Well, I was thinking more in terms of a logical prior over single statements, see my favorite here.

But yeah I guess I was missing the point of the problem.

Also: suppose Omega comes up to you and says "If 1=0 was true I would have given you billion dollars if and only if you would give me 100 dollars if 1=1 was true. 1=1 is true, so can you spare $100?" Does this sound trustworthy? Frankly not, it feels like there's a principle of explosion problem that insists that Omega would have given you all possible amounts of money at once if 1=0 was true.

A formulation that avoids the principle of explosion is "I used some process that I cannot prove the outcome of to pick a digit of pi. If that digit of pi was odd I would have given you a billion dollars iff [etc]."