from the universe, but as a numbers game that rewards persistence and exposure.
3️ Most “Miraculous” Events Aren’t Miracles—They Are Expected Outcomes Over Time
If you live long enough, something statistically improbable will eventually happen to you.
You might:
- Have a near-death experience and walk away unscathed.
- Meet a stranger who turns out to be your long-lost relative.
- Accidentally sit next to your future spouse on an airplane.
But these events aren’t miraculous—they are just the natural result of millions of interactions happening over years of life.
This is why:
- A one-in-a-million event happens 8,000 times a day on Earth.
- Even the rarest coincidences will eventually occur if given enough time.
- The reason we find them shocking is because we fail to consider the sheer number of opportunities for them to happen.
A lottery feels impossible to win when you’re buying a single ticket. But when millions of people play, someone will always win.
A near-death escape feels supernatural, but in a world where people are constantly in dangerous situations, some will inevitably survive against the odds.
Once we realize that impossible moments are actually just probability unfolding, we stop seeing luck as a mystical force and start seeing it as a mathematical certainty.
How to Engineer Luck in Your Own Life
If luck isn’t something that happens to us but something we can actively cultivate, then the most powerful question we can ask is:
How do we create more of it?
🔹 Increase the number of chances for luck to find you.
- Meet more people. Try more things. Say yes to more opportunities. The more doors you open, the more likely one will lead to something life-changing.
🔹 Put yourself in environments where “lucky” opportunities happen.
- If you want to be a filmmaker, don’t wait for fate to introduce you to the right person—go where filmmakers gather.
- If you want to find your soulmate, don’t sit at home waiting for a miracle—go out and interact with new people.
🔹 Adopt a mindset that recognizes and acts on lucky breaks.
- Many people encounter great opportunities but fail to act on them. A person who meets the right investor for their idea but never follows up might assume they’re unlucky when in reality, they simply failed to capitalize on luck.
Luck Isn’t Just Randomness—It’s a Skill
The most successful, fortunate, and “lucky” people in the world aren’t just the ones who happened to be in the right place at the right time.
They are the ones who:
✅ Put themselves in the right place over and over again.
✅ Recognized an opportunity when it arrived.
✅ Took action instead of waiting for fate to intervene.
This means that luck is not just something that happens to us—it is something we can create, shape, and engineer through our choices.
And if that’s true, then the best way to become “luckier” in life isn’t to wait for a lucky break.
It’s to increase your chances until luck has no choice but to find you.
Rewriting Our Understanding of Luck
So, what does this all mean?
It means that luck is not as mystical as it seems.
It means that:
✅ Winning streaks are real, but they are just statistical patterns.
✅ Lucky coincidences happen all the time, but they are inevitable in a world of billions.
✅ What we see as a supernatural force is often just randomness we struggle to comprehend.
Understanding the math behind luck doesn’t mean we can control it, but it does mean we can work with it.
It means we can:
✔ Recognize when we are seeing patterns that don’t actually exist.
✔ Put ourselves in situations where probability is on our side.
✔ Make better decisions by knowing when luck is just randomness.
Because if luck is just probability in motion, then the secret isn’t hoping for luck.
It’s understanding the numbers—and learning how to stack the odds in our favor.
The Role of Probability and Randomness in Daily Life
At its core, probability is the science of uncertainty—a way to measure how likely something is to happen. While we often associate probability with gambling and statistics, it governs nearly every aspect of our lives.
From the weather forecast to the stock market, from sports predictions to medical diagnoses, probability is quietly shaping our decisions, often without us even realizing it.
For example:
- When a doctor tells you that a new drug is 90% effective, they aren’t guaranteeing a cure; they are saying that in a large enough group, 90 out of 100 people will see results.
- When meteorologists predict a 70% chance of rain, they don’t mean it will definitely rain—they mean that out of 10 similar weather conditions, 7 times it rained, and 3 times it didn’t.
- When an insurance company calculates your premium, they are using probability to estimate how likely you are to have an accident based on thousands of similar cases.
But while probability is mathematically precise, our brains are not wired to think probabilistically. We struggle to interpret randomness, overestimate rare events, and see patterns where none exist.
And nowhere is this more evident than in casinos.
Why Casinos Always Win: The Law of Large Numbers
If luck is truly random, then why do casinos always make money?
The answer lies in a simple but powerful principle in probability: The Law of Large Numbers.
This law states that over time, random events start to reflect their true probabilities.
For example, if you flip a coin once, you might get heads. If you flip it 10 times, you might get 7 heads and 3 tails. But if you flip it 10,000 times, the results will get closer and closer to the true 50/50 split.
Casinos exploit this law to ensure that while an individual gambler may win in the short term, the casino always wins in the long run.
Every game in a casino—from roulette to blackjack—is designed so that:
✅ The house always has an edge, even if it’s just 1-5%.
✅ Short-term wins for players are possible, but the longer they play, the more likely they are to lose.
✅ Casinos make their money by playing the long game, letting probability do the work.
Take roulette, for example.
- If you bet on red, you might think you have a 50% chance of winning.
- But the green 0 and 00 spaces mean the real odds are about 47.4% in your favor, 52.6% in the house’s favor.
- Over thousands of spins, this tiny edge ensures the casino always profits.
This is why “lucky” gamblers who win big often lose it all if they keep playing. The longer they stay at the table, the more probability tilts the game against them.
So does this mean winning streaks don’t exist?
Not quite—but they’re far less magical than people think.
Winning Streaks and the Myth of the Hot Hand
In sports, gambling, and even business, people often talk about “hot streaks”—periods where someone seems unstoppable.
A basketball player hits five shots in a row.
A gambler at the blackjack table wins seven hands straight.
A stock trader makes three perfect investments back to back.
This feels like luck in action, but probability tells a different story.
In 1985, researchers studied basketball free throws and found that players who had just made a shot were no more likely to make their next shot than usual. This disproved the widely held belief in the “hot hand” effect—the idea that success increases the chance of further success.
What was really happening?
- Random streaks are inevitable in large samples.
- Our brains are wired to notice patterns, even when none exist.
- The more chances you take, the more likely a streak will appear.
This last point is key. The more shots a player takes, the more likely they are to have a streak at some point—just like flipping a coin will eventually result in five heads in a row.
The problem?
Our brains remember the streaks but forget the randomness that led to them.
Coincidence vs. Causation: How Often Do Lucky Events Really Happen?
Have you ever been thinking about someone, only for them to suddenly call or text you?
Or maybe you ran into an old friend in a random city halfway across the world?
It’s tempting to believe that these events are more than coincidences—that they are signs, fate, or proof of some deeper connection in the universe.
But statistically speaking, coincidences aren’t actually rare.
In a world of 8 billion people, with billions of interactions happening every day, the probability of a seemingly impossible coincidence occurring somewhere at some time is actually quite high.
This is why lottery wins, rare medical recoveries, and bizarre encounters happen more often than we might expect. Given enough time and enough chances, even the most unlikely events will eventually occur.
One of the most famous demonstrations of this is the birthday paradox.
The Birthday Paradox: Why The Impossible Happens All the Time
Imagine you walk into a room of 23 strangers.
What are the odds that two people in the room share the same birthday?
Most people assume the chances are low—after all, there are 365 possible birthdays. But in reality, the probability is over 50%.
Why?
Because we aren’t comparing one person’s birthday against a set number—we are comparing every person’s birthday against every other person’s.
This means:
✅ The more interactions we have, the more “rare” coincidences become inevitable.
✅ The world feels full of “crazy luck” because probability dictates that unlikely things must happen eventually.
And yet, even when we understand this mathematically, we still struggle to accept it emotionally.
What This Means for Luck
After everything we’ve explored—the mathematics of probability, the illusions of winning streaks, the inevitability of coincidences—what does this all tell us about luck?
It tells us that luck is not some magical force, nor is it entirely out of our control. It tells us that what we call “luck” is often just probability unfolding in ways we don’t expect. And most importantly, it tells us that luck is something we can work with, shape, and even create.
Let’s break it down.
1️ Luck Is Not Magic—It’s Probability Playing Out in Unexpected Ways
We love to believe in luck as something mystical, something reserved for the chosen few.
- A gambler who keeps winning assumes he’s on a hot streak.
- A musician who gets discovered out of nowhere believes they were born under a lucky star.
- A person who finds the perfect job after one interview assumes it was meant to be.
But the truth is less magical, yet more empowering:
🟡 Luck is just probability expressing itself over time.
- If you flip a coin enough times, streaks will happen.
- If millions of people buy lottery tickets, someone will win.
- If you interact with enough people in your life, you will experience seemingly impossible coincidences.
Luck isn’t an outside force blessing certain people—it’s just math doing its thing.
But if that’s true, then why do some people seem to have more luck than others?
2️ Winning Streaks, Lucky Breaks, and Coincidences Are Often Statistical Inevitabilities
We tend to overestimate the rarity of unlikely events.
- Meeting the love of your life in a random place seems miraculous—until you realize that you cross paths with thousands of people in a year.
- Running into an old friend in a distant city feels like fate—until you consider that millions of people are traveling every day, increasing the odds of overlap.
- Seeing the same number everywhere feels like a sign from the universe—until you learn about the psychological effect of frequency illusion (where your brain starts noticing things it wasn’t paying attention to before).
These things feel special because our brains aren’t wired to understand large numbers and probability.
In reality, what we think of as rare events are often just inevitable over time.
And the more chances you have, the more likely you are to experience something that feels like a lucky break.
3️ People Who Experience “More Luck” May Simply Be Exposing Themselves to More Opportunities
This is where luck becomes a game of strategy.
Let’s say two people are looking for a job:
- Person A applies to five companies.
- Person B applies to 100 companies.
Who is more likely to get a job?
Person B. Not because they’re luckier, but because they gave probability more chances to work in their favor.
This applies to everything in life:
✅ Want to meet the right person? Expand your social circles. Talk to more people. Increase the number of chances for a great connection to happen.
✅ Want to start a successful business? Try multiple ideas. The more attempts you make, the greater your chances of striking gold.
✅ Want to get better at something? Practice more. The more times you repeat an action, the more likely you are to improve and have a breakthrough moment.
Luck isn’t about waiting—it’s about exposure.
The people who seem “lucky” are often just the ones who put themselves in more situations where probability can work in their favor.
4️ Understanding Probability Doesn’t Eliminate Luck—But It Helps Us Work With It
Here’s where things get interesting.
Even if we understand that luck is probability, it doesn’t mean we can eliminate it or predict every outcome.
What we can do, however, is position ourselves in ways that allow us to benefit from luck when it appears.
Instead of hoping for a lucky break, we can:
- Take more shots – More attempts mean more chances for something great to happen.
- Recognize opportunities – When a coincidence or lucky moment happens, we need to act on it.
- Stay adaptable – Sometimes luck presents itself in unexpected ways, and we need to be ready to seize it.
Think of it like surfing. You can’t control the waves, but you can learn to ride them.
Luck will always be unpredictable, but the way we respond to it makes all the difference.
So, Can We Tilt the Odds in Our Favor?
If luck is just math, then the real question isn’t whether we’re blessed or cursed.
The real question is:
Can we tilt the odds in our favor?
- Can we structure our lives in ways that attract more lucky opportunities?
- Can we develop habits that maximize our chances of experiencing luck?
- Can we shift our mindset so that we see and act on luck when it appears?
The answer is yes.
Luck isn’t just something that happens to us.
It’s something we can actively cultivate.
And that’s exactly what we’ll explore in the next chapter.