The Science of Luck

Image by nitrolxstock on deviantart.

It happens to all of us every now and then. Something good happens that we didn’t expect, or that is incredibly unlikely. We get a check in the mail. We win at a game we aren’t very skilled in. The rain lets up just as we have to go outside, despite a forecast of unrelenting downpour. Then, it happens again. And again. And we get a feeling of elation, as if something unseen is messing with the fabric of reality. Or, the opposite happens. We lose the game by a one-in-a-million chance occurrence. An apple falls in the mud, and the one drop it throws out lands on our nice white clothes. And these things start happening one after another, and we feel an otherworldly sense of despair, as if the universe itself were conspiring against us. In both instances, our minds search for an explanation, and we call it “luck.”

The gambling type like to link luck with feelings, going with their gut whether or not to make another bet or play another round. The rationalist type like to say luck doesn’t exist, that it’s just an illusion. Who is right? You’re probably expecting me to side with the rationalists, being one myself. But as much as I am a rationalist, I am also a non-conformist, and I choose a third option: to examine the idea of luck from a philosophical perspective.

In our last discussion, about God, we talked about open and closed definitions, and this seems a good time to put that concept to use. If we give luck a closed definition, it would say something like, “luck is an immaterial force that is sometimes aligned with your wellbeing and sometimes against it,” and the question would be whether or not it exists. On the other hand, if we give it an open definition, “luck is the explanation of why strings of unlikely things happen,” then we are describing something that definitely does exist, and the question becomes, “what is it?”

Instead of coming up with some hypothesis to test, let’s first see what we would expect based on known science and math. We’ll start with the simplest random system, flipping a coin. If it’s a well-balanced coin, it has a 50% chance of landing on heads and a 50% chance of landing on tails. So we expect if we flip it a bunch of times, we will get roughly half heads and half tails. If we were to flip 10 heads in a row, we would say that is sufficiently far from the expectation that it counts as luck.

What is the probability of flipping 10 heads in a row? Well, if each individual toss gives us a probability of 50%, or 1 in 2, or 1/2, then the probability of each subsequent head multiplies it by another 1/2. Let’s look at what we need to get a second head. The second head is also 1/2, but it only counts if we get the first head, making it 1/2 of 1/2, or 1/4. If we want a third head, it becomes 1/2 of 1/4, or 1/8. We see the pattern, the probability of getting n heads in a row is 1/2ⁿ. Thus, the probability of flippeing 10 heads in a row is 1/2¹⁰, or 1 in 1024.

But wait, we said it would count as luck if we flipped 10 heads in a row. But if we flip 10 coins 10,000 times, we’ll see 10 heads in a row a few times by sheer probability! In fact, if 10,000 people flip 10 heads once, we expect to find several of them have flipped 10 heads in a row, and for these individuals to get excited about it.

Now extend this to everyday experiences. If the probability of something happening to any given person at any given opportunity is 1 in a million, it’s not really that unlikely. There are billions of people in the world, and they may each have many opportunities a day for 1 in a million events to happen. Although the chance at any one time is very small, we should not be surprised when we see them happening all the time, and even to the same person in a row every now and then. No magic, no mysticism, we have found the explanation for luck in good old fashioned mathematics!

This tells us something else about luck; it is only an observation of the past, and cannot be used to predict the future. When we get “on a roll,” with lots of good things happening in a row, we feel like it is more likely for the next outcome to be a good one too. But unless there is some causal connection between past events and future events, the probability of the next good thing happening is the same regardless of what came before it. The probability you will roll a seven on a pair of fair dice is 1 in 6, regardless of whether this is your first throw, or you have already rolled eight sevens in a row. Your luck so far is not a good predictor for what will happen next. There is a chance, of course—1 in 6 is not that bad of odds—but there is no mystical force influencing the outcome in your favor.

When strings of unlikely things happen to us, we shouldn’t be surprised. It’s perfectly normal, just what we would expect in a universe governed by plain old natural statistics. Maybe you think that’s boring, and I’m taking all of the wonder out of luck. But I see it as the opposite: keeping the wonder of luck in a deterministic, mathematical world. The universe is stranger and more amazing than we can fathom, and the nature and logic behind the scenes doesn’t have to change any of that.