I don't know about most streaks will end at 3 or less. Many years ago, I looked at a set of about 1000 shoes and also did a test with random number generator. By doing so, you will find out the number of singles will equal that of doubles, doubles equal 3s, 3s equal 4s and so on. That's because singles will be compared to doubles, 3s, 4s and so on. While you may see more singles than doubles, 3s contain doubles, 4s contain doubles, 5s contains doubles and so on.
By cutting doubles and 3s and not playing singles, you have more on the shorter end. Playing a short game though, the distribution isn't the same. For this reason, no progression will always work and guessing the kind of streaks you will get is impossible. Only way to do it is to force it to happen.