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Boltzmann, incomprehensibly great genius though he was, had no concept of how old the universe was; cosmology did not exist in any serious, let alone quantitative way in the 19th century.

Consequently, the likelihood of Boltzmann brains, and other statistical horrors he envisioned are so low as to be zero for ALL practical purposes.

People like to point out the monkey typing randomly for an infinite amount of time producing all the works of Shakespeare as an example of just what bizarre consequences randomly occurring events can produce without exploring the practical consequences of this thought experiment, but doing so puts you in touch with how large infinity is.

For example, under some reasonable assumptions about how fast he types, the monkey will produce many English phrases, including all the works of Shakespeare, in fact every book ever written, including every version of the Bible after a very long time. Before he types out the complete works of Shakespeare in order, he will have repeated many lines from Shakespeare over and over, many times.

How long does it take him to type just the first recognizable sentence of twelve words or longer from Shakespeare? I believe the estimate we came up with in my first graduate class in statistical mechanics was 10^48 years. Compare this to ~10^13 years for the age of the universe. That's right. Our universe, and the next universe after ours, and so on and so on, could consecutively be born and die more than Avagadro's number of times before he types just ONE moderately long sentence.

In mathematical terms, 10^48 is closer to zero than it is to infinity. "A LOT" closer.

You won't be seeing Boltzmann brains popping up anytime soon...