I've got a few questions about Newcomb's Paradox. I don't know if this has already been discussed somewhere on LW or beyond (granted, I haven't looked as intensely as I probably should have) but here goes:

If I were approached by Omega and he offered me this deal and then flew away, I would be skeptical of his ability to predict my actions. Is the reason that these other five people two-boxed and got $1,000 due to Omega accurately predicting their actions? Or is there some other explanation… like Omega not being a supersmart being and he never puts $1 million in the second box? If I had some evidence that people actually have one-boxed and gotten the $1 million then I would put more weight on the idea that he actually has $1 million to spare, and more weight on the possibility that Omega is a good/perfect predictor.

If I attempt some sort of Bayesian update on this information (the five previous people two-boxed and got $1,000) these two explanations seem to equally explain this fact. The probability of Omega putting the $1,000 in the previous five peoples' boxes given that he's a perfect predictor seems to be observationally equivalent to the probability that Omega doesn't ever put $1 million in the second box.

Then again, if Omega actually knew my reasoning process, he might actually provide me with the evidence that would make me choose to one-box over two-box.

It also seems to me that if my subjective confidence in Omega's abilities of prediction are over 51%, then it makes more sense to one-box than two-box... if my math/intuition about this is correct. Let's say my confidence in Omega's abilities of prediction are at 50%. If I two-box, there are two possible outcomes: I either get only $1,000 or I get $1,001,000. Both outcomes have a 50% chance of happening due to my subjective prior, so my decision theory algorithm is 50% * $1,000 + 50% * $1,001,000. This sums to a total utility/cash of $501,000.

If I one-box, there are also two possible outcomes: I either get $1,000,000 or I lose $1,000. Both outcomes, again, have a 50% chance of happening due to my subjective probability about Omega’s powers of prediction, so my decision theory algorithm is 50% * $1,000,000 + 50% * -$1,000. This sums to $499,000 in total utility.

Does that seem correct, or is my math/utility off somewhere?

Lastly, has something like Newcomb's Paradox been attempted in real life? Say with five actors and one unsuspecting mark?