For myself at least, it's not just having a succession of poor rolls that I don't like, it's having my actions be subject to the whims of the dice. It is, however, specific to my actions: I rather like randomisation of the playing field--both physical and metaphorical. For example, I don't like my hits and misses being determined entirely by die-rolls; I want my hits and misses to stem from my skill. (I don't mind a small element of random number generation; for example, I'd be happy enough if spells occasionally produced a more- or less- powerful effect, or a slightly different one, or if sword-hits were occasionally "critical" hits, etc.) On the other hand, I do like having randomly-generated levels, and randomly-generated loot; I like the idea, for example, of getting a sword on one run and a wand of fireball on the other. This sort of randomisation changes which options I have available, rather than changing the outcome of my selection from those options.
Put another way, think of it like a card game: I like playing with a shuffled deck, not knowing what options I'm going have available in a given hand, but I don't want to be told that my play simply doesn't work just because a die-roll says so.
However, this is very much personal preference; you say that you do like randomness in your gameplay, which is fair enough.