Likewise, the winner of the lottery observes the same number twice, which is some evidence for various crazy hypotheses where the selection of "I" necessarily coincides with the winner.

In my example of two worlds, the odds of observing the observed evidence is the same in both worlds and so there is no update.

What set of worlds are you postulating for your "two numbers" example? Because your example, as far as I understand it, doesn't seem at all analogous.