why i can't win at the stock market

a few weeks ago, planet money decided to run an experiment.  they asked readers to pick a number between 0 and 100, with the goal being to pick the number closest to half the average of all the guesses. so here's how to you play the game.  if you assume everyone is guessing randomly, the average would be 50, so you'd pick 25.  however, knowing that everyone else knows what you know, and are all guessing 25, you should pick 12.5, however knowing that everyone else knows what you know, and are all guessing 12.5, you should pick 6.25, and on and on and on until you wind up with some number which for all intents and purposes is zero.  makes sense right?  how could a reasonable, rational person pick anything else?  well planet money released the results along with a graph of the distribution of guesses, to which i have added my own interpretation.  for the record, the actual winning number turned out to be 11.53.  i picked zero.

this whole experiment and ensuing debates with coworkers reminds me of this...