A Magic System for Exquisite (maths questions)

[Shreyas Sampat]

So, I'm trying to design two parallel magic systems for my game Exquisite.

As it stands, there are 15 'facilities' a character has; these are the product of three attitudes (Forceful, Artful, Mindful) and five applications (physical, social, and three that are rather in flux).  They all have names: Destroy, Create, Sustain being those of the Physical mode.  An ability test involves rolling a dicepool of the application's size; the attitudes determine the die type, and results are found like in Godlike, looking for matching sets.  Magic is supposed to work by making tests easier.

The magical abilities are of two types, Book and Sword:
Book magic is "overt"; it has flashy effects.  Sword magic is "covert"; it's a kind of stunt system.  As a general rule, Book magic's effects are less predictable (in terms of the dice effects) than those of Sword magics.

Zikr the thief is trying to get inside a house.  He's running from the palace guards, so he doesn't have a lot of time to play around; he decides to break the door down rather than trying to finesse it.
This is Destroy; Zikr checks his chart and sees that he has 7 dice in Physical and d8 in Forceful.  The door looks pretty hefty.  He's not sure he can pull it off.

Zikr takes a deep breath, covers his ears, and whispers a Word of Remembrance.  The wooden door, recalling its leafy past, turns into a rapidly growing oak sapling.  Zikr slips by it before it thickens to block the doorway and his pursuit.  The mud bricks round the doorframe look distinctly wet.  This is Book magic.
A guard turns the corner and sees Zikr at the door.  He throws a hammer at Zikr's head.
Zikr whips his foot around in a whistling arc, deflecting the hammer so it smashes the door's lock.  It swings open, and he dashes inside.  This is Sword magic.

So, what I'm asking is, how can this be accomplished, mathematically?  I don't understand the dice system's probabilities, but I suspect that there will be a very sharp differentiation between the effectiveness of attitudes, the applications being a secondary consideration.  Also, very high attitude ratings will guarantee at least minor success with even the smallest dice pools.  Are there too many dials in this system?  Should I simplify it?

[Mike Holmes]

I think we need more data, but my first guess is that it's more complex than it needs to be. BTW, this system reminds me of Matt Snyders first system for Dreamspires in some ways.

Anyhow, what we need to know is what dice types go with what levels of ability. There is a strong problem of conflict here. Which is, you need a bigger die type to get a greater "Height", or the actual matching number (to use the Godlike term), but having a larger die type makes "Width", the number of matches, smaller on average.

What do you intend Height and Width to represent?

Mike

[Shreyas Sampat]

Sorry, big blunder on my part:
Smaller values (and thus smaller dice) are better.

I'm thinking that Height will be a measure of quality, and Width will be ... something else, maybe an unrelated reward (if this were Cornerstone, Width would let you set facts or pick up karma.)

[szilard]

So the attitudes are rated in die types and the applications have numbers of dice... and the best combination would be many dice of a low die type (for more matches)? The lower the height, the better, right?

Just trying to get on the same page, here.

Stuart

[Mike Holmes]

OK, that makes sense. There is another way to do it, where a high Height is good. Just add a flat bonus. Thus, you might have, from lowest level to highest:

d12
d10+2
d8+4
d6+6
d4+8

Anyhow, if you decide to stay with low=good, then perhaps you could call it Depth instead of Height?

What are the potential ranges of stats? Or is that what you're looking for?

Here's the average number of maximum matches (max width) for a given number of dice and a given die type.

Code Select Expand

                  Die Type
# of  -----------------------------------
Dice   d4      d6      d8     d10     d12
1     1.0     1.0     1.0     1.0     1.0
2     1.3     1.2     1.2     1.1     1.1
3     1.7     1.5     1.4     1.3     1.3
4     2.1     1.8     1.6     1.5     1.5
5     2.5     2.1     1.9     1.8     1.7
6     2.8     2.4     2.2     2.0     1.9
7     3.2     2.7     2.4     2.2     2.0
8     3.6     3.0     2.6     2.4     2.2
9     3.9     3.2     2.8     2.6     2.4
10    4.2     3.4     3.0     2.7     2.5

The number on the high matching set is much more difficult to calculate.

Mike

[Shreyas Sampat]

Here's an idea.

Depth is a good term.  Depth determines the quality of a success.
Width, renamed Force, is a measurement of "authority".  That is to say, higher Force rolls can simply whiff lower ones.

I like the set of 4-12 sides for attitudes; let's keep that.  1-10 is another nice set of numbers for applications.  I gather that the odds are still poor, even in the high numbers, for very large matched sets.  That's good; there shouldn't be a great deal of need for Force variation.  On the other hand, characters unassisted aren't very effective.

This is where magic comes in.  Either way, you can buy dice.  Just buying extra dice seems not-too-interesting, so we'll leave it at that.  To provide the differentiation between mechanics:
Book magic lets you bring a second ability to bear on a problem, to get a more enduring result.  You make a roll with this second ability and add its Force to your original roll, as long as the second ability's Depth was better.
Sword magic lets you do the same, but with a result that's simply better.  You make a roll with the secondary ability and reduce your primary roll's Depth by its Force, as long as the secondary Depth was better.  Yes, this means you can get negative Depth.

So, with the Zikr example, in the first case he didn't really do too well with opening the door, because it closed almost immediately after, but it's going to be a heck of a problem getting through now: high Force.  In the second case, he opened the door quickly and elegantly, but he was seen and left the door open behind him - it's not going to be difficult to follow.

[szilard]

I think I am a little lost. Here are some questions, maybe the answers to them would help:

Why were Forceful and Physical (what substat?) applicable to turning a door into a sapling?

What second ability was brought to bear here? What first ability was it assisting?

How is the effect determined (why did it turn into a sapling)? Is magic wholly freeform?

Stuart

[Shreyas Sampat]

Ok.

The ability matrix has fifteen points, which besides being the intersections of an application and an attitude, are in themselves specific abilities, and sometimes their scope is wider than is obvious.  So the Physical and Social abilities aren't just PxF, PxA, PxM, SxF, SxA, SxM; they're Destroy, Create, Sustain, Coerce, Influence, Poise.

Destroy is being used for its effect: destroying the obstruction so Zikr could get by.  Let's suppose that magic isn't freeform, and that the secondary ability is the means by which the end (the primary ability) is reached.  Then perhaps the secondary ability is Herd (Natural, Artful); the ability which influences non-human things.

Does that help?

[Shreyas Sampat]

Another maths request, if someone's willing:

I'm wondering the odds of any success - Width 2 or greater - with the various dice rolls.  Obviously where the XdY & X>Y, this is 100%, so those are unecessary, but otherwise...  (I'm trying to figure out how the curves look.  I'd actually also like to know the odds of any particular roll beating another, but that's an incredibly hairy problem.)

[Mike Holmes]

Chance of rolling at least one Width 2 with x dice of y type based on 3000 sample rolls of each combination.

Code Select Expand

                     Die Type
-------------------------------------------------
Dice   d12      d10        d8        d6        d4
-------------------------------------------------
2     8.03%    9.73%   11.80%    17.03%    25.17%
3    23.23%   27.63%   33.73%    46.00%    63.00%
4    41.63%   48.37%   58.43%    74.13%    91.37%
5    61.67%   69.40%   79.40%    91.63%   100.00%
6    77.67%   84.57%   91.73%    98.53%   100.00%
7    88.90%   94.07%   97.97%   100.00%   100.00%
8    95.10%   98.23%   99.80%   100.00%   100.00%
9    98.43%   99.63%  100.00%   100.00%   100.00%
10   99.33%   99.97%  100.00%   100.00%   100.00%
11   99.40%  100.00%  100.00%   100.00%   100.00%
12   99.57%  100.00%  100.00%   100.00%   100.00%
13+ 100.00%  100.00%  100.00%   100.00%   100.00%

Mike

[szilard]

Hmnmm....

The threshholding effect of having a number of dice above the # of sides on the die-type (which would always result in at least one match) is something you may want to keep in mind - particularly with the d4.

Stuart

[Mike Holmes]

Good point, Stuart. I was assuming that the range of dice would be similar to the range of die types, however. So, with five levels that gives us a range of 2-6 on number of dice. Which works pretty well. Only in a when you had five or six dice with the d4 will success be automatic. Makes the d4 just that much more interesting.

And there's still the consideration of how large the width will be.

That said, the width range is not that large in this case. The biggest swing is going from 1.3 to 2.8 average width which is going from two to six dice using d4s.

Mike

[Shreyas Sampat]

Thanks for the numbers, Mike.

Regarding the threshholding effect:
I think that this is actually good for genre emulation; Exquisite is unfolding as a kind of Arabian Nights thing.  I've observed that the characters of the Nights have this phenomenon - they perform quite predictably once they reach a certain level of skill, but it's never possible to perfectly predict whether their work can be undone.

So, the fact that you can get a significant success with relative ease is pretty neat, and as long as you know the Width of a particular fact, you know how easy it will be to counteract it.  So you can have cities of smoke that withstand monsoons, and iron towers that crumble to rust under a djinni's exploring hand...

Which leads me to my next idea: Effort.  Effort lets a character modify the size of his dice pools - you can spend Effort to buy extra dice (up to a point) and similarly, you can buy Effort by giving up dice, with the restriction that you only begin gaining Effort as your dicepool gets smaller than your die type (I'm in fact assuming a stat range between 1 and 10 where 3 is around average and 5 is high; a 1 can be successful, with Effort, and the 10s get diminishing returns from being very high, and equally diminishing returns from being lazy, with the smaller dice.)