My question is different from this previous question: Does repeating one word to form a password result in a similar pattern in its encrypted format?. I'm specifically wondering about brute force attacks. Based on my experiences with John The Ripper, I doubt that repeating a pattern in a password would shorten the time to successfully brute force a password like f00B@rf00B@rf00B@r as opposed to a random string of equal length. However, my doubt is based on the fact that, according to the documentation, JTR does not include a specific attack mode for repeating patterns. JTR, and presumably other brute force tools, can be customized for any arbitrary attack mode. But we can't know how often attackers bother to customize attacks in this way. So then the question becomes mathematical. Please forgive the awkward pseudo mathematical notation.
T = brute force cracking time PL = pattern of characters of length L N = number of times PL is repeated R(LN) = string of random characters of length (L times N)
Would it be true that
If true, then a repeating pattern password would not affect brute force cracking time. But is it true?