I am not entirely familiar with modern day algorithms behind brut force attacks, but the math I described above is the theory behind them. I would imagine that

I am not entirely familiar with modern day algorithms behind brut force attacks, but the math I described above is the theory behind them. I would imagine that it would have to be in some kind of ordered sequence so that you didn't miss any possibility and that your brut force time would average out (assuming infinite number of tries over rendom selection of passwords). It is, however, reasonable to assume that once the attack got part way though a word, that it would then try most common words etc. But assuming a random compilation of characters, sequential would be the most efficient over many number of tries. Note: the above does not apply to brut force attacks that try most common passwords and other techniques that include human element. It's just math behind the algorithm.