Try this: Faking random

You will need

  • Pen
  • Paper
  • A die, or two dice

What to do

  1. Draw up a grid five squares wide and five squares tall. If you don’t want to draw them, you can download a sheet here. (Six grids per page.)
  2. Imagine this grid is a paved area, and it’s just starting to rain. Draw where the first nine raindrops might fall, trying to be as random as possible.
  3. Take some time to look at how the rain fell on your paving. Do you think it looks random?
  4. Consider the following two questions:
    • Did more than one of your drops fall into any of the squares?
    • We can see that 16 out of the 25 squares are on the outer edge of the paved area. This is more than half. From your nine drops how many fell on the outside squares?
  5. Now repeat the activity, but use rolls of a die to work out where the drops fall. Roll for the row and then the column. Re-roll any 6s (because there are only five columns and rows)
  6. How does this new pavement compare to the first one? Which one is more random?

What’s happening?

In this activity there are 16 pavers on the perimeter. Each raindrop has a 16/25 or 64% chance of falling in a box on the perimeter, which means that overall, there’s a pretty good chance that more drops will fall there. Maybe more surprisingly, there’s an almost 90% chance that two or more raindrops will fall on the same paver.

There are many mistakes that people make when they try to fake a random process. Some people assume that random numbers are more likely to happen near the middle or average. True random numbers happen all over the place, and a result all the way in the corner is just as likely as one in the middle. In fact, it’s more likely, because there are four corner pavers, and there’s only one middle paver!

Because the chance is the same for each paver, you might try to spread the dots out as evenly as possible. You might look at your grid and put the next dot in the largest gap. A random process will sometimes put a dot in the biggest gap, but sometimes it will put it in a small gap, or in the same square as another dot.
Applications

Imagine you did this activity with several classmates, and at the end, you mixed all the grids you drew together into a big pile. Do you think you could separate the made up ones from the ones drawn with dice?

Some of the made up pavements might be very easy to spot. If the drops make a smiley face, or they make a checkerboard, then there’s a very low chance they came from the dice. A statistician would be able to spot more detailed patterns. In one demonstration, statisticians were able to pick between 100 flips of a coin, and a made up list.

Detecting fake random numbers is very important for stopping crimes. These sorts of techniques have caught people cheating on their taxes, and even detected possible vote tampering in elections!

instruction1

Try to put drops as randomly as possible.

instruction2

Use this table to help you find the right square.

instruction3

If you have two different dice, you can roll row and column at the same time!

instruction4

Compare the dice roll results with the fake random grid you did first.