"Stupid Question - D15?" Topic

Looking over an old ruleset I'm thinking of trying, the author refers to a 1-15 roll, defined as a D20 (marked 0-9 twice) and one D6, added together (0 counting as zero, not ten).

I could probably dig a marked twice 20 sider out of my dice bin, but if I just used a standard D10 isn't that the same thing? Or is there some probability curve mojo associated with an old-school D20?

I'd just use a d20 and reroll 16+. Or a d16 and reroll, um, 16.

That proscribed method sounds REALLY wonky to me!

Chance of getting any particular number on the d20 is in 10 the same as the d10.

The d15 is rather odd though.
1 and 15 – one way
2 and 14 – two ways
3 and 13 – three ways
4 and 12 – four ways
5 and 13 – five way
6, 7, 8, 9, 10, 11, 12 – six ways

Two dice as prescribed gives a bell curve, which may have been the goal of the design. Changing to one die might create undesired results.

I do think that might be the design intent – wanting most results being in the average range but keeping a chance for outlier extremes.

But yes, the first and only time I've seen a game built around 1-15!

I have seen games that use 2 and 3 different dice added.

I am now trying to think what the WWII game that I used to play had that mechanic?

German troops got best two of three D8 -1? or something like that

No difference between a d10 and a d20 (if you drop the 10's place), you get a 1/10 chance for any given number.

I was going to suggest rolling 2d6 to get your number:
red d6 roll of 1-2 = +0
red d6 roll of 3-4 = +5
red d6 roll of 5-6 = +10

add the roll of a black d6 to the bonus above (reroll if a 6)
But it looks like the original intent was a bell curve

D20s roll better though, so seem to be less prone to rerolling the same number, especially if you just spin and drop it/them, as opposed to rolling them.

I'd just use the D20, and reroll 16 – 20, as suggested.

There are D16s though, so you could use those as well.

As mentioned though, you don't get that bell curve in the middle.

The bell curve isn't "in the middle". It's all the way along. It's more an trapezium anyway, in this case.

A straight D15 has a 1/15 chance of a score of 1.

A D0-9 + D6 has 1/60 of the same thing, so exactly a quarter the chance.

(Even at 13+, the two dice added together is 1/10, compared to the 1/5 of the single dice, so twice the chance).

If you substitute a single 1-15 roll for the original system, you will be getting far more extreme results, not just a few.

In the olden days, most d10s (or percentage dice as they were often called as you rolled two of them were actually D20 with 0-9 printed twice. I have quite a few. In fact, I have a few with each 0-9 coloured differently that were used as d20s – the different colour was 11-20. Nothing special about d20 than d10s.

I can only assume you are talking about Knights and Magic. While statistically different, my initial plan when I was thinking of using these rules was just going with 2d6+1 for 3 to 13 rather than 1d10+1d6 (1-15)

Also in that era many gamers only had one set of polyhedral dice.

A designer today who wanted a pair of dice producing 1-15 would probably use 2D8-1. This gives a more standard bell curve.

You'd have to inspect the results table for this game to determine if switching to 2D8-1 would significantly change the game.

Anydice.com is a great tool for resolving questions like this.

The %distribution for d10+d6-1 (-1 for d10 being 0-9):

1 1.67
2 3.33
3 5.00
4 6.67
5 8.33
6 10.00
7 10.00
8 10.00
9 10.00
10 10.00
11 8.33
12 6.67
13 5.00
14 3.33
15 1.67

This is triangular distribution with its top "flattened", or something that looks more like a trapezium. It results from the convolution of two uniform distributions – a convolution is the mathematical operation needed to get the resulting probability distribution when adding two other probability distributions.

And please (yes, this is a pet peeve of mine), don't use the term "bell curve" for anything that is not a uniform distribution. A bell curve is a precisely defined term in probability theory, and simply adding 2 dice together is NOT a bell curve. I know many use the term "bell curve" for e.g. 2d6, but it is factually incorrect to do so.

Another online dice roller is orokos.com. You'll have to register, but it's free. I've been using it for my online games.

If you'd rather roll actual dice, get a d30 from your FLGS. Just divide the result by 2 and round up.

Or .. you could just roll a real D15

link

This is actually the definition of a Bell Curve.
link
I'll stop using it when the Internet stops calling multiple building blocks 'Legos'. Or stop saying 'Could care less' instead of 'Couldn't care less'.

The D10+d6-1 actually looks like a good curve to use in a game.

I make the Standard Deviation on 2d6 3.317 Calculated from here.
link

All results from 4-10 lay within 1 sd of 7 (mean). That is 30 out of 36 results, approximately 84%, not the 66% called for. Sotechnically 2d6 isn't a Bell Curve, but it does look like one, and is handy shorthand.

Kevin – those were some crazy dice* on that link!

2d8-1 would do me, I have to say

John T

* And spinners and stuff that'd do much the same job, I guess

D30/2?