kurt_w wrote:You could have a single universe that lasts forever, but in which the same events keep happening over and over again
This is theoretically possible, but doesn't seem to be a description of the universe in which we live, as ours appears to have directionality in time as well as a definite beginning. That is, our universe was born in the Big Bang and has steadily expanded and cooled to produce everything we see around us (and which will eventually expand and cool so much that processes requiring energy can no longer be maintained.) For your scenario to play out, the universe would have to be reborn -- that is, there would need to be a new Big Bang event following from which everything would unfold exactly as it has (at least once) before. But if there's a new Big Bang, is it correct to think about it as being the same universe? I don't think so, but your ymmv.
kurt_w wrote:In contrast, the many-worlds interpretation of quantum dynamics really would lead to all possible outcomes.
This hardly guarantees that you would become Supreme Ruler or be adept at wearing hats. It could simply be that there are no points from which another universe could diverge from our own where circumstances permit these possibilities. On the other hand, they are both theoretically possible, so again, given an infinite amount of time and infinite space to work with, they would eventually happen because probability says they must. Heck, if the universe is already infinitely large (a very distinct possibility), that means there are portions of it so distantly separated from us that they can never be observed and no interaction between them and us will ever be possible. In such a scenario, it's actually pretty likely that there's already
a kurt on another Earth who reigns supreme and is dashingly behatted.