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Manfred comments on Rationality Dojo - Less Wrong
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Perhaps they could program something specifically related to rationality.
One example: the activity leader gives everyone else a standardized input/output structure to move around a soccer field/gladiatorial arena/asteroid mining station/scene of the crime, then the group members write a program that they think will win whatever the game is. The activity leader throws the group's programs in a file together (maybe after writing some competitors obeying simple principles, so that the group leader has something to do and the players have a benchmark), and out spits a detailed analysis of what happened and who won. Then people get to apply their skills to understand why things turned out as they did.
You could also do it without the actual programming if the overhead of writing things gets in the way (it would for most people).
If it is a simple enough game, people could design their algorithm and then step through it manually with each other. The difference between this and strategy-based board games would be sticking to an explicitly written down strategy.