Creating compound dice using your standard RPG dice

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Creating compound dice using your standard RPG dice

Post by Tim Baker » Fri Jan 11, 2019 5:31 am

Here's an interesting approach to using standard RPG dice to create a lot more random numbers.
https://goblinshenchman.wordpress.com/2 ... -two-dice/

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Re: Creating compound dice using your standard RPG dice

Post by Khedrac » Fri Jan 11, 2019 8:28 am

There are lots of ways of doing compound dice, that one is good - but does need players competent at mental arithmetic.

This topic does remind me of one of the odd side-effects of the D10. Back when I was first playing AD&D, I could look at almost all the variable ranges given for things and easily see (what I believed to be) the intended dice to generate the numbers.
For example:
  • 2-7 = 1d6+1
  • 2-12 = 2d6
  • 2-20 = 2d10
Now there are multiple ways to come up with some of these, e.g. 2-10 could be 1d8+1d12 but 2d10 makes more sense - it is "simpler".

So question - how do you roll 3-12?
Is it 3d4 or 1d10+2? Both methods are, to me, equivalent in their simplicity - but they generate very different probability distributions...

[For comparison, I looked at the differences between 2d10 and d8+d12 for 2-20. They are very similar bell curves, but 2d10 has the higher peak in the middle and slightly less spread. Curiously the number of results that give X are identical except for 10, 11 and 12 (8 each with d8+d12, 9 for 10 and 12 and 10 for 11 with 2d10), however the probabilities are increased for d8+d12 because they come from 96 rolls not 100.]
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Re: Creating compound dice using your standard RPG dice

Post by Ashtagon » Fri Jan 11, 2019 9:02 am

The system they outline gives a flat-line (no curve) probability distribution. For the maths involved, I'm not sure it's worthwhile.

I've seen some rulebooks (GURPS I think) use 2d6 to create a "d36", treating one die as a tens digit and the other as the units digit. This obviously skips 7-10, 17-20, 27-30, 37-40, 47-50, and 57-60, and has 66 as the highest possible result. That feels like a workaround to create large numbers of possible results with a system that boasts of using d6s exclusively.
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Re: Creating compound dice using your standard RPG dice

Post by Big Mac » Fri Jan 11, 2019 11:47 am

Ashtagon wrote:
Fri Jan 11, 2019 9:02 am
The system they outline gives a flat-line (no curve) probability distribution. For the maths involved, I'm not sure it's worthwhile.
I think that is the entire point of this system (to create a new die from two other dice).
Ashtagon wrote:
Fri Jan 11, 2019 9:02 am
I've seen some rulebooks (GURPS I think) use 2d6 to create a "d36", treating one die as a tens digit and the other as the units digit. This obviously skips 7-10, 17-20, 27-30, 37-40, 47-50, and 57-60, and has 66 as the highest possible result. That feels like a workaround to create large numbers of possible results with a system that boasts of using d6s exclusively.
That's a lot of faffing around. I can see how it would be super-useful for a d6 player, and the results are obviously in Base 6, so there are not really gaps, from that point of view. But, as a D&D player, I'd rather use d100 dice for a big table. I have a 10xd10 die*, so don't have to deal with the "Which d6 is the tens?" issue.

* = I had someone suggest I was cheating at d100 rolls before I got a 10xd10 dice. That annoyed me, as I had no idea if rolling high or rolling low was better.
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Re: Creating compound dice using your standard RPG dice

Post by Big Mac » Fri Jan 11, 2019 12:36 pm

Khedrac wrote:
Fri Jan 11, 2019 8:28 am
There are lots of ways of doing compound dice, that one is good - but does need players competent at mental arithmetic.
Goblin's Henchman explains how you can do this method, but not why you might want to use it.

I can't really see why someone would need a d144. (Not unless they had a really big weapon that did a gross amount of damage.)

So it's kind of a solution looking for a problem. But, if someone can come up with the problem that this method solves (and have that problem be something that doesn't occur enough to warrant going out and buying a bespoke die, then this would be really useful. (I think the table was the best way to do this.)
Khedrac wrote:
Fri Jan 11, 2019 8:28 am
This topic does remind me of one of the odd side-effects of the D10. Back when I was first playing AD&D, I could look at almost all the variable ranges given for things and easily see (what I believed to be) the intended dice to generate the numbers.
For example:
  • 2-7 = 1d6+1
  • 2-12 = 2d6
  • 2-20 = 2d10
Now there are multiple ways to come up with some of these, e.g. 2-10 could be 1d8+1d12 but 2d10 makes more sense - it is "simpler".

So question - how do you roll 3-12?
Is it 3d4 or 1d10+2? Both methods are, to me, equivalent in their simplicity - but they generate very different probability distributions...

[For comparison, I looked at the differences between 2d10 and d8+d12 for 2-20. They are very similar bell curves, but 2d10 has the higher peak in the middle and slightly less spread. Curiously the number of results that give X are identical except for 10, 11 and 12 (8 each with d8+d12, 9 for 10 and 12 and 10 for 11 with 2d10), however the probabilities are increased for d8+d12 because they come from 96 rolls not 100.]
Bell curves seem to mostly get used in tables where random results translate into things like monster encounters. (And that takes a designer who understands what monsters they want to make more and less common.) I get the impression that most people would find it easier to work with percentage tables, as it's easier to figure out the percentage chance of something happening.

Is there ever a time when a RPG uses a bell curve and leaves the result as an actual number?
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Re: Creating compound dice using your standard RPG dice

Post by Khedrac » Fri Jan 11, 2019 1:06 pm

Big Mac wrote:
Fri Jan 11, 2019 12:36 pm
Is there ever a time when a RPG uses a bell curve and leaves the result as an actual number?
OD&D stat generation on 3d6 is a bell curve.

If you mean a bell curve is used for things like random encounter determination then yes - I am sure that 2d6 bell curves have been used in a lot of d6-based games, e.g. Traveller and GURPS.
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Re: Creating compound dice using your standard RPG dice

Post by Ashtagon » Fri Jan 11, 2019 1:18 pm

The 1st edition Manual of the Planes iirc pioneered a 1d8+1d12 system for determining random encounters. I don't think it ever saw use anywhere else.
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Re: Creating compound dice using your standard RPG dice

Post by Khedrac » Fri Jan 11, 2019 3:16 pm

Ashtagon wrote:
Fri Jan 11, 2019 1:18 pm
The 1st edition Manual of the Planes iirc pioneered a 1d8+1d12 system for determining random encounters. I don't think it ever saw use anywhere else.
That must be where my brain produced it from - I had no idea it was a real system! Nice find. :)
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Re: Creating compound dice using your standard RPG dice

Post by shesheyan » Fri Jan 11, 2019 7:03 pm

Ashtagon wrote:
Fri Jan 11, 2019 1:18 pm
The 1st edition Manual of the Planes iirc pioneered a 1d8+1d12 system for determining random encounters. I don't think it ever saw use anywhere else.
The odds of 1d8+1d12 produces a low bell curve with a plateau compared to 2d10.
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Re: Creating compound dice using your standard RPG dice

Post by Tim Baker » Fri Jan 11, 2019 7:33 pm

Khedrac wrote:
Fri Jan 11, 2019 8:28 am
So question - how do you roll 3-12?
Is it 3d4 or 1d10+2? Both methods are, to me, equivalent in their simplicity - but they generate very different probability distributions...
That's interesting. While other ranges in old D&D books made me stop and think about more than one way they could be generated, this range didn't. I don't think I often look at adding more than 1 as a constant to the roll. It was always 3d4 in my mind.

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Re: Creating compound dice using your standard RPG dice

Post by Big Mac » Sat Jan 12, 2019 2:59 am

Khedrac wrote:
Fri Jan 11, 2019 1:06 pm
Big Mac wrote:
Fri Jan 11, 2019 12:36 pm
Is there ever a time when a RPG uses a bell curve and leaves the result as an actual number?
OD&D stat generation on 3d6 is a bell curve.
Of course! Thanks!

I knew there would be something useful out there, but could not remember it. And there it was, hiding in plain sight!
Khedrac wrote:
Fri Jan 11, 2019 1:06 pm
If you mean a bell curve is used for things like random encounter determination then yes - I am sure that 2d6 bell curves have been used in a lot of d6-based games, e.g. Traveller and GURPS.
I have seen them used for that, but it's kind of artificial, as the designer stacks the odds and could stack the odds equally well with a flat percentage table.

I was looking for an example where the bell curve stays as a number, and you have it! :cool:
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Re: Creating compound dice using your standard RPG dice

Post by Dread Delgath » Sat Jan 12, 2019 11:00 am

I've never heard of this described as 'compound dice' before, but this is kind of meta- to me. I've seen this in use mostly in tables. Either in d66 tables in Traveller, Warhammer FRP, or some other older 80's era games. Mostly used in a table, where the resulting number is looked up and referenced something specific that is important NOT the number generated itself.

Most numbers on a bell curve in AD&D 1e on wandering monster tables were of this sort too. They were arranged on the bell curve on purpose, their frequency of appearing coinciding with the bell curve of the dice on the table.
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