Feb 14, 2014
Feb 14, 2014

# Guess The Number

Over 1,600 of our customers played Guess the Number – the first Pinnacle Puzzle. All those entries have been summed, averaged and multiplied by two-thirds producing a winning number of 20. See if you were one of the three lucky first prize winners.

### 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 would therefore be 33.

Anyone applying a first level of processing would assume that the majority of participants wouldn’t guess at random which brings the likely winning number down, and if you continue to eliminate what are considered 'weakly dominated strategies' you would end up with a guess of 0, which is the theoretical 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

Theory aside, let's look at how Pinnacle's customers approached Guess the Number.

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:

Winners:

• Zac - Australia
• Artem - Germany
• Markus - Austria

Runners-Up:

• Jimmy - Denmark
• Kamil - Czech Republic
• Maciej - Poland