The hold option should forever ban Quirrell from offering that exact source code string again (equivalent is fine, just not identical), and also cost some non-zero number of points. Unfortunately, Quirrell can trivially generate a vast array of identical programs, thus making “hold” a problematic choice. I don’t see how to ban that without solving the general program-equivalence problem, which is halting complete.
If holding costs nothing, write “if score > 2^100, walk away, else if p is equivalent to this, double down, else hold”. Then tell Quirrell that you’ll only accept that program for your first move, and will hold until he produces it. Congratulations, you now have an exceedingly boring stalemate.
I don’t see a way to make the hold option interesting.
The hold option should forever ban Quirrell from offering that exact source code string again (equivalent is fine, just not identical), and also cost some non-zero number of points. Unfortunately, Quirrell can trivially generate a vast array of identical programs, thus making “hold” a problematic choice. I don’t see how to ban that without solving the general program-equivalence problem, which is halting complete.
If holding costs nothing, write “if score > 2^100, walk away, else if p is equivalent to this, double down, else hold”. Then tell Quirrell that you’ll only accept that program for your first move, and will hold until he produces it. Congratulations, you now have an exceedingly boring stalemate.
I don’t see a way to make the hold option interesting.
Well, as you have pointed out (I mean: http://lesswrong.com/lw/e4e/an_angle_of_attack_on_open_problem_1/7862 ) , we are probably already dealing with non-real-line utilities. So we could just lose one hold point per hold.
Also, we could require Quirrell to present each source code string infinitely many times.
This would remove stalemates of Quirrell not offering some string at all, and would give us some incentive to accept a many programs as we can verify.