M always wants to play games. Sometimes we play chess, but I think he is a bit discouraged that he can’t beat me. Last Friday, while V was in Oslo, I decided to teach him backgammon. He took to it like a salmon to a stream and had the rules figured out after just a few minutes (most grownups I’ve taught take longer).

 

We’ve played two times and he has won both, but I’ve helped him with a few moves. His rolls have just been better than mine. I told him that the secret of the game is learning to understand the probabilities. I proposed a scientific experiment with dice and he instantly accepted, being a lover of any activity which involves recording information in one of his notebooks.

 

We started with a simple experiment with one die which we rolled repeatedly, recording the results. I explained how each number should appear an equal number of times, but the 4’s won out. Markus particularly like the competitive aspect of the experiment and rooted for different numbers at different times.

 

We then moved to a two dice experiment. First, we calculated the expected number of occurrences of each number between 1 and 12 and created the pie chart on the right.

 

Then we rolled the dice 401 times, stopping at 5 points to record and graph the results. A and her friend JM joined in and did their part. Even Tiger the cat, who likes to sit on anything in the house that has moved, got into the act.

 

As expected, the numbers diverged away from the ideal, but converged the more times we rolled.

 

We were worried about our dice after the first 94 roles because 4 and 8 were well above expectations. This, combined with the first experiment, got us wondering if there was something wrong with the dice. After 401 rolls, however, the numbers converged nicely.

 

Printouts were duly made and marked confidential and M was proud of his work. Despite the secrecy of the experiment, he has consented to publishing this on the Internet so that Grandma and Grandpa can see it which the proviso that the results should be kept secret.

 

 

The next experiment is to work with all the possible backgammon combinations from 2 to 36. This is a much harder problem.