Picking Random Numbers: It's More Complicated Than You Think

Have You Ever Wondered How Random Random Numbers Really Are?

Picture of a Row of Brightly-Colored Dice
Dice Are One of Our Oldest Ways of Picking Random Numbers.

Image (c) Ilona Nagy / Getty Images

We all know that sweepstakes are giveaways where the prizes are awarded at random. The easiest way to draw a winner is to assign each entrant a unique number and then use a random number generator to pick one of those numbers to receive a prize.

But have you ever stopped to wonder how generating random numbers really works? Choosing a truly random number is harder than you might imagine. Here's why.

What Is Randomness, and Why Do We Need It?

Before you can think about whether the numbers you generate are truly random, you need to define what, exactly, you mean by "random". Merriam-Webster has a few definitions of random, including: "lacking a definite plan, purpose, or pattern" and "a set each of whose elements has equal probability of occurrence".

That sounds right when it comes to random numbers. When you choose a prize winner, you want every person who participated to have an equal chance of winning. You don't want people who entered early in the competition or people whose last names start with a specific letter to have better odds of winning. One entry, one shot.

When it comes to multi-million dollar lotteries like Powerball, it's even more important for the winning numbers to be truly random with no way of predicting them. Any weakness that makes the winning numbers more predictable makes the game unfair for players — and could be devastatingly expensive for the companies running the lotteries.

Cryptography, or creating strong codes, is another industry that relies on randomness. Randomness is vital to protect your passwords and credit card numbers online. If hackers can guess the pattern credit card companies use to encrypt your sensitive data, they can break the encryption.

In World War II, when Alan Turing cracked the seemingly-uncrackable Enigma machines that Germans used to encrypt military orders, he uncovered something that made the random signals less random. Although the machines had a huge number of potential combinations for the code they produced, they also had physical quirks that caused them to choose certain numbers more often than others. Turing was able to exploit these to crack their encryption... in a matter of hours.

Human Brains Are Terrible at Randomness

Quick, think of a random number between 1 and 10!

Have one in mind?

If your number was 3 or 7, you're in the majority. Human brains are terrible at picking random numbers. If they weren't, when asked a question like this, there would be an even distribution of answers between 1 and 10. Each number would have a 10% chance of being chosen and even and odd numbers would be chosen 50% of the time.

But that's not what happens. Our brains tend to default to picking certain numbers when faced with a question like this, either because we have a preference for certain numbers or because some numbers "feel" more random than others.

According to a study by Waseda University in Japan, given the question above, 7 was chosen 22.50% of the time, more than twice its expected frequency, and 3 was chosen 16.24% of the time. Odd numbers were chosen more often than average: 68.35% of the time.

1 and 10 are rarely chosen because they are the biggest and smallest numbers. Even numbers feel less random than odd numbers, and 5 is out because it's right in the middle. 9 is a multiple of three, which makes it seem less random. That leaves 3 and 7: of the two, 7 is most often chosen because so many people think it's a lucky symbol.

Humans are really bad random number generators, so you need to choose another method if you want true randomness.

Randomness Is So Hard to Achieve, We Rarely Use It

Imagine that you're standing on the top of the Eiffel Tower with a bag of leaves and below you've created a grid of numbers from 1 to 1,000. Now try to predict which number a single leaf will land on if you drop it on a breezy day. It seems impossible. The number the leaf hits should be random, right.

However, if you could write a program that perfectly analyzes factors like the size and shape of the leaf and the strength and direction of the wind, it would be no problem to predict which number the leaf will land upon.

Most things that seem random are actually just extremely difficult to predict.

It's so hard to come up with things that are truly random and cannot be predicted that we simply don't do it. Outside of some tricky elements of quantum physics, things happen due to a natural order that can theoretically be predicted. How random a number truly is depends on how much information you have about the method that generated it.

Most random number generators actually work on the principle of "pseudorandomness." This means that the method of choosing numbers could be predicted in theory, but in practicality, it's basically impossible.

Random number generators use a variety of interesting, difficult-to-predict methods to approach true randomness... like a wall of lava lamps or the number of protons a laser emits.

So the next time you just pull up a random number, take a moment to consider how difficult, or even impossible, it is to be truly random!

Where to Get Random Numbers

If you need to draw a sweepstakes prize winner or otherwise pick a random number, here are six reliable free random number generators.