okay so it turns out the main thing i find myself wanting to repeat is "this is a test of theory of mind" lemme tell a story. at science camp in high school we played a game called "guess 2/3rds of the average." it's exactly what it sounds like: everyone picks a real number between 0 and 100 and the winner is the person who gets closest to 2/3rds of the average. take as much time as you want right now to think about how you, personally, would play this game before reading on --- here's how you analyze this game """rationally.""" the highest the average can possibly be is 100, which would make 2/3rds of the average 66.6... this means there's no reason to play higher than this. but if everyone knows that, the real highest average becomes 66.6..., which would make 2/3rds of the average 44.4... but if everyone knows that... every time you repeat this chain of reasoning the highest average decreases by a factor of 2/3, and eventually you conclude that the nash equilibrium of the game is that everyone plays 0. in any other outcome the person who played the highest number always regrets their choice and wishes they'd played lower afterwards because they always end up too far away from 2/3rds of the average --- now for the punchline: this is never what happens when people play this game in real life. as wikipedia says the winning guess is often ~30, iirc when i played it was ~20. i also personally played 100 to troll the other players b/c the prize wasn't big enough that i actually cared about winning what actually happens in real life even when there are meaningful stakes is that a group of people never goes through the above argument infinitely many times (which is essentially what the nash equilibrium is doing) but, loosely speaking, a finite number k times, which roughly corresponds to the depth of theory of mind the group uses and anticipates other people using. the weak point in the above argument turns out to be "but if everyone knows that"; at some point this is no longer a safe assumption to make! the game theory argument goes through, as wiki explains, if and only if every participant is perfectly rational and this fact is common knowledge. this is a technical concept meaning everyone knows it, and everyone knows everyone knows it, and so on. when you iterate the game theory argument k times this depends on k levels of common knowledge of the group's rationality (or at least their willingness to pursue this line of reasoning). in some groups it wouldn't even be safe to assume this once! so the way you play this game is to roughly assess how willing you think other people in the group will be to run through the above argument, then guess 2/3rds of the corresponding average. or just guess something based on vibes. loosely speaking you want to guess a lower number the smarter, more technical, etc. the group is. the point is that 1) the very strong common-knowledge-of-perfect-rationality assumption that powers the game theory argument never even comes close to holding in real life and 2) that means you have to think about what the other people in the game will actually do instead of what a """rational""" theory says they're supposed to do en.wikipedia.org/wiki/Guess_…