(Sorcerer) dice system analysis

[Tom]

For a new game I'm working on I opted to use the Sorcerer dice mechanics and Ron gracefully allowed me to (well, there's a general permission to everyone in some file on his site, but I asked personally anyways).

Before settling on a dice mechanic, I like to put some thought into it and the probabilities and statistics. Since I'm writing a rule-book, I put my analysis into the rules, and shared it with Ron who proposed I post it here.

So, without further ado, my statistical analysis of the Sorcerer dice mechanics, with lots of thanks to the Troll dice roller:

https://dl.dropboxusercontent.com/u/9638874/explorers/sorcerer-dice.pdf


Sorry for posting just a link to a PDF, but there's a lot of graphics in there.

[Ron Edwards]

Hi Tom! Thanks for posting this here, and also for the kind words in the document.

For some history, we discussed this stuff a bit in Sorcerer Dice Mechanics, Examined but nowhere near as carefully as you've done here.

In practical-play terms, I think one of the real skills to develop in using these mechanics is to prepare for narrating failed rolls. They do crop up, often at important moments, and to impart forward motion to the fiction at these times is a big part of play. Too much role-playing design has been predicated on successful rolls, with failures elided through narration that skates you through the problem anyway ("you're disarmed! but you were slammed into the wall! and there's an axe mounted there!"), applied in utterly non-fun ways ("let's see ... OK, you're dead"), or treated as speed-bumps on a path that by God will be trod anyway, just a little longer now.

Best, Ron

[Christoph]

Hi Tom!

Nice analysis and graphs! I especially liked the compared effects of varying the dice shape, I had always wondered what it looked like quantitatively, but never bothered to pump out the graphs. I agree that taking out the ties is better for visualization.

I'm not sure I get your last point about variance. Sure, the variance of the roll increases with the number of dice, but so does the mean. The comparison with shooting an arrow seems a bit misguiding, since the example doesn't establish how one decides where the arrow hits. I might model it with concentric rings (like a... target) and N success is hitting the target in the outermost ring, then N+1 is getting further inside, N+2 further still, etc. Somebody who gets way too many successes would get to narrate some very weird shit (splitting a previous arrow in two f.ex.) Anyway, my point is: better results on rolls on average means a lesser variance on our imagined target! Of course, one could model things differently (since my model doesn't allow a beginner to hit the bullseye), but what I'm trying to say is that the variance is not the same on the roll than it is on a given physical event. When one tries to get consistently N or more success, the more dice, the better. What the variance does indicate is that added dice yield progressively diminishing returns (your article shows this nicely).

One could argue that Sorcerer isn't interested about such fine-tuned resolution... but I enjoy such discussions anyway.

[Tom]

Thanks, Ron. I actually remember having seen that post, but it didn't go into enough detail for me to decide whether or not to use that system for my own game.

@Christoph: What I mean is best explained in the article that I mentioned. Sorry, the PDF export stripped the links.

Basically, with any system that gives you more dice if you are better comes the stochastic effect that your spread increases, while in real life more competence at a task usually makes your results more consistent, i.e. reduce the spread.

To be honest, almost no dice system gets that part solved, so Sorcerer is actually pretty good compared to other dice mechanics because its spread only increases slightly.

I played around with a few ideas to solve this, but they are all either counter-intuitive, too complicated, or when plotting them out I realized they don't actually solve the issue at all. Most of them have to do with allowing higher skill values to eliminate dice selectively.