The Non-Euclidian Staircase

I've spoken about this at length on other forums (like, say, here), but usually kind of glossed over the question of needing random factors at all.

Here's my opinion, ground down to its essence...

The role of dice (or any similar random factor, including spinners, cards, or quick rounds of "rock, paper, scissors") in an RPG is to provide (as random information) the details necessary to decide a contest which are not provided by the characters' abilities, the players' play, the GM's scene-setting, and the story's needs.

So, from that perspective, Narrative Guy is on reasonably firm footing (if you have enough info from character, player, GM, and story to decide, then just decide) and System Mechanic has, IMO, a misunderstanding of dice's role. Telling a story between multiple participants within a structure of rules is gaming (perhaps not Role-Playing Gaming, depending on how individualized and immersive the individual character roles are) no matter if it has dice or not. The role of dice isn't to make it a game, it is to fill in the spaces in the story no one wants to bother with.

As for the rest of SM's points...

Dice don't provide fairness, they provide randomness; random isn't fair because it doesn't care who it screwed last time, it'll happily screw them again.

Dice don't provide consistency, they provide randomness; random is inherently inconsistent (or else it isn't random).

Dice do not protect you from capriciousness, they provide randomness; random is inherently capricious in ways humans can't even approach.

All of which isn't to say dice are bad. Dice are great if there are numerous factors weighing on a situation that are not within the control of the character/player (usually true... even an Amberite has a finite degree of control of everything around them, and they're very, very high on the "control" scale), are not pre-decided by the GM (usually true... most GM's leave a ton of minor details undecided by simple necessity of time/attention budgeting), and are not of sufficient story impact to be clearly non-decisions (again, usually true... while the story would object to the endangered princess suddenly deciding the prince is a big jerk because he rolled a 1 and instead shacking up with the dragon, it has no problem with a random loose stone coming underfoot or a drip of sweat stinging the prince's eye at a critical moment to make for a flubbed attack and draw out the fight a bit longer). Which means they're usually great, because usually the undetermined factors in an action/contest are proportionally of significant weight next to the determined ones.

One problems with them, though, (and why Narrative Guy is so put off by them) is that Dice (and most system mechanics) don't know how to scale their impact up or down based on how much freedom for uncertainty there is in a scene. The prince in the above story example is just as likely to roll a 1 on his "first impression" social scene with the princess as when he swings his sword at the dragon, but one scene had a lot more "wiggle room" than the other.

Which is one reason why we need a GM-as-referee (as opposed to the other roles of the GM) to override the dice when they go too far.