• What’s 2/3 of the Average?

    Here’s a well known and subtly interesting game. If it is new to you, ponder it for a bit of weekend fun. Or better, pose it to your friends and family. I’ll post analysis on Monday. Later on I’ll apply the analysis to the real-world issue of speculative bubbles in financial markets.

    Suppose everyone in your town selects a real number between 0 and 100, inclusive (i.e. 0 and 100 are both possible choices, as is any other number between). The winner is the individual (or individuals) who selects the number closest to 2/3 of the average of numbers chosen. What number do you choose? Why?

    Just to be clear, suppose there are three players who select the numbers 10, 20, and 30. The average is 20, and 2/3 of the average is 13.333… . Therefore, the winner is the individual who selected 10 because it is closest to 2/3 of the average.

    • Hm. Great game.

      I could be way off base, but here’s my thinking:

      It depends entirely upon how clever you expect everybody else to be. The more thought you expect each person to put into it, the lower you should guess (all the way down to zero, I think).

      • @ObliviousInvestor – I should embargo your comment because it is a two sentence summary of the analysis I’ll post Monday. Well put. (Anyone reading this should immediately visit ObliviousInvestor’s blog — http://obliviousinvestor.com . He clearly knows how to sum things clearly and briefly.)

    • I blogged on this game recently.

      • @jeff – Indeed you did. I deleted the link in your comment in keeping with my policy to do so when the comment text doesn’t add any additional information to the discussion beyond advertising the link. If you’d like to comment again with something more substantive I can leave the link in place. Sorry. That’s my policy.

    • @tie: perhaps you should restore the link that you deleted, because now, we can’t know what he was blogging about, unless we get lucky and find his article in a search.. I believe that posting a link is perfectly acceptable (unless it’s pure spam of course), and saves a lot of time to everyone (both poster and reader) compared to having to copy and paste something that already exist somewhere else… It looks like the articles I found all refer to the same danish study where the number of average iterations was 1.07. I am hoping to find more studies.

      • Sorry. Blog-wise, this is ancient history. The link wasn’t saved anywhere. What was done here doesn’t even reflect current policy. Nothing to be done. I may just delete the whole exchange as it adds nothing as is. One more comment about it (the exchange, the edited comment, and so forth) and I likely will because it is not worthwhile at this point.