endoself comments on Zendo-like Induction Game for Playing Online - Less Wrong
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One issue with Zendo that doesn't necessarily make it a great game for actually improving rationality is that the rules are made by humans, so you can use psychology to get information. For example, I was playing with my family a few nights ago and my mother guessed a certain rule, my little brother immediately said "That's not Josh's rule. it isn't elegant." And sneakier players can do even worse stuff using sidechannel attacks. In particular, how long it takes for the Master to judge whether different configurations fit the rule can give a lot of information about the rule form.
Humans are the only things capable of reliably generating things that seem non-obvious to humans. The only reason the universe seems so good at it is because we pay less attention to the obvious things. I don't think we can improve on this issue easily enough for it to be useful for the purposes of the game.