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Dodgy dice

By David, 14 September 2015 Activity

Six swuares with dots on them, arranged in a cross shape.

Cut out one of the cross shapes.

Here’s a surprising pair of dice that you can make yourself!

You will need

  • Adhesive putty
  • Marble or small stone
  • Glue
  • Scissors
  • Marker
  • Pen and paper
  • A copy of the dice template, printed on thin cardboard

Making the dice

Someone has rolled the cross shape so the top and bottom are next to each other.

Glue the tab on the 4 side to the 5 side.

  1. There are two cross shapes on the template. Cut out one of these.
  2. Fold along the edges of each square on the template. Make sure the dots are on the outside of the dice.
  3. Glue the tab attached to the 4 dots square, and stick it to the edge of the 5 dots square.
  4. Glue the tabs around the 6 square and stick it to the 2, 4 and 5 dot squares to make an open box.
    A little cubic box with dice dots on each face. The lid is open and someone is sticking putty to it.

    Put a lump of putty inside the 1 face.

  5. Stick a pea-sized lump of adhesive putty on the inside of the 1 square.
  6. Glue the tabs around the 1 dot square and stick it down to make a cube.
  7. Mark the dice so you know this one has putty in it.
  8. Repeat steps 1–4 with the other copy of the template.
  9. Instead of putting adhesive putty on the 1 square, put a marble inside the second dice.
  10. Glue down the 1 dot square to finish the second dice.
    Two dice made of paper.

    The completed dice.

  11. Mark the second dice so you know it has a marble in it.

The experiment

  1. Roll each dice 20 times. Record the results of each roll and which dice you were using.
  2. Look at your results – do your dice look fair?
  3. Looking at your results, predict what the next 20 rolls of each dice will be.
  4. Check your predictions by rolling each dice 20 more times and recording the results.

What’s happening?

You probably found the putty dice is not rolling fair. The 1 side is heavier than the other sides and falls to on the bottom of the dice. The 6 dot side, opposite the 1, ends up on top more often than the other numbers.

You may have noticed that other numbers were still rolled. Just because it is unfair does not mean the dice will always roll 6. The level of unfairness depends on the size and position of the blob – a tiny lump won’t change much, and a large enough lump will fill the entire dice!

The dice with the marble is probably reasonably fair. Since the marble can roll around it doesn’t favour any one side. You may have noticed some sides rolling more than others, but that’s normal. Fair dice doesn’t always roll each number the same amount all the time – that would require the dice to remember what it had rolled.

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