Guess the Number - Theory
It was mathematically impossible for the winning number to have been higher than 66 because this would suggest the average of guesses was greater than the upper limit for guesses (100).
If all participants in Guess the Number picked a number at random the average of guesses should be 50 and the answer
The beauty of the game is that not all participants are rational, and the broad array of guesses which we received illustrates this point (see our infographic). So the winners were those who not only understood the game but also correctly gauged the behaviour of other participants who didn’t.
Guess the Number - What happened in practice
As our first chart shows 2% of guesses were in the range 67-100 which as the theory states were mathematically impossible.
The most popular guess was 33 which corresponds with the first level approach.
2.5% were sophisticated enough to give the theoretical answer of 0, which didn't account for the irrational participants.
The winners were the participants who were able to both understand how the game worked and accurately account for the behaviour of those that didn't.
There were 32 correct entries from which we drew 3 winners and 5 runners-up at random. Congratulations to:
- Zac - Australia
- Artem - Germany
- Markus - Austria
- Jimmy - Denmark
- Kamil - Czech Republic
- Maciej - Poland
- Gregg - Canada
- Clint - Australia
Guess the Number - Other factors to consider
There were other factors to take into consideration as well as a few clues. The layout of the entry form may have had some unintended influence requesting a number between 0-100 which may have acted as an anchor for participants. An anchor being a ready hypothesis that by human nature we tend to respond to whether relevant to the question in hand or not.
Given the low barrier to entry, many participants may have skipped the details and simply followed the simple instruction to pick a number between 0 and 100.