Why Not More Rounded Dice?

On Jul 3, 2:00 am, torb....RemoveThis@pc-003.diku.dk (Torben Ęgidius Mogensen)
wrote:

> The first three steps give a d18. You can use that to get a d9 by
> dividing the result by 2 (rounding up).

All this is well and good, but if one needs a wildly varying set of
dice, conversion tables at least avoid memorization.

What had inspired my web page was my feeling that I had come up with a
chart that would almost let one look up any combination of three dice,
even the ones with all three numbers different, at a glance - because
those with three numbers different were in vertical columns based on
the separation between the highest and lowest number, in horizontal
rows based on the total, and in diagonal areas, color-coded, based on
the middle number.

Rather than simply adding swords to a game with, say, 3d7 damage, or
3d11 damage, and so on, conversion tables could also let one simply
choose a normal distribution with a standard deviation selected
directly, and one could multiply and divide by certain factors instead
of just adding and subtracting - perhaps on a scale of uniform
logarithmic steps.

The 53rd root of 2 happens to provide nice approximtions to
multiplying by 3 and 5...

John Savard

On Jul 3, 2:37 am, Quadibloc <jsav....DeleteThis@ecn.ab.ca> wrote:

> Rather than simply adding swords to a game with, say, 3d7 damage, or
> 3d11 damage, and so on, conversion tables could also let one simply
> choose a normal distribution with a standard deviation selected
> directly, and one could multiply and divide by certain factors instead
> of just adding and subtracting - perhaps on a scale of uniform
> logarithmic steps.
>
> The 53rd root of 2 happens to provide nice approximtions to
> multiplying by 3 and 5...

After looking up how to calculate the error function, using binary
search to find its inverse, and various other steps, a short BASIC
program let me find the numbers I needed to produce a table of the
kind I was thinking of on the page

http://www.quadibloc.com/other/bo020103.htm

of course, someone may already have devised a game system on this
principle...

John Savard

Michael Jung <miju.DeleteThis@golem.phantasia.org> writes:

> d17 anyone?

With the full pythagorean collection, I would just roll a d20 and
reroll on 18-20, but using only d6s, it is a bit harder.

A fairly simple solution would be to roll two d6s of different colour
and do the following:

- If the dark die is 1-2, the light die is the result.

- If the dark die is 3-4, add 6 to the light die to get the result.

- If the dark die is 5-6, add 12 to the light die to get the result.

- If the result is 18, reroll from scratch.

The first three steps give a d18. You can use that to get a d9 by
dividing the result by 2 (rounding up).

Torben

On Jul 3, 6:46 am, torb....RemoveThis@pc-003.diku.dk (Torben Ęgidius Mogensen)
wrote:
> But then you
> would not likely use them to emulate other dice, but instead design
> the rules so you only need d6s in simple ways.

As you'll see from my later post, I have indeed been thinking this
way.

Basically, for many purposes, when games say this spell does 3d6
damage, or this sword does 4d8 damage, the idea is that a normal curve
is being approximated.

So what I've now added to my site, at

http://www.quadibloc.com/other/bo020103.htm

are some example tables where the rolls of differnent types of dice
are converted, not to the distribution given by some other dice, but
to a normal distribution with a given standard deviation.

And so that multiplication as well as addition can be used for
adjusting effects, I scale the normal curve in uniform steps such that
20 steps correspond to multiplying by ten. So as long as one accepts a
certain degree of coarseness, one has a general ability to multiply or
divide by moving a certain number of rows up or down in the table (the
number of rows corresponds to the logarithm of the multiplying
factor).

So one obtains a high degree of flexibility - yet with ease of use,
without having too much in the way of tiresome calculations to worry
about.

John Savard

On Thu, 03 Jul 2008 14:46:03 +0200, torbenm.TakeThisOut@pc-003.diku.dk (Torben
=?iso-8859-1?Q?=C6gidius?= Mogensen) wrote:
>
>For newbie players that can't be expected to have polyhedral dice
>around the house, you might want to design RPGs that only use d6s (and
>it has been done, e.g., in West End Games' d6 system). But then you
>would not likely use them to emulate other dice, but instead design
>the rules so you only need d6s in simple ways.

I probably have more d6 only games than not: GURPS, Hero, PDQ, Toon --
there are a lot of them out there.


--
chuk

torbenm.RemoveThis@pc-003.diku.dk (Torben Ęgidius Mogensen) writes:
> Michael Jung <miju.RemoveThis@golem.phantasia.org> writes:
>> d17 anyone?
> With the full pythagorean collection, I would just roll a d20 and
> reroll on 18-20, but using only d6s, it is a bit harder.
>
> A fairly simple solution would be to roll two d6s of different colour
> and do the following:
> - If the dark die is 1-2, the light die is the result.
> - If the dark die is 3-4, add 6 to the light die to get the result.
> - If the dark die is 5-6, add 12 to the light die to get the result.
> - If the result is 18, reroll from scratch.
> The first three steps give a d18. You can use that to get a d9 by
> dividing the result by 2 (rounding up).

That's what I meant. The general rule is: To get a d<n>, you roll the
next highest die you are familiar with and reroll the results <n+1>
and above (which are not allowed). With just one d6 you can now roll
d4 and d5 (d2 and d3 are trivial). With a a bunch of d6 (which can be
distinguished) it's easy to roll d6, d12, d18, d36 in the way
described, basically all divisors of 6 multiplied by 6. But with d4
and d5, its also easy to roll d24 and d30.

Whith these mechanisms in mind you can achieve many results. The aim
is not to get the least rolls but to provide an easy to memorize
algorithm with a vast variety.

Sidenote: the algorithm is not unique.

Depending on such methods can be tiresome: Use all randomizers at your
disposal to speed up the processes. Also design the results to fit
the randomizers you have.

Michael

On Jun 30, 4:58 pm, Charlton Wilbur <cwil... RemoveThis @chromatico.net> wrote:
> >>>>> "Q" == Quadibloc <jsav... RemoveThis @ecn.ab.ca> writes:
>
> Q> The tetrahedron, for d4, isn't a very practical shape for a
> Q> die. I'm surprised it hasn't been replaced by an octahedron with
> Q> the numbers 1 through 4 repeated twice.
>
> This happens for much the same reason as the distinctly shaped d10: you
> don't want to have to look for an 11 or a 17 on your icosahedron to
> determine whether it's numbered 1-10 or 1-20, or for a 5 or a 7 on your
> octahedron to determine whether it's numbered 1-4 or 1-8. Being able to
> distinguish based solely on the shape of the die is a good thing.

I have since found that at least one company still does allow people
to avoid the caltrop-shaped die if they choose: an "8 Sided 1-4 Twice
(True d4)" is mentioned on the page

http://www.nobleknight.com/ViewProducts.asp_Q_ProductLineID_E_488_A_Ma...acturer

as made by Gamescience. Of course, they're the company that innovated
the Zocchihedron, and makes d14s, d16s, and d24s, in addition, of
course, to the almost pedestrian d30.

John Savard

On Jul 4, 2:39 am, torb... DeleteThis @pc-003.diku.dk (Torben Ęgidius Mogensen)
wrote:

> I never liked the Zocchihedron: It takes long to stop rolling (though
> later models added some sand or such inside to make it stop faster),
> it is hard to read and I don't believe it is fair.

You are quite right; it is not a shape that is necessarily fair.

> In particular the last point is a killer for me. Why would you want a
> single-die d100 when you can roll two d10s, one of which is marked 10,
> 20,...,00? The latter is arguably fair and easier to read.

Oh, absolutely.

While I don't necessarily think it was a good idea, I still salute the
company for being willing to try something original, though.

John Savard

Quadibloc <jsavard DeleteThis @ecn.ab.ca> writes:

> an "8 Sided 1-4 Twice (True d4)" is mentioned on the page
>
> http://www.nobleknight.com/ViewProducts.asp_Q_ProductLineID_E_488_A_Ma...acturer
>
> as made by Gamescience. Of course, they're the company that innovated
> the Zocchihedron, and makes d14s, d16s, and d24s, in addition, of
> course, to the almost pedestrian d30.

I never liked the Zocchihedron: It takes long to stop rolling (though
later models added some sand or such inside to make it stop faster),
it is hard to read and I don't believe it is fair.

In particular the last point is a killer for me. Why would you want a
single-die d100 when you can roll two d10s, one of which is marked 10,
20,...,00? The latter is arguably fair and easier to read.

Torben

On Jun 30, 4:58 pm, Charlton Wilbur <cwil... DeleteThis @chromatico.net> wrote:
> >>>>> "Q" == Quadibloc <jsav... DeleteThis @ecn.ab.ca> writes:
>
> Q> The tetrahedron, for d4, isn't a very practical shape for a
> Q> die. I'm surprised it hasn't been replaced by an octahedron with
> Q> the numbers 1 through 4 repeated twice.
>
> This happens for much the same reason as the distinctly shaped d10: you
> don't want to have to look for an 11 or a 17 on your icosahedron to
> determine whether it's numbered 1-10 or 1-20, or for a 5 or a 7 on your
> octahedron to determine whether it's numbered 1-4 or 1-8. Being able to
> distinguish based solely on the shape of the die is a good thing.

That's true, and it is also true that a d20 can very easily be used as
a d10; just ignore the first digit.

But I would think it would be easy to tell the icosahedral dice apart.

The numbers would be printed bigger on the d10, and on the d20, since
over half the numbers run from 11 to 20, unless the low numbers are
all on one side, it should be always possible to see one.

And a die marked with 00, 10, 20, 30, 40, 50, 60, 70, 80, and 90 twice
should be easy to tell apart as well.

With the octahedron, of course, it is not quite as easy. Even an
octahedron perhaps would spin better as eight circular faces on a
spherical body - like some Chinese d6 dice - I tend to think, but I
have to admit that it probably is true that doing the d20 or the d12
that way would make it roll for too long.

But here's an idea...

make a four sided die as a dodecahedron (or d12) with the numbers from
1 to 4 repeated three times... but make them out of dots, like on
conventional d6 dice. Double-nine dominoes show how to make 7, 8, and
9 from dots, so that could be used on an icosahedral d10!

Following that convention, the cubical d6 would have numbers on its
faces... but the one serving as a d3 would have dots. As for the d8,
the octahedron could be replaced by a d24 shape!

John Savard

Quadibloc <jsavard.DeleteThis@ecn.ab.ca> writes:


> But here's an idea...
>
> make a four sided die as a dodecahedron (or d12) with the numbers from
> 1 to 4 repeated three times... but make them out of dots, like on
> conventional d6 dice. Double-nine dominoes show how to make 7, 8, and
> 9 from dots, so that could be used on an icosahedral d10!

I have seen a d10 that uses domino-style dot patterns. It was a
"real" d10, not a double-numbered d20, though. Also, it had a company
logo instead of 0/10.

> Following that convention, the cubical d6 would have numbers on its
> faces... but the one serving as a d3 would have dots. As for the d8,
> the octahedron could be replaced by a d24 shape!

If the purpose is to make the dice roll better, I think it is better
to make them more rounded. But I think a d8 rolls well enough without
any rounding.

If you use a cup to roll (which I mostly do due to limited table
space), rolling is not a problem even for d4s. The main problem I see
with the standard d4 is reading the result. This is particularly bad
for the old-style d4s that had numbers near the edges, so you would
read the bottom edge to see the value. It is much better with the
newer d4s that have numbers near the vertices, so you read the number
near the top vertex. Even so, it would be better to have a face
facing up, which you can get with a square rod with rounded or pointed
ends.

Torben