# Guess 2/3 of the average, the results

So, the calculation of the results of the game "Guess 2/3 of the average,% username%" is over . A total of 357 people took part. Are rational people? What is most often used as a decimal separator: a period or a comma? Who, in the end, was the winner?

I will not pull, I will start with the main results. The average of 354 numbers (why not 357? See below) is 16.6844657552. Two-thirds of this number is 11.1229771701 . The closest was Alexander Artyushkin with the number 11.12 . Hurrah!!! Because it is not registered on a habr, then as a prize he receives an invite earned thanks to the previous post.

Now some statistics. Of the 357 participants, 176 were from Habr, 181 took part via e-mail. 3 votes were declared invalid due to the lack of a number in the message :) Special thanks to those 40 people who sent messages with several numbers (for example, a voice and explanation with formulas or a phone number in the signature) or letters without text / plain. These messages had to be processed manually.

Of the 151 decimal fractions, in 63 cases, a comma was used as a separator, and in 88, a period. Apparently this is due to the fact that programmers are used to using the dot everywhere.

Finally, we turn to the analysis of the results. Below you see a histogram of votes. Immediately striking is its general similarity with the histogram from Denmark. Peak at 0, although more, but slightly. 11 people decided to spoil the guesses of the rest and chose numbers greater than 66, (6).

The most popular number was 15 - 22 votes. In second place - 0 (13 votes), in third - 1 (11 votes), fourth and fifth divided 10 and 14 (10 votes each).

If you remember, in a previous post I said that I have a theory about how voices are distributed. I reasoned as follows. Participants can be categorized according to how many iterations ahead they calculate the expected result. It is logical to assume that the ratio of the sizes of the categories is approximately constant. Consider those who do not calculate the actions of others at all, i.e. chooses his number almost by accident. In the original game, the average voice in this category was 50, in our game it is likely to be 21.6. Note that 21.6 / 50 is almost exactly equal to (2/3) ^ 2. Those. It turns out that on average, the results of a game on the Habré will be approximately 4/9 times less than the results of the game in Denmark.

Check if this is so? On the one hand, 11.12 / 21.6 = 0.51, which is quite far from (2/3) ^ 2 = 0.44. However, we multiply all the numbers by (3/2) ^ 2 and construct a new histogram. We will get the following graph:
Pay attention to the peaks we know at points 22 and 34. Anyway, the graph is very similar to yesterday, including a small peak of about 50. So, although my theory did not help to guess the winning number, it predicted quite accurately general nature of the game.

UPD: by the way, if you drop the obviously losing votes (over 66, (6)), then the winning number becomes 9.5379997616, which is already very close to 21.6 * (2/3) ^ 2 = 9.6.