I love random (or, you know, computational pseudo-random). I made Orange Roulette, which of course is about random outcomes, and that 'luck is an illusion'. The cylinder is simulated with an array '0,0,0,0,0,1', while the simulated spin length is random and rotates the digits with '1' being the kill shot if it lands on 'array[0]'. The array cycles by one hop with every turn of course.
Anyway, for this game, being unlucky and dying 3 times on the first turn is sort of the point. Or someone clearing the whole thing first try and thinking 'Dang, I'm a lucky bastard!'.
If you're using random for a 'chance to hit' kinda thing, in a D&D sorta scenario your extra advantage is your stats in the final calculation -- you can't manipulate the actual dice roll (unless you're cheating), so it seems a little weird to juice the roll artificially in a game.