It seems to me that for one to engage in solo roleplaying some sort of random input is needed to direct one's imagination. Without it, the exercise becomes plain creative writing, or storytelling.
Still, engaging a randomizer results in a break in the flow of imagination as you interpret the results. The break in the flow might be short, but it is there. I've found that trying to keep a cohesive feeling to the story sometimes means that the breaks are longer as I try to make sense of some random result in context of what has happened in the story prior to that.
What is your sweet spot in terms of percentages? Do you have any rules of thumb as to when to call upon Randomness?
I have created a little poll to see if I can get a feeling of how often folks engage their randomizers:http://poll.pollcode.com/7v8uy