Last year I played the 2/3 numbers game, also called the Keynesian Beauty Contest with my first year maths class. The discussion can be found here: http://www.mathemafrica.org/?p=11143 I wanted to know if, telling my class the results from last year (including sketching for them the histogram of results), would change how they chose their numbers this year. Of course I can’t tell if it changed them, but what is fascinating is that either:

- Their guesses (if I didn’t tell them about the results from last year) would have been very different from those last year, or:
- They were completely unaffected by knowing what people did last year, which really means that they believed that the rest of the class would have been unaffected.

I plot here the results from the last three years and you can see how similar the results are, year on year.

You can see that the distributions are relatively similar, and the means are extremely close. This year’s mean was a little under last year’s, but not by a great deal. The same goes for the median guesses.

This year’s winners are two students who both guessed 18, which is the closest to 2/3 of 27.5. I’ll be announcing the winners in class on Monday.

Incidentally, I happen to know that the person who guessed 100 this year did so to throw the distribution. This is a perfectly fair way to play the game, and knowing that people can do this may affect other people’s strategies.

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