DanielLC comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
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You have an entire universe to consider. You don't deal with just possible universes just began. You deal with all possible universes. There are simple universes that eventually come out to this, but no simple ones that start this way. Also, a limited speed of light is not guaranteed. As far as we can tell, it's limited, but it might not be.
If you can always calculate it so it's 50%, along with any other probability, you're clearly doing something wrong. It should only calculate to one value.
You can also add on modified versions that are coupled, or things like that. It's a bit more complicated than I said, but there's still a good chance (as in more than 1/3^^^^3) that the mugger isn't bluffing.