If at least one type of BBs is measure-dominating, we are BBs. To explore chances for that, we need a classification of the possible BBs. Around 10 types of BBs so far identified and are listed in our article "Types of Boltzmann brains."
However, there it is not a big problem to be a BB. Firstly, because BB-observer-moments could create chains, like in Egan's "dust theory", and these chains will look like normal worlds. Second, because for any BB there is a real world mind in the same observer state (if any real world minds exist).
Also, the argument for randomness of experiences of BBs is not working, because if you are a BB, you can't make true judgements about the randomness of the things you observe. One could see completely random mess and still think that it is in order.
Another source of non-randomness in BBs is that they may be structured as random neural nets, because it is needed to make an "act of observation". A cat-dog classifier would classify any random input noise as either "cat" or "dog", thus increasing the orderliness of the output, despite the randomness of the input.