There are 50 people in a room. Each is asked to pick a number from 0 to 99. The winning number will be calculated by taking two-thirds of the average of the numbers picked by the 50 people. What number would you pick in order to win?

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Some common answers:

  • 33: All things equal, in a random, normally distributed sample, the average would be 50. So, taking 2/3 of 50 = 33.
  • 0: As above, but, since everyone “should” follow the above line of thinking, take 2/3 of 33. But wait, everyone should do this also, so take 2/3 of 2/3 of 33. Continue until you’ve multiplied by two-thirds all the way to nearly 0.

From a statistics standpoint, 33 is the “right” answer. But, this answer undervalues the level of thinking that others will apply to the problem.

From a game theory standpoint, 0 is the “right” answer. But, this answer presupposes that everyone “will think through the problem to the same degree as you”.

To win, you really want to balance between the above two approaches. If you expect that most will pick 33, then taking 2/3 of 33 = 22 will be a “good” pick with a “good” chance of winning.

When this test was administered to 5 different classes with ~50 students in each class, the average number picked was 34.72, meaning that the winning number would be ~23.

I bring this up because the professor went on to explain that most companies make business decisions that resemble picking “33” in this scenario. Companies typically tend to ignore the thinking of others (competitors or customers) when making a business / technical decision.

I’m sure OSS vendors & enterprise software vendors are equally guilty of this.