I'm not a great fan of random, aside from small variances based on known variables which encourage additional thought and minor gambling, but when things get too random it annoys me greatly. Let's compare a few games to illustrate the point:
Medieval: Total War versus Civilisation III. With M:TW you always have the same map but can choose a different nation. I really, really enjoyed this game but it has limited life, at some point there's little point repeating the process. Civilisation III I don't enjoy so much, but play it more, because it has more variables and an almost inexhaustible supply of new scenarios via tweaking options. So if I was stuck on a desert island with just one game for eternity, I'd go for Civilisation III, even though it's random is mostly infuriating but if I wanted to buy a new game that I could have a strong memorable experience with I'd go for M:TW. I'd rate C3 as an imbeween game to play while waiting for a new cool game to play and M:TW as a cool game.
Likewise for King's Bounty: The Legend versus Heroes of Might and Magic III or Icewind Dale versus Diablo/clones. KB:tL and ID are cool games, where as HoMaM and D/c are just excellent fillers, and it's the random which is the main factor in this viewpoint. Ideally I like to play games which don't make me rage, the rage from random is just a side-effect or downside to the longevity of replayability.
This kind of viewpoint won't be the same for everyone because, as you suggest, some people simply enjoy the masochism. It's very rare to find a game that provides both eternal random plus predictable scenarios/combat etc, just another reason why Chess manages to remain so popular, even in a booming games market, it's still quite unique in this field.