Games, bias and statistics

Otaku Cedric posted this in his blog: Do you want to play a game?

People are apparently fascinated by these mathematical mind games. Count the comments here if you don't believe me.

What's common about these puzzles is there's usually one answer that is more attractive than the others. Reaching the attractive conclusion often requires a bit of logical reasoning, but that's not always the rule.

Considering that mind games (especially the statistical varieties) would not be very interesting if the correct answer was the obvious one, would it be safe to read their intentions and always assume that the attractive answer is wrong?

If you are a Bayesian filter only looking for the numeric/boolean solution, probably yes. People, on the other hand, work differently: the naive gamers will take the bait of the attractive answer and lose the game; the keen gamer will still be drawn into each individual game's rule set, rather than considering that a generic probabilistic approach based on the question's bias will win most of these games, regardless of their rule sets.

The devil is, of course, in the details. Even though these types of games never explicitly ask for the reasoning behind answers, merely knowing the correct answer is not as desirable as knowing why that is so (for us humans, anyways).