It's amazing, the results people come up with when they don't use TDT (or some other formalism that doesn't defect in the Prisoner's Dilemma - though so far as I know, the concept of the Blackmail Equation is unique to TDT.)

(Because the base case of the pirate scenario is, essentially, the Ultimatum game, where the only reason the other person offers you $1 instead of $5 is that they *model you* as accepting a $1 offer, which is a very stupid answer to compute if it results in you getting only $1 - only someone who two-boxed on Newcomb's Problem would contemplate such a thing.)

Ok so there's a good chance I'm just being an idiot here, but I feel like a multiple worlds kind of interpretation serves well here. If, as you say, "the coin is deterministic, [and] in the overwhelming measure of the MWI worlds it gives the same outcome," then I don't believe the coin is fair. And if the coin isn't fair, then of course I'm not giving Omega any money. If, on the other hand, the coin is fair, and so I have reason to believe that in roughly half of the worlds the coin landed on the other side and Omega posed the opposite question, then by giving Omega the $100 I'm giving the me in those other worlds $1000 and I'm perfectly happy to do that.