On how diced systems should work:
When you roll the dice, as often as possible, *something* should happen. The result should add interest.
Caveat: systems like D&D combat that break down single tasks into many rolls, with the random results contributing to the ebb and flow of tactics, can escape this to some extent---but this is why D&D combat is more fun than D&D skill resolution.
Corrolary: for the most part, players should be reasonably aware of what they can accomplish. This is particularly true on non-tense rolls: you should never have a 60% chance to "do something cool" unless the sum possibility of "partial success" and "interesting failure" is at least 35%. It doesn't matter whether the 60% is for a random acrobatic jump or to personally invoke the presence of a deity. It doesn't even really matter if it's "become a deity," unless you get retries, because that leads to "okay, darn it, I give up. I'm BECOMING A DEITY." 62%. "Oh. Or not!"
This is because the player, in deciding to do something, generally weights success towards "interesting" and makes ordinary failure less interesting. If you're doing it as a long shot, a 10% roll in the hopes that this'll be the time you get lucky, then you can account for that. If you're doing it because you think you can, but it's also pretty likely you can't, then you're running the danger of thinking like Jackie Chan when you're actually playing Van Damme.
Rebecca