You are one of a countably infinite number of blindfolded people arranged in a line. You have no idea where in the line you are. Each person tosses a independent fair die, but doesn't get to see or feel the result.
Case 1: What is the probability you tossed a six?
Case 2: You are informed that, surprisingly, all the even-numbered people tossed sixes, and all the odd numbered people tossed something else. What is the probability you tossed a six?
It sure seems like it's no longer 1/6. For suppose it's still 1/6. Then when you learned that all the even-numbered people tossed sixes and the odd-numbered ones didn't, you thereby received evidence yielding probability 5/6 that you were one of the odd-numbered ones. But surely you didn't. After all, if there were ten people in the line and you learned that all but the tenth tossed a six, that wouldn't give you probability 5/6 that you were the tenth!
But as long as infinitely many people tossed six and infinitely many didn't (and with probability one, this is true), there is always some ordering on the people such that relative to that ordering you can be correctly informed that every second person tossed a six. That puts the judgment in Case 1 into question.
Moreover, why should the alternating ordering in Case 2 carry any weight that isn't already carried by the fact which you know ahead of time (with probability one) that there are equally many sixes as non-sixes?
But if the judgment in Case 1 is wrong, then were we to find out we are in an infinite multiverse, that would undercut our probabilistic reasoning which assumes we can go from intra-universe chances to credences, and hence undercut science. Thus, a scientific argument that we live in an infinite multiverse would be self-defeating.
I don't exactly know what to make of arguments like this.