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Warrigal comments on A Series of Increasingly Perverse and Destructive Games - Less Wrong Discussion
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Game1 has been done in real life (without the murder): http://djm.cc/bignum-results.txt
Also:
Can't do that, unless you already know the programs will halt. The winner of the actual contest used a similar strategy, using programs in the calculus of constructions so they are guaranteed to halt.
For Game2, if your opponent's program (say there are only 2 players) says to return your program's output + 1, then you can't win. If your program ever halts, they win. If it doesn't halt, then you both lose.
Whelp, that's it, then. Ralph Loader has discovered the largest integer.