American, Chinese, and casino dice

American, Chinese, and casino dice (Photo credit: Wikipedia)

Your grandchildren may play board games that use two dice, like Parcheesi, a current grandchild favorite.

Have you ever wondered what is the most common number you can get when you roll two dice and add them together, or if there even is a number that comes up more often?

Here is an easy way to show that you can predict the most common sum of two dice.


  • two dice
  • 36 M&Ms, buttons, colored beads or marbles in the same number of colors as of grandchildren playing the game, that is, 36 green and 36 red, for instance, if it is you and your grandchild playing
  • pencil or pen
  • paper


  • Ask your grandchild to draw a grid on the paper that is 6×6, that is, with lines intersecting to make six squares across the top and six squares down the left, for a total of 36 squares. Make the squares big enough to hold lots of M&Ms, buttons or beads.
  • Ask your grandchild to label the grid with 1 on top of the first square on the left edge of the top row, across the top row to 6 on top of the last square on the right
  • Ask your grandchild to label the grid with 1 to the left of the first square, down the left side with 6 to the left of the bottom-most square on the left
  • Ask your grandchild to add the numbers at the top and side of each square and write the sum in the square. That is, the top, left-most square will have a 1 on the top and a 1 on the side, so they should put 2 in that square, because 1+1=2.
  • Fill in all the squares. Numbers on the top row of squares should be: 2, 3, 4, 5, 6, 7 (1+1=2, 1+2=3, up until 1+6=7)
  • Numbers on the second row should be: 3, 4, 5, 6, 7, 8. You are adding 2+1, 2+2, through 2+6).
  • Finish adding and writing in the sums in all six rows. These are the sums of all the possible dice combinations you could throw, since the dice have the numbers 1 through 6.
  • Now, each of you and each of your grandchildren should write down predictions: which square (of the 36 squares) will get the most rolls of the dice, which number will get the most rolls (1 through 12) or will they all be equal?
  • Roll the dice 36 times each. With each roll, add the two dice and put one of your colors on the square that represents the sum of the two dice.

What Should Happen?

The most M&Ms will be on the squares with 7 in the middle.


There are more 7s than any other number.

If you look at the grid, you will see there are:

  • One 2
  • Two 3s
  • Three 4s
  • Four 5s
  • Five 6s
  • Six 7s
  • Five 8s
  • Four 9s
  • Three 10s
  • Two 11s
  • One 12

Another way to look at this distribution is:

  • One 2 and 12
  • Two 3s and 11s
  • Three 4s and 9s
  • Four 5s and 9s
  • Five 6s and 8s
  • Six 7s

The more occurrences there are of a number, the more likely, or probable, that that number will be rolled with the dice.

Thus, the sum of the numbers that equal 7 is going to come up more often when you roll the dice.


  • Make a bar chart with lines representing 1 through 36 on the left side.
  • Count out how many of each number was rolled, that is, how many of each color of M&M is on each square.
  • Draw a bar of that color to the height of the line representing that number
  • The bars should represent about the same distribution as the number of times that number occurs in the 6×6 grid.

Why Is This Important?

Probability is used in weather prediction.

The National Weather Service, for example, provides a color-coded map of the probability that different areas of the country will have more than one inch of snow in the next 24 hours.

While on any given roll of the dice, the number could be any of the numbers on the grid, on average, 7 will come up more often.

The same way, on any given day, it may or may not snow, but, on average, the weather service can predict when it is likely to snow.

Thank you to for this activity.

This post first appeared at


Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers


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