You don’t want to randomize in this case. Omega has given you a unique ID. Exploiting that information in a well-chosen deterministic strategy gets you a higher chance of winning than does picking randomly.
1A 2B makes more sense than the reverse—I would go with that.
The “by symmetry” argument in the post should be rejected, since being given “1″ and being given “2” are not really “symmetrical”.
You don’t want to randomize in this case. Omega has given you a unique ID. Exploiting that information in a well-chosen deterministic strategy gets you a higher chance of winning than does picking randomly.
1A 2B makes more sense than the reverse—I would go with that.
The “by symmetry” argument in the post should be rejected, since being given “1″ and being given “2” are not really “symmetrical”.