More Number Picking

In a previous post, I mentioned the Pick-a-Number game that the folks at NPR’s Planet Money were running:

Pick a number between 0 and 100. The goal is to pick the number that’s closest to half the average of all guesses. For example, if the average of all guesses were 80, the winning number would be 40.

If everyone picked randomly, you would expect the mean to be approximately 50, in which case the winning number would be 25. So, you’d choose 25, right? But if everyone uses that same logic, then the mean would be 25, and the winning number would be 12.5. So, you’d choose 12.5, right? But if everyone used that same logic…

Well, you get the point.

When making your choice, it starts to feel like a game against Vizzini, the Sicilian from Princess Bride.

Only a great fool would reach for what he was given. I am not a great fool, so I can clearly not choose half the expected mean. But you must have known I was not a great fool, so I can clearly not choose half of half the expected mean…

Well, the results are in, and you can view them (and an explanation) here.

I take a minimal level of pride in receiving one of 772 honorable mentions for my guess of 12. (Don’t look for my name in the list, though. I used my son’s name as a pseudonym.)

Here’s a very simple pick-a-number game:

Pick a number between 12 and 5.

Make your pick before reading the next paragraph.

Did you pick 7? Most people do. My theory is that the magnitude and order of the numbers matters. Because the larger number is given first, and because the difference between the numbers falls within the appropriate range (12 – 5 = 7), it’s the “obvious” choice.

The trick would probably work equally well if the set-up were, “Pick a number between 19 and 6.” I suspect the most common choice would be 13.

Of course, this is just pop math psychology.

Speaking of “picking” and “numbers,” here’s a line a friend of mine used on an attractive waitress:

How can it be it that I’ve memorized the first 100 digits of π, yet I don’t know the 7 digits in your phone number?

For the record, I condone neither hitting on a waitress nor using that line.