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Jonathan_Graehl comments on Pract: A Guessing and Testing Game - Less Wrong
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This is not a great game for competitive humans to actually play. It's a decent game to think about playing to win. You could have some fun with programs given an agreed upon representation language for sequences.
The first human player to use e.g. "md5(3891*seq) odd", wins. You can quibble over how long it should take to describe how a sequence is encoded into a bitstring, but even sets where every sequence is of length 1 can be infinite.
If I'm allowed to use any number of functions with widely agreed upon names, I don't see much hope for my opponent.
Or heck, how about just the binary representation of pi? You don't even need any functions beyond basic arithmetic (eg. if all the famous constants are well known, just pick the decimal expansion of some suitable rational).