The Odds of Everything: Why We Are So Bad at Understanding Luck

 Have you ever bumped into an old friend in a completely different city? Or maybe you were thinking about a specific song, and two seconds later, it started playing on the radio?

When things like this happen, our first instinct is usually to look for a deeper meaning. We call it fate. We call it destiny. We say, "What are the chances?" implying that the universe is conspiring to tell us something.

But if you look at the world through the lens of mathematics, specifically probability, the answer is usually much less mystical. The answer is often: "Actually, the chances were pretty good."

I’ve been reading a lot about probability lately, and the main takeaway is humbling: human brains are terrible at understanding randomness. We are hardwired to find patterns, even where none exist. We crave a narrative so badly that we reject the idea of pure coincidence.

The Birthday Paradox

Let’s try a classic example that still messes with my head. Picture a room with 23 people in it. Just 23. What do you think the odds are that two of them share the same birthday?

Intuitively, most of us would say the odds are tiny. There are 365 days in a year, right? So you’d probably guess around 5% or 10%.

The actual mathematical answer is 50%.

If you increase the number of people to 75, the probability of a shared birthday rises to 99.9%. It feels wrong. It feels like magic. But it’s just math. The reason we get it wrong is that our brains try to compare one person against the group, rather than comparing every single person against every other person. The number of possible connections grows exponentially, not linearly.

Why does this matter? Because it reminds us that "rare" events aren't actually that rare if the sample size is large enough. In a world with 8 billion people, one-in-a-million miracles happen 8,000 times a day.

The Gambler’s Fallacy

Another trap we fall into is thinking that the universe keeps a scorecard.

Let’s say you are flipping a coin. You get heads five times in a row. Heads, heads, heads, heads, heads. You are about to flip it a sixth time. You feel, deep in your gut, that it has to be tails this time. It’s "due" for a tails, right?

Nope. The coin has no memory. The odds are still exactly 50/50.

This is called the Gambler’s Fallacy, and it ruins lives in casinos every day. But it also affects how we live our regular lives. We think that because we’ve had a string of bad luck—maybe your car broke down, you lost your keys, and it rained on your holiday—that good luck is just around the corner to "balance it out."

Mathematics tells us a harsher truth: randomness is clumpy. It doesn't spread out evenly like butter on toast. Sometimes, bad things happen in clusters, and it doesn't mean anything other than... well, bad luck.

Finding Peace in the Numbers

At first glance, this might seem depressing. It sounds like I’m saying the world is cold and random. But strangely, I find comfort in it.

Understanding probability takes the pressure off. When something goes wrong, you don’t have to ask, "Why is the universe punishing me?" You can just realize you fell into the wrong percentage of a probability curve. It’s not personal. It’s just statistics.

It also helps with decision-making. Instead of relying on "gut feeling" (which is usually just fear or hope in disguise), you start thinking in terms of risk and reward. You stop buying lottery tickets not because you hate fun, but because you understand the expected value is negative. You start investing or learning new skills because the compound probability of success over time is in your favor.

The "Spotify Shuffle" Effect

Here is a funny final example of how bad we are at this. Did you know that when Spotify first launched its "Shuffle" feature, it was truly random? But people complained. They said, "It’s not random! It played three songs by the same artist in a row!"

Mathematically, true randomness allows for clusters. If you flip a coin enough times, you will get streaks. But to humans, that didn't "feel" random. So, Spotify had to rewrite their algorithm to make it less random in order to make it feel more random to users. They had to engineer the playlist to separate artists so our pattern-seeking brains would be satisfied.

We want the world to make sense. We want order. But math teaches us that chaos is the natural state of things.

So the next time something incredibly unlikely happens to you, don't look for a ghost or a sign. Just nod at the math gods and appreciate that you witnessed a statistical outlier. It’s not magic, but it’s still pretty cool.