That is why i dislike using D&D as an example for anything. The game has way too much depth to prove one thing one way or the other. Anyway, i was just looking at the "PC level up" aspect of the game, (and i really don't want to get into an argument on D&D mechanics, i do that almost every time i play ANY D&D), but the logic is that - hypothetically, someone with a +1 to any one roll, can beat a 10 difficulty attempt if he rolls high enough. Someone who put points (or feats, or w/e) towards that roll has a "better chance", not because their roll isn't die dependent (all things are and SHOULD BE die dependent, because well, this is D&D after all), but because you'd typically expect them to have a base of +5 (or some such). Hypothetically, roll bonuses get so high that you could auto-pass a lot of rolls (that's what leveling up does for you in a vacuum). However, because the nature of pen and paper games allows them to keep the area difficulty (talking about "the difficulty of the area" here, not the technical term) ahead of your level, you end up, in practice, with what strom describes (a bloody lot of PRAISE THE LORD, JESUS CHRIST AND PEANUT BUTTER rolls as you go deeper into the game). Unless your GM arbitrarily decides (or for plot reasons), to keep the area difficulty below your levels, randomness will remain a big factor. Also, absurdly high rolls is also how D&D balances out an environment where you have multiple players with specialist roles. If a wizard could burn a roll or two and disarm every trap he comes across for minimal pain, that would be a major kick in the nuts for the rogue who put a million points in disable device for this express purpose. As such, having high difficulty rolls doesn't just help to keep things random for specialists (which you may or may not agree on as a mechanic), but it does make a great deal of actions impossible for non-specialists (which i think we can all agree on as a mechanic - you should reward/punish for taking/not taking points in an ability in a tangible way). Nonetheless, that's just how D&D balances out a (bonus to roll) mechanic that, unless you keep pushing the roll difficulty up and up, will very quickly become roll-irrelevant in a context that very much assumes multiple players in specialist roles. My point here is that you CAN create a system that achieves luck independence by borrowing a couple of pages of a D&D rulebook - the emphasis here being on a "couple of pages" (e.g. the re-roll mechanic is a great way to take randomness out of the game, which is why D&D does not have a lot of it - nothing stops YOU from having a LOT of re-roll mechanics though). If you borrow ALL the pages, then well you're just gonna end with Dungeons & Dredmor.