Boltzmann brains, like Doomsday, require no explaining

Brothers and sisters I have none, but that man's father is my father's son. Who am I?— ancient riddle In Eliezer Yudkowsky’s post this week, he writes: “Our current experience -- your own experience, at this very moment, of seeing ordered letters on a screen -- therefore seems to provide overwhelming anthropic evidence against any model of reality or physics which would imply that most brains are Boltzmann brains.”I hope it’s fair for me to roughly present this line of reasoning like so:If Boltzmann brains are possibleAnd if Boltzmann brains would severely outnumber ordered brainsAnd if each observe is a random draw among all observersThen finding ourselves to be non-Boltzmann brains should come to us as a huge surpriseMeaning either one of the prior premises is false, or we need (in all likelihood) a theory of the universe that can compensate for this severely unlikely observationI take the side that “one of the prior premises is false”. Can you guess which one?What follows is a post about the Doomsday Argument, but everything I write equally applies to the idea that the possibility of Boltzmann brains presents a problem that theories of the universe must solve.The Doomsday ArgumentThe Doomsday Argument has been debated among philosophers for decades. It seems to indicate that the number of future humans should be roughly equal to the number of past humans—though that obviously can't be true among all points in time. I believe most people reject the argument, but how they do so can widely vary. For instance, some folk believe in compensating theories that end up implying the opposite: that actually there can never be an ultimate Doomsday, because the number of humans (or at least, the number of conscious observers) is infinite.To understand the argument works, let's start with a game. There's a deck of cards that can be any size N between 1 to 100, though you don’t actually get to see the deck. A random card will be chosen from the deck and shown to you. If the fift