Let's Talk About Core Game Mechanics

I think it represents something significant coming into being play. Whatever that is, it wasn't present before.
Here's an example, from the last Torchbearer 2e game that I GMed:

The PCs are in a room which has many weapons, of various sorts and degrees of quality, on its walls.

Player of the Elven Dreamwalker, who is proficient only in the use of the half-moon glaive, and who lost her half-moon glaive many sessions ago: "I look to see if there's a half-moon glaive on the wall."

GM: It's possible. <Pointing to map> You'd agree that Megloss [a now-dead NPC Dreamwalker, who was the PC's enemy] might have come here?

*Player": "Yes, absolutely."

GM: "OK, test Scavenger against Ob 3.​

We start with a situation. Then an action declaration, with some stakes established: the player (and the PC) hope to find a half-moon glaive, which might be there because Megloss might have travelled to this place. There's a difficulty, that sums up the likelihood of finding a glaive without complication; and the framework/context for complications - Megloss might have travelled to this place - has been established.

That's the establishment of a fiction, with an inner logic and some possible trajectories. There's a lot of representation.

Then the dice pool is assembled - based on the PC's Scavenger skill, and possible other buffs (I can't recall if any were used for this roll). That's representational: the skill rating represents the PC's ability to forage, gather, scavenge, and otherwise find the stuff that they want even in unlikely places.

Then the dice are thrown. This doesn't represent anything. It's a decision procedure: it tells us - the game participants - how and what we are to go on imagining. On this particular occasion, the roll was a success, and so we all agree the PC finds a half-moon glaive on the wall, undoubtedly left behind by Megloss, for some reason. Had the roll failed, as GM I would have narrated some appropriate consequence consistent with the rules, and drawing on the established fiction with its established inner logic.

The significance lies in the fiction, and its inner logic and possible trajectories, which the dice choose between and contribute to by forcing one or another sort of narration and agreement. The roll of the dice itself doesn't represent anything in the fiction.
 

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@pemerton - that the game presents a difficulty number means it's applicable to the die roll, correct? That doesn't change anything I said.
I don't know what you mean.

In Burning Wheel and Torchbearer, the Obstacle is representational. The rulebooks are clear about this, and BW in particular offers a lot of GM commentary on how to use Obstacle numbers to convey important features of the setting.

The roll of the dice is not representational, though. It doesn't correspond to anything in the fiction:

*The fictional situation is represented by words - a description - and by the corresponding Obstacle, which gives game-mechanical heft to those words.

*The character attempting their action is represented by the player's action declaration, which again is a description accompanied by the building of a dice pool by reference to skills and other PC attributes/features.

*What happens as a result of the character's attempted action is represented by the consequence narration. Sometimes, but not always, this is accompanied by something mechanical (eg the character suffers a wound, or gains an Affiliation, or . . .) or something non-mechanical but still formal (eg the character adds an item to their equipment list).​

What is said, at that final step, depends on how the dice turn out. They determine important features of the narration. (That's why I call them a decision procedure.) But they don't represent anything. As per my three points, there is nothing beyond them in the fiction to represent, and the dice aren't doing any of the representing in any of them.
 

Then the dice are thrown. This doesn't represent anything. It's a decision procedure: it tells us - the game participants - how and what we are to go on imagining.
it represents the character’s chance in the fiction of finding a glaive in this location, and that likelihood was negotiated a little earlier

GM: It's possible. <Pointing to map> You'd agree that Megloss [a now-dead NPC Dreamwalker, who was the PC's enemy] might have come here?

*Player": "Yes, absolutely."

GM: "OK, test Scavenger against Ob 3.

If all that mattered was that you have an answer to whether the character finds a glaive, you can do away with all of this and just toss a coin instead. That you did not pretty much shows that this is more than just a means to arrive at an outcome and is representative of something in the world

The significance lies in the fiction, and its inner logic and possible trajectories, which the dice choose between and contribute to by forcing one or another sort of narration and agreement. The roll of the dice itself doesn't represent anything in the fiction.
feels too abstract for me but I guess I can see where you are coming from
 

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