General comment: As different things get "strongly" coupled to each other, one needs to take more and more steps into account to get a reasonable answer.
The question I have is this: Is there any way to figure out how many steps the other people in the situation will be using?
Many people will assume nobody will think about the problem (1 step thinkers). A few people will assume someone will think about the problem who thought about the people who won't think about the problem (2 step thinkers).
I think most 3+ step thinkers will take the problem to it's most logical inclusion (making them n-step thinkers). Why stop arbitrarily at 3 or 4? They've recognized that people who exist who will think other people exist who thought about the problem. At that point they should be able to recognize that this pattern will continue to n. While I am sure there are 3->(n-1) thinkers, they'll be more rare than n-step thinkers, I'd reason.
There are a number of 0 step thinkers who read the question and answered 33 though.
Now I have a question: Is the person who answers 0 smarter than the people who happened to guess the right answer at the proper point of time, even if at the current time (and possibly indefinitely) they got the problem wrong? aka "I only got the answer wrong because other people didn't think hard enough."
I think I either underestimated how many people would share this on Facebook, or perhaps, the audience that will go to a New York Times page is different than the audience that will go to "Only geniuses will be able to get this..." type quizzes. Of course, it could be that HN skewed the results in favor of a true mathematical + predictive model.
What cards do I have (1S), what does my opponent have (2S), what does my opponent think that I have (3S), and what do I think that my opponent thinks that I have (4S). I have found that beyond 4S, the analysis really loses its value even in the toughest games.
Paradoxically, I have found these tools are a detriment to easier games because the game is dominated by 1S and 2S thinkers and a 4S analysis often results in the wrong conclusion.
That's a great observation, and I wonder if anyone has done a serious study on the optimal season to sell a house.
(And the peak at 66 is rather disconcerting; there's no rational reason for that choice other than innumeracy or misreading the question.)
The NYT glibly informed me my choice was 'not even close'.
So the answer to this headline, finally, is "yes." Eat it, Betteridge.
Also, I don't see why N-step arguments are invalid; everyone who went for the Nash Equilibrium is wrong (the average is not 3/2 * 0); you just need to predict how many step-thinkers people are :P
(I guessed 6, which is approx 2/3 of 2/3 of the winning answer... so presumably I'm two steps too deep :P)
