Guess the 2/3 average 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 habroles rational? What is more often used as a decimal separator: a comma or a comma? Who in the end was the winner?
I will not pull, I'll start with the main results. The average of 354 numbers (why not 357? See below) is 16.6844657552. Two thirds of this number - 11,1229771701 . The closest was Artyushkin Alexander with the number 11,12 . Hooray!!! Because if it is not registered on Habré, then as a prize it receives an invite, earned due to the previous post.
Now some statistics. Of the 357 participants, 176 were from Habra, 181 took part via email. 3 votes were declared invalid due to the lack of a number in the message :) A special “thank you” to those 40 people who sent messages with several numbers (for example, voice and explanation with formulas or 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 cases - a period. Apparently this is due to the fact that programmers are accustomed to using the point everywhere.
')
Finally, we turn to the analysis of the results. Below you can see a histogram of votes. Immediately striking is its overall similarity with the histogram from Denmark. The peak at 0, although more, is insignificant. 11 people decided to spoil the guesswork of the others and chose numbers greater than 66, (6).
The most popular number was 15 - 22 votes. In the second place - 0 (13 votes), in the third - 1 (11 votes), the fourth and fifth divided 10 and 14 (10 votes each).
If you remember, in the previous post I said that I have a theory about how the 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 in general, i.e. chooses his number almost randomly. 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 game results in Habré will be about 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 rather far from (2/3) ^ 2 = 0.44. However, we multiply all the numbers by (3/2) ^ 2 and build a new histogram. We get the following schedule:
Notice the familiar peaks at points 22 and 34. Anyway, the schedule is very similar to yesterday's, including a small peak around 50. So, although my theory did not help me guess the winning number, it fairly accurately predicted the overall nature of the game.
UPD: by the way, if we discard the obviously losing votes (more than 66, (6)), the winning number becomes 9,5379997616, which is already very close to 21.6 * (2/3) ^ 2 = 9.6.
UPD2: Sent numbers are available at spreadsheets.google.com/ccc?key=rCrpB3z283H9hYcNBd8unXA
UPD3: the winner is registered on the habr : stahon
Thank you all for participating and, once again, congratulations to the winner!
I will not pull, I'll start with the main results. The average of 354 numbers (why not 357? See below) is 16.6844657552. Two thirds of this number - 11,1229771701 . The closest was Artyushkin Alexander with the number 11,12 . Hooray!!! Because if it is not registered on Habré, then as a prize it receives an invite, earned due to the previous post.
Now some statistics. Of the 357 participants, 176 were from Habra, 181 took part via email. 3 votes were declared invalid due to the lack of a number in the message :) A special “thank you” to those 40 people who sent messages with several numbers (for example, voice and explanation with formulas or 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 cases - a period. Apparently this is due to the fact that programmers are accustomed to using the point everywhere.
')
Finally, we turn to the analysis of the results. Below you can see a histogram of votes. Immediately striking is its overall similarity with the histogram from Denmark. The peak at 0, although more, is insignificant. 11 people decided to spoil the guesswork of the others and chose numbers greater than 66, (6).
The most popular number was 15 - 22 votes. In the second place - 0 (13 votes), in the third - 1 (11 votes), the fourth and fifth divided 10 and 14 (10 votes each).
If you remember, in the previous post I said that I have a theory about how the 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 in general, i.e. chooses his number almost randomly. 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 game results in Habré will be about 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 rather far from (2/3) ^ 2 = 0.44. However, we multiply all the numbers by (3/2) ^ 2 and build a new histogram. We get the following schedule:
Notice the familiar peaks at points 22 and 34. Anyway, the schedule is very similar to yesterday's, including a small peak around 50. So, although my theory did not help me guess the winning number, it fairly accurately predicted the overall nature of the game.UPD: by the way, if we discard the obviously losing votes (more than 66, (6)), the winning number becomes 9,5379997616, which is already very close to 21.6 * (2/3) ^ 2 = 9.6.
UPD2: Sent numbers are available at spreadsheets.google.com/ccc?key=rCrpB3z283H9hYcNBd8unXA
UPD3: the winner is registered on the habr : stahon
Thank you all for participating and, once again, congratulations to the winner!
Source: https://habr.com/ru/post/62789/
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