Now that is a pretentious title.
Commenting on someone else's blog on an unrelated matter made think about when I choose to roll and not to roll in a game. I say "I choose" but I here mean "I choose to, or I require" a die roll.
In general, I roll when:
. . . there is a chance of failure or of great success, and the consequences of failure or success can be interesting. Combat is a great example. There is a chance of failure, and failure can be interesting. It isn't always, but it can be. Screwing up in combat is a potential source of fun in games. The reverse, too - we still talk about crazy unlikely critical successes in combat years after the dice stopped rolling. The involvement of the dice make it more fun for me, so there are a lot of rolls here.
You could easily create a game where there is no randomness to combat (Amber Diceless did that, didn't it?). You could play a game where the results of combat are purely a result of player description of their actions in the situation - no dice, no randomness, just player ability vs. the GM's vision of how that description would play out. Oh sure, that's rare, but I figure that's more of a function of the original RPG's (D&D's) origin from a dice-based wargame.
But I grew up playing role-playing games where the dice results matter so I'm biased towards that approach - so we roll a lot of dice in combat. Not for everything, though - I'll roll randomly to see which way an unconscious NPC falls or I might just say "You hit him sideways towards your right, so he falls to his left." I might rule a grenade bounces long and only roll for the yardage, even though I've got rules to see if it bounces long, short, or wide.
I keep this philosophy outside of combat, too. If I haven't pre-determined an NPC's reaction (overall or to a given approach), I'll roll reaction rolls. Chance of "failure" (bad reaction) or "success" (good reaction, maybe especially good) and the consequences can lead to more fun. I'll have you roll Area Knowledge if there is a time constraint on finding a place or not finding it means you can't get something you need to pull off a job. I'll call for a roll against Merchant if you're trying to get a deep discount or sell some oddity for a high price.
This doesn't mean that if there is a possibility of failure you must roll. I won't require rolls for most basic stuff - you don't roll Area Knowledge to find your way back home, or Merchant to sell items or buy items, or make a reaction roll from the town guards every time you enter or leave town. I don't require rolls to slit throats of helpless foes, either. The consequences of failure, high or low, aren't interesting - there is no time constraint, not real "opposition," and a failed roll or great success doesn't make the game better.
But I'll also roll . . .
. . . when I have no idea what could or should happen. Everything from stocking a dungeon to reaction rolls from random people or a chance of coincidence or how much damage you take. I just don't have an idea, and I need one. So I ask the dice. If it's out-of-game but game related, I might discard it and roll again - the dice say there's a dragon and I'm rolling for a tiny room, well, I might roll again and see what other ideas the dice have. In game, I'll keep it and live with it.
This also applies to the situations above - I could really decide the results of everything in my games. It's possible to play games like this, with or without a GM and with or without rules (hey, free kreigspiel). But like I said above, I grew up dropping dice so I like games where I have rules for that for anything I need, just in case I don't already know what happens.
Of course, you can convince me there is really only one thing that can happen, and I'll just rule it happens. That's fine (and encouraged!) as long as it is in-character and makes sense in-game. That's part of playing a role, and it's always welcome (and it always gives bonuses even if I'm inclined to make you roll).
And finally, I'll roll . . .
. . . because, against all odds, it's possible your crazy idea might work. You might manage to sneak in plate armor. You might manage to convince the guards you're one of them despite the fact that they've all worked together for years. Sure, it's possible that you might roll a "3" and hit the bad guy on the other ship at maximum range with your unaimed spear toss in the dark into a confused melee. (He did, and rolled crazy damage and mortally wounded him.)
Yes, disguising your pirates as plague victims so they can get through Spanish territory unmolested might work, but it also requires a lot of things to go your way (disguises, acting by pirates, explaining the presence of all those weapons and such, and overcoming pirates who don't want to play along). So I'll let you roll because, what the hell, it might work. (It didn't, mostly due to the last bit about not everyone want to try and make the ploy work.) You might convince your mafioso brother that you're not with those nutty adventurers, you're just tagging along with them until you could join the Black Hand mafia and work side-by-side with him! (Amazingly, that worked, despite the brother theoretically knowing better.) It seemed unlikely, but it was possible, so I rolled. I could have just decided either way, but it seemed more interesting and more "fair" (in the eyes of myself and the players) to roll and see. Because, you never know.
The rules don't really determine this, although they (obviously) heavily influence what we roll and how it plays out. I'm more likely to roll skills in a skill-based game and more likely to roll attributes in an attribute-based game, or not roll at all in a game with no interesting consequences for success or failure (we didn't spend a lot of time doing non-combat rolls in my Car Wars campaigns, for example).
I often skip rolling when it won't matter, or failure will annoy me in real life. That's why sometimes there are no wandering encounters on the way home from the dungeon at 8:00 pm on a Sunday when I have to wake up at 4:15 am on Monday. Or why I'll say "You've wiped out the leaders and there are only a few turned zombies huddling in the corner. We can just say you kill them all." Failure wouldn't make the game more fun, nothing much is in doubt, and the flow of play would be disrupted if we rolled.
The short version: I roll dice when rolling them will, in my opinion, make for a more fun and interesting game. Sometimes this means rolling dice until your hand cramps, and sometimes this means barely rolling anything at all.