Why Picking Random Numbers Is More Complicated Than You Think

Have You Ever Wondered How Random Random Numbers Really Are?

Picture of a Row of Brightly-Colored Dice

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Random numbers are a vital part of making sure that sweepstakes prizes are awarded fairly. The easiest way to draw a winner is to assign each entrant a number and then use a random number generator to pick one of those numbers to receive a prize. But have you ever wondered how random number picking really works? Choosing a truly random number is harder than you might imagine.

What Is Randomness, And Why Do We Need It?

Before we can think about whether the numbers we pick are truly random, we need a definition. Merriam-Webster's definitions of random include: "lacking a definite plan, purpose, or pattern" and "a set each of whose elements has equal probability of occurrence".

That sounds about right when it comes to random numbers. When we are choosing prize winners, we want every person who participated to have an equal chance of winning. We 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 chance.

When it comes to multi-million dollar Powerball lotteries, it becomes even more important that the numbers chosen as the winners are truly random and that there is 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 is another industry that relies on randomness. Randomness is absolutely vital to protect your passwords and credit card numbers online. If hackers can guess the pattern, they can break the encryption.

This is what happened during World War II when Alan Turing managed to crack the seemingly-uncrackable Enigma machines which the Germans used to encrypt military orders. Although there were a huge number of potential combinations for the code, the machines themselves had physical quirks that Turing was able to exploit 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 are in the majority. Human brains are terrible at picking random numbers. If they weren't, there would be an even distribution of numbers between 1 and 10. Each number would have a 10 percent chance of being chosen and even and odd numbers would be chosen 50 percent of the time. But to our brains, some numbers "feel" more random than others.

According to a study by Waseda University in Japan, 7 was chosen 22.50 percent of the time, more than twice its expected frequency, and 3 was chosen 16.24 percent of the time. Odd numbers were chosen more often than average, 68.35 percent 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, and 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 we need to choose another method if we want to be truly random.

Randomness Is So Hard to Achieve, We Rarely Use It

Imagine that you are standing on the top of the Eiffel Tower with a bag of leaves and below you have spread a grid of numbers. Now try to predict which number a single leaf will land on if you drop it on a breezy day. It seems impossible, and that the number the leaf hits will be random.

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

It is 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 used to generate it.

Most random number generators actually work on the principle of "pseudorandomness." This means that the method of choosing numbers could theoretically be predicted, but in practicality, no one can. Random number generators use a variety of interesting, difficult to predict methods to approach true randomness.

Where to Get Random Numbers

If you need to draw a sweepstakes prize winner or otherwise pick a random number, here are some free resources:

  • Random.org offers a variety of random number pickers for different purposes including a lottery quick pick, an integer generator, and more.
  • If you type "random numbers" into Google.com, it will give you a simple random number generator.
  • Stat Trek lets you create a list of random numbers, based on variables that you specify.