|The throwing of these dice is discouraged.|
I've been thinking a lot about dice recently. The vast majority of people in this hobby play the world's premiere fantasy RPG or some analog of it, and that means linear rolls. Now, I don't dislike linear rolls, but I do think they make play experience more finicky This is partially their implementation. A very large number of games, possibly the majority, do not have rules for gradients of success; you either pass or fail. I cannot count the number of times that I have watched a party fail miserably due to the dice. Conversely, there have been just as many overwhelming successes. I will forever remember the final encounter of my last Pathfinder campaign, where the first player to act rolled two natural 20s and hit for something like 140 damage right out of the gate.
It's when the opposite happens that you feel the tendency to fudge rolls or allow re-rolls. That's even worse! But nobody wants the campaign to fall apart just because you rolled a failure at some critical (or trivial) moment. At the same time, I am strong proponent of the "Let it Ride" rule from Burning Wheel. The results are a binding and, fail or succeed, you better make the consequences interesting.
I suppose that's why I've been itching to play other games that use the alternative: a dice pool. This, in my opinion, is much preferable simply because these games almost always have rules for gradients of success, which makes it much harder to get fucked by the dice. The good news is I have two Burning Wheel campaigns slated to begin soon.