A three-way diagram / chart / table perhaps a weird question)

[Thieves]

Well... I didn't know what forum to put it in, so I decided to use the one that the purpose of this diagram is for. Perhaps this belongs to a maths forum.

Long story short: I'm making a mechanic that uses three variables. It's for attack damage, and the thing is that, in D&D terms, you get +1 damage to a damage roll for every 5 points of Attribute A, 10 points of Attribute B and 20 points of Attribute C. Basically, it's as if giving someone bonus damage not only for Strength, but also some for Dexterity and Wisdom as well.

The question: Do you know of a table or diagram or chart form that can use three input variables A, B and C to show the total for X, which is damage. Normally tables use A and B for variables, and at the cross-section, there is X. I'm asking for three.

This diagram / table / chart is meant to be used in printable form, so any 3D stuff that would require selective view / transparent layers is out. And preferably understandable for someone not studying maths. Readability is top-priority, as it is meant to be a form quick-reference.

(I am aware that using two tables for A & B and then A+B & C is much easier, but, also as part of the vital quest for knowledge, I nevertheless inquire about the three-sided one)

Any help there? Or maybe you can suggest a friendly-neighborhood maths forum?

Edit: now that I think of it, it probably shouldn't be called diagram, a trigram or something...

[DracoDei]

Just have the players do the addition if it is a simple:
X = Floor(A/5) + Floor(B/10) + Floor (C/20) operation

[Thieves]

I know it is, in fact, simple. The thing is, I am looking for a way to represent it graphically. Also, as I said, as part of a quest for knowledge, because I have never seen such a chart and can't really conceive how it would look like.

[DracoDei]

Well, you can make each cell of the x/y table a two-column mini-table if that is what floats your boat... you could also use color as an axis somehow maybe, but I wouldn't recommend it.

Other than that and similar measures... I am going to go out on a limb and say it is geometrically impossible since you have three input variables and an output variable you are trying to put onto a 2-D surface.

[Thieves]

Nay, dividing it up would make a total mess out of it, imagine the scale.

I imagine it can't be 2D, as well, and would rather expect it to be something chart-like. Then again, looking at what people who spend their whole life in maths sometimes come up with, I'd be cautious about saying something's impossible

Anyways, thanks for your input! I'll try spacing the search out to a more specialized forum.

[Peregrine]

The question: Do you know of a table or diagram or chart form that can use three input variables A, B and C to show the total for X, which is damage. Normally tables use A and B for variables, and at the cross-section, there is X. I'm asking for three.

Certainly a 3D chart would be the mathematically appropriate way to do this, but as you say, it's not really practical. How common is it to have 20+ points in C, though? If it's not common, you could do a two-way table for A and B, and then either just let players add +1 for every 20 points of C, or perhaps do a single second table for 20 <= C < 39. Like so (A across the top, B down the left):

C: 0-19
{table=head]B\A|0-4|5-9|10-14|15-19|20-24|25-29|30-34|35-39
0-9|+0|+1|+2|+3|+4|+5|+6|+7
10-19|+1|+2|+3|+4|+5|+6|+7|+8
20-29|+2|+3|+4|+5|+6|+7|+8|+9
30-29|+3|+4|+5|+6|+7|+8|+9|+10
[/table]

C: 20-39
{table=head]B\A|0-4|5-9|10-14|15-19|20-24|25-29|30-34|35-39
0-9|+1|+2|+3|+4|+5|+6|+7|+8
10-19|+2|+3|+4|+5|+6|+7|+8|+9
20-29|+3|+4|+5|+6|+7|+8|+9|+10
30-29|+4|+5|+6|+7|+8|+9|+10|+11
[/table]

Edit: now that I think of it, it probably shouldn't be called diagram, a trigram or something...

Actually, "diagram" doesn't mean anything to do with "two" (except through distant etymological connections); the Greek root "dia-" means "line", thus "dia-gram" = drawn or written using lines. Yes, I am both a maths and a language geek.

[DragoonWraith]

A series of tables (each being a "layer" of a 3D chart) would be the correct way to do this.

[Lev]

Seems 5 for STR 10 for DEX and 20 for WIS is best simplified to this:

4 points for each point of STR, 2 points for each point of DEX and 1 point for each point of WIS

Amass 20 points and you get another +1

[mroozee]

If someone put a gun to my head, I would either make the chart as a hologram or using stereoscopic images.

[I_Got_This_Name]

There's a fairly elaborate, math-heavy article on how to make these, if you have a solid equation to derive things from, here.

Useless for things that are purely arbitrary, though, if I understand right. Also, the charts take a straight-edge to read. Still simpler than a solver program, which takes a computer.

That, or a whole mess of different charts. The minimum is two: for d = f(a, b, c), you take i = g(a, b), d = g(c), if you can get consistent results that way. A lot of the time, you can't.

[Gralamin]

A Circuit would be a good way of representing this if your PCs understand it. If not, you can have a psudeo-circuit. For Example:



Where Input is a variable, Op1 is the operation to apply to it, Combine is the operation to derive the bonus from these adjusted variables, and Result is the result.

This is, also, an upside down Trinary Tree.