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Kaj_Sotala comments on The Fundamental Question - Rationality computer game design - Less Wrong Discussion
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This sounds like the perfect game.
Perhaps look at the design of other puzzle games for guidance. One of the most successful, Professor Layton, is excellent, and introduced better thinking habits to me (Kahneman's famous €1.10 Bat and Ball problem was brought to me here). It made sure that if you wanted to get the most out of the game, you had to check your thinking - I got the bat and the ball problem right, because I'd learnt to check carefully. It wasn't, however, designed with rationality in mind. It could've been a lot better.
Please post updates about how the game develops :-)
Damn, I don't have a DS. Might have to ask some friend to lend theirs. :)
I'll do my best to post updates.
If you do a little googling + torrenting, it can be free on a computer ;)