Just How Do the Dice Really Fall?

I teach math. One of the topics I cover in a math class that is geared for liberal arts is basic probability. I like to show students how games of chance are not "lucky" but are actually somewhat predictable. Here is how I approach the fact that "lucky sevens" aren't really derived from luck.

I start with a chart showing all the different pairings we can get when we roll a pair of dice. The pairs start with rolling a two and end with rolling a twelve. We look at die 1 and die 2. If the same number is rolled on each die, we only consider it that one time, but if I roll a three on die 1 and a four on die 2, it is considered different from a four on die 1 and a three on die 2.

Here is a rough view of what I give them.

There is only one way to roll a 2: (1, 1)
There are two ways to roll a 3: (1, 2) and (2, 1)
There are three ways to roll a 4: (1, 3), (2, 2), and (3, 1)
There are four ways to roll a 5: (1, 4), (2, 3), (3, 2), and (4, 1)
There are five ways to roll a 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1)
There are six ways to roll a 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1)
There are five ways to roll an 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2)
There are four ways to roll a 9: (3, 6), (4, 5), (5, 4), and (6, 3)
There are three ways to roll a 10: (4, 6), (5, 5), and (6, 4)
There are two ways ro roll an 11: (5, 6) and (6, 5)
There is only one way to roll a 12: (6, 6)

This gives us a chart showing the way the dice can fall. If you notice, there are more combinations that will give us a SEVEN than any other number. In this way, we can see that our probability of rolling a seven is higher than rolling any other number -thus sevens are not lucky, they just have a higher probability of being rolled.

I then have students to take a pair of dice and roll them 25 to 50 times. They work in pairs; one person rolls the dice and the other person records the data. Then they switch roles. Once both partners have had a chance to complete 25 to 50 dice rolls, they complete a frequency distribution for their data and compare it to the chart I have presented at the beginning of the lesson.