A Boltzmann brain would seem to be rarer than a universe, to me anyway, a universe can be sort of a random blob with laws of physics conducive to evolving complex behavior, a Boltzmann brain has to go "SNAP I am a brain now!"
The average Universe probably never creates a Boltzmann Brain.
But there are still infinitely many, just like there are infinitely many integers.
For that matter, consider what happens if you notice that "I think therefore I am." applies to data about a Boltzmann brain. It doesn't have to be in any specific laws of physics other than numerical logic.
Then of course we point out that Not only does Quantum Mechanics demand a continuum number of universes based on our laws of physics, but Logic itself demands an infinite number of logically inaccessible universes with whatever self-consistent laws of physics they could possibly have, sans simulator.
So we can exist either as a simulated entity, or one that isn't simulated.
Which is more likely? I am gonna say the second due to the odds of random goop being googols of orders of magnitude more likely in any given rule-set than sentient beings randomly forming.
Think of it this way, Nobody ever proposed the theory of Random idiot design for why we exist.
On the other hand, while top-level Boltzmann brains would be exceedingly unusual and rare, top-level universes would produce brains that may act the same.

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