Dice notation

[Asmor]

Well, I guess ENWorld just isn't the teeming hive of theoretical arithmeticists that I thought it was.

 

[Loonook]

Well, I guess ENWorld just isn't the teeming hive of theoretical arithmeticists that I thought it was.

It is not about 'theoretical mathematics' ... It is hackneyed symbolic logic. We all know the meaning of 1d4. The format is pretty simple...

XdY
X - Number of Dice rolled.
d - Die 'constant'
Y - Sides of rolled die.

In and of itself XdY is an rule. For every appearance we known to roll X number of Y sided die. We also know, per inference, that no displayed value for X, as in the argument (d4, or -d4 for holding place clarification) makes the pre-d value known as X=1.

Thus, your discussion of 1d4d4 presents two separate arguments:

(1d4) and (-d4). -d4 = 1d4, so we are presented with the argument of 1d4 and 1d4. Two separate arrangements.

A couple accepted formats for a multiplying (at least in the very rare case I have seen shorthand on the subject, as it isn't unheard of but odd):

1d4*d4, 1d4*1d4, or d4*d4
1d4Xd4, 1d4X1d4, d4Xd4
All read the same.

Again, it's been awhile since I did any higher maths, but the XdY rule comes as a set. Treat each separate appearance as a unique number, similar to the use of any abstract symbol to 'solve for'.

Slainte,

-Loonook.

 

[prosfilaes]

Well, I guess ENWorld just isn't the teeming hive of theoretical arithmeticists that I thought it was.

This isn't theoretical math. It's just notation, and undirected notation isn't terribly interested. 1d4d4 could mean a lot of things, but it doesn't matter unless you want to use those things.

I did find that the mathematical notation APL (A Programming Language, but historically a mathematical notation first) does support this. 1 ? 6 would return a random integer between 1 and 6 inclusive. 5 ? 6 would return 5 such integers
[*]; if you wanted the sum, you'd use the summation operator +/.

+/ 3 ? +/ 4 ? 6 would basically be 3d(4d6).

The catch is, "4 * 5 + 3" would be 32, since APL has no precedence and always goes right to left. That's why this is so uninteresting; because it doesn't matter what precedence d has if used as an operator, except in that you and your readers need to be on the same track. APL says "4 * 5 + 3"; Forth says "5 3 + 4 *"; most people say "4 * (5 + 3)"; it's all the same, as long as everyone is on the same page.

* A beautiful picture, spoiled by an ugly fact; ? returns distinct integers for x ? y if x is less than or equal to y. "+/ 6 ? 6" is always 21. I'm sure an APL fan could show you a quick way around that problem, but I have at best the most passing knowledge with the language.

 

[Umbran]

You want the hive of mathematicians? Fine. "dx" already has a formal mathematical meaning in differential calculus. No mathematician worth his salt would then use "d" as a binary operator.

"d" means "generate a random integer between 1 and the quantity on the right-hand side, inclusive, a number of times equal to the quantity on the left-hand side. Then sum the random numbers so generated."

Not always. "4d6 drop lowest" is common terminology, but you don't sum all 4 dice. "d" in this sense is not an operator, but is a natural language shorthand, and should be parsed as such.

Which is a good thing, because anyone designer who is taking things to the power of a random number is producing a game with too much math.