Second, repeating the Counterfactual Mugging more than once tends to obscure the point,
Surely if you'd take the bet once, you'd take it any number of times, so this shouldn't make much of a difference- and I can't see how stopping algorithm / fixed number of rolls makes a difference.
I'm going to test just how much the people here are committed to paying a Counterfactual Mugger, by playing Omega.
I'm going to roll a die. If it doesn't come up 5 or 6, I'm going to ask Eliezer Yudkowsky to reply to this article with the comment "I am a poopy head." If I roll a 5 or 6, I'm going to donate $20 to SIAI if I predict that Eliezer Yudkowsky will post the above comment.
Because Eliezer has indicated that he would pay up when counterfactually mugged, I do predict that, if I roll a 5 or 6, he'll respond.
::rolls die::
Darn it! It's a 5. Well, I'm a man of my word, so...
::donates::
Um, let's try that again. (At least I've proven my honesty!)
::rolls die::
Okay, this time it's a 1.
So, Eliezer, will you post a comment admitting that you're a poopy head?