Why Not More Rounded Dice?

>>>>> "Q" == Quadibloc <jsavard 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 I'm surprised it hasn't been replaced by an octahedron with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.

Charlton


--
Charlton Wilbur
cwilbur DeleteThis @chromatico.net

On Tue, 01 Jul 2008 00:16:21 +0100, Jim Davies wrote:

> On the grave of Charlton Wilbur <cwilbur.RemoveThis@chromatico.net> is inscribed:
>
>>>>>>> "Q" == Quadibloc <jsavard.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 I'm surprised it hasn't been replaced by an octahedron with Q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've seen prismatic d4s, just long cuboids with rounded ends.
>
> Also irregulat tetrahedral d4s: get a d4 and pull on two of the opposing
> edges. The top side is a long triangle with the short edge touching the
> table and the far vertex at the highest point off the table.

My old game-store had alternative d20s: rather cylindrical objects with
20 sides which you could roll (like you would roll a pencil or
something).
And roll they did.
I'm no physics major, but somehow they managed to let them take about
half a minute until it finally showed the number. Everybody hated them,
they were in the store as long as it existed and nobody ever bought them.

On Jun 30, 9:03 pm, Robert Socrates <robert.socra....RemoveThis@gmail.com> wrote:
> On Tue, 01 Jul 2008 00:16:21 +0100, Jim Davies wrote:
> > On the grave of Charlton Wilbur <cwil....RemoveThis@chromatico.net> is inscribed:
>
> >>>>>>> "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've seen prismatic d4s, just long cuboids with rounded ends.
>
> > Also irregulat tetrahedral d4s: get a d4 and pull on two of the opposing
> > edges. The top side is a long triangle with the short edge touching the
> > table and the far vertex at the highest point off the table.
>
> My old game-store had alternative d20s: rather cylindrical objects with
> 20 sides which you could roll (like you would roll a pencil or
> something).
> And roll they did.
> I'm no physics major, but somehow they managed to let them take about
> half a minute until it finally showed the number. Everybody hated them,
> they were in the store as long as it existed and nobody ever bought them

I would have. :-.)

I don't really have the "collector gene" but I bought every kind of
RPG die on the market for a few years there, including a D30 and a
couple diffeent D%. They weren't expensive and I would try to create a
rules/situation where my new dice could be used. I remember the
transition from D10*2 to true D20 and how one of our players hated
it.

--
Will in New Haven
Sunspear, who walked the length of Shadows Dance

On Jul 1, 2:47 am, torb... RemoveThis @pc-003.diku.dk (Torben Ægidius Mogensen)
wrote:

> The old-style dice were cast from liquid plastic, but the new dice are
> pressed and heated from powder,

Ah, I didn't know this. I had thought that the changeover was from
dice made of some rather odd and cheap plastics to dice made of
polystyrene, and finally, in the present day, to cellulose acetate.

While Bakelite and allied materials (i.e. Catalin) were used at one
time, I thought that was long ago.

> then coated in paint and finally
> tumbled with polishing powder to make them smooth and to remove the
> paint except from in the numbered indentations. This tumbling also
> rounds the edges. As you can imagine, the paint is very durable to
> survive this treatment.

I'm properly astounded they wouldn't tumble first and paint later.

> You can also find d24s and other strange shapes. Not all are
> demonstrably fair, though.

Of course, d24 is an example of a number for which a demonstrably fair
die is possible: one example is a cube with a very shallow pyramid
applied to each face, although a better alternative involves kite-
shaped faces.

> See some more discussion about possible
> fair dice shapes at

> http://www.rpg.net/columns/rollthebones/rollthebones7.phtml

> Alternatively, you could embed an numbered opaque
> tetrahedron upside-down inside a clear tetrahedron. This would be
> rather costly, though.

Doing that inside the die with four circular flat areas on a sphere
might work well, considering your comments later about a rounded
tetrahedron.

> This die has an

octahedral

> cavity where a heavy ball settles in one of
> the vertexes. In general, the cavity would be the dual solid to the
> "outside", so you would have a cubic cavity for a d8 and a tetrahedral
> cavity for a d4 (since the tetrahedron is its own dual).

Yes. I know this stuff...

http://www.quadibloc.com/math/acsint.htm

but I had imagined that the cavity inside a spherical six-sided die,
instead of being octahedral, was some type of multi-chambered curved
space, such as eight spheres linked to a ninth central sphere by
cylindrical tunnels.

> This would
> be a far more readable d4, but also far more expensive -- and easier
> to cheat with. You wouldn't find any gambler who would accept such
> clearly loaded dice.

Indeed, they work _because_ they're loaded, so there is no way to tell
that they're not loaded unfairly... but I suppose one _could_ make
spherical dice out of clear plastic.

(quoting me)
> > Leaving that out of consideration, I have some dice from
> > inexpensive games that are in the Chinese style - the numbers 1 and 4
> > being in red - where the shape is a sphere with six flat circular
> > faces obtained by trimming pieces off of the basic spherical shape.
>
> This is not essentially different from polyhedral dice with rounded
> edges -- you can't make (fair) dice with a number of sides you can't
> get with polyhedral dice.

Yes, I know that. Of course, it might be thought of as helping a bit
with the unfair dice: *somewhere* between the cuboctahedron and the
truncated octahedron, there has to be a fair d14 - at least for one
particular surface and method of rolling...

> If you have more than eight faces, polyhedral dice with sharp
> edges roll well enough and if you round the edges, they tend to take
> too long to settle.

And apparently the teetotum-like dice have that problem too; I thought
the reason they weren't more popular was simply because they didn't
look as cute as the Platonic solids; it seemed to me they were a
design likely to yield less biased results.

John Savard

On Jul 1, 8:58 am, Will in New Haven <bill.re....DeleteThis@taylorandfrancis.com>
wrote:
> On Jun 30, 9:03 pm, Robert Socrates <robert.socra....DeleteThis@gmail.com> wrote:

> > My old game-store had alternative d20s: rather cylindrical objects with
> > 20 sides which you could roll (like you would roll a pencil or
> > something).
> > And roll they did.
> > I'm no physics major, but somehow they managed to let them take about
> > half a minute until it finally showed the number. Everybody hated them,
> > they were in the store as long as it existed and nobody ever bought them
>
> I would have. :-.)

A comics store in my neighborhood has a complete set from d4 to d20
like that. So I think they're still around, although I couldn't find
them in a brief search to find who makes them. Apparently, Zocchi,
Koplow, and Chessex are the three big names.

John Savard

On Jul 1, 9:55 am, Quadibloc <jsav....RemoveThis@ecn.ab.ca> wrote:
> On Jul 1, 8:58 am, Will in New Haven <bill.re....RemoveThis@taylorandfrancis.com>
> wrote:
>
> > On Jun 30, 9:03 pm, Robert Socrates <robert.socra....RemoveThis@gmail.com> wrote:
> > > My old game-store had alternative d20s: rather cylindrical objects with
> > > 20 sides which you could roll (like you would roll a pencil or
> > > something).
> > > And roll they did.
> > > I'm no physics major, but somehow they managed to let them take about
> > > half a minute until it finally showed the number. Everybody hated them,
> > > they were in the store as long as it existed and nobody ever bought them
>
> > I would have. :-.)
>
> A comics store in my neighborhood has a complete set from d4 to d20
> like that. So I think they're still around, although I couldn't find
> them in a brief search to find who makes them.

Another try did turn something up:

http://www.crystalcaste.com/mm5/merchant.mvc?Screen=CTGY&Store_Code=CC...tegory_

> Apparently, Zocchi,

That should be Gamescience

> Koplow, and Chessex are the three big names.

John Savard

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

> Back when polyhedral dice for role-playing games first came out,
> because they were not a common or standard product, they were
> different from what they are today.
>
> The numbers were usually unpainted; the edges were fairly sharp; and
> d10 was usually an icosahedron with the numbers repeated twice.
>
> Now, because such dice are a popular mass-manufactured item, they're
> generally as rounded as ordinary 6-sided dice for ordinary games, and
> they are made of the same sort of very hard plastic, and so on.

The old-style dice were cast from liquid plastic, but the new dice are
pressed and heated from powder, then coated in paint and finally
tumbled with polishing powder to make them smooth and to remove the
paint except from in the numbered indentations. This tumbling also
rounds the edges. As you can imagine, the paint is very durable to
survive this treatment.

> Also, a sort of bi-pyramidal die (the shape is more complicated than
> that, with a half-face offset, so that one side is up) is used for
> d10, with the icosahedron used for d20. There's also a d30 that was
> innovated by a company called The Armory, but that hasn't made it
> into the standard repertoire.

You can also find d24s and other strange shapes. Not all are
demonstrably fair, though. See some more discussion about possible
fair dice shapes at
http://www.rpg.net/columns/rollthebones/rollthebones7.phtml

> I'm surprised, though, that some other changes haven't taken place.
>
> The tetrahedron, for d4, isn't a very practical shape for a die. I'm
> surprised it hasn't been replaced by an octahedron with the numbers 1
> through 4 repeated twice.

As others have said, easy distinguishability would be lost. For a
more readable d4, you could use a short rod with square cross section
(i.e., a prism). Alternatively, you could embed an numbered opaque
tetrahedron upside-down inside a clear tetrahedron. This would be
rather costly, though.

> There are novelty six-sided dice in the shape of a sphere which are
> made to come up on one of six faces by the settling of an internal
> weight.

This die has an octagonal cavity where a heavy ball settles in one of
the vertexes. In general, the cavity would be the dual solid to the
"outside", so you would have a cubic cavity for a d8 and a tetrahedral
cavity for a d4 (since the tetrahedron is its own dual). This would
be a far more readable d4, but also far more expensive -- and easier
to cheat with. You wouldn't find any gambler who would accept such
clearly loaded dice.

> Leaving that out of consideration, I have some dice from
> inexpensive games that are in the Chinese style - the numbers 1 and 4
> being in red - where the shape is a sphere with six flat circular
> faces obtained by trimming pieces off of the basic spherical shape.

This is not essentially different from polyhedral dice with rounded
edges -- you can't make (fair) dice with a number of sides you can't
get with polyhedral dice.

> This style of die, I would think, might be a very good idea for the
> various polyhedral dice, since issues with pointy corners not rolling
> well would be dealt with. On the other hand, of course, it could be
> that such dice would roll too much.

Indeed. If you have more than eight faces, polyhedral dice with sharp
edges roll well enough and if you round the edges, they tend to take
too long to settle. For an alternative d4, it would be a good idea,
though. You could paint the numbers opposite the facets so they are
more easily readable. You would need to finetune the size of the
facets to allow maximum space for numbering outside facets without too
much risk of having the dice settle on the rounded surface.

Torben

Incidentally, I recently turned up your paper on dice combinations on
the Web, and found it of great interest.

Although here I show interest in fancy polyhedral dice, on my page at

http://www.quadibloc.com/other/bo0201.htm

I note that one can manage, with a little extra effort, to use three
identical plain six-sided dice to serve a great many purposes.

John Savard

On Jul 1, 5:48 pm, Ben Finney <bignose+hates-s...@benfinney.id.au>
wrote:
> Quadibloc <jsav....DeleteThis@ecn.ab.ca> writes:
> > On Jul 1, 2:47 am, torb....DeleteThis@pc-003.diku.dk (Torben Ægidius Mogensen)
> > wrote:
>
> > > then coated in paint and finally tumbled with polishing powder to
> > > make them smooth and to remove the paint except from in the
> > > numbered indentations. This tumbling also rounds the edges. As you
> > > can imagine, the paint is very durable to survive this treatment.
>
> > I'm properly astounded they wouldn't tumble first and paint later.
>
> You're not thinking like a manufacturing designer. Painting later
> would mean they'd need the machine to get it exactly into the design
> on each face, with any overspill being seen by the buyer as a defect.
>
> It's much simpler to be inaccurate with the paint and then let the
> tumbling clean up while it smooths, leaving the design on each face
> look crisply painted no matter how much overspill occurred during
> manufacture.

I can see a little tumbling afterwards, then, to touch up the paint
job. But I would have thought that anything that effects a major
change to the shape of the dice also removes the paint over the areas
that were removed.

John Savard

On Tue, 1 Jul 2008 07:58:58 -0700 (PDT), Will in New Haven
<bill.reich DeleteThis @taylorandfrancis.com> wrote:

>I don't really have the "collector gene" but I bought every kind of
>RPG die on the market for a few years there, including a D30 and a
>couple diffeent D%. They weren't expensive and I would try to create a
>rules/situation where my new dice could be used. I remember the
>transition from D10*2 to true D20 and how one of our players hated
>it.

Do you have any d24s? I have two myself. Perfect for
random hour of the day.
--
Doesn't the fact that there are *exactly* 50 states seem a little suspicious?

George W. Harris For actual email address, replace each 'u' with an 'i'

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

> On Jul 1, 2:47 am, torb....TakeThisOut@pc-003.diku.dk (Torben Ægidius Mogensen)
> wrote:
>
> > then coated in paint and finally tumbled with polishing powder to
> > make them smooth and to remove the paint except from in the
> > numbered indentations. This tumbling also rounds the edges. As you
> > can imagine, the paint is very durable to survive this treatment.
>
> I'm properly astounded they wouldn't tumble first and paint later.

You're not thinking like a manufacturing designer. Painting later
would mean they'd need the machine to get it exactly into the design
on each face, with any overspill being seen by the buyer as a defect.

It's much simpler to be inaccurate with the paint and then let the
tumbling clean up while it smooths, leaving the design on each face
look crisply painted no matter how much overspill occurred during
manufacture.

--
\ "In case you haven't noticed, [the USA] are now almost as |
`\ feared and hated all over the world as the Nazis were." —Kurt |
_o__) Vonnegut, 2004 |
Ben Finney

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

> Incidentally, I recently turned up your paper on dice combinations on
> the Web, and found it of great interest.
>
> Although here I show interest in fancy polyhedral dice, on my page at
>
> http://www.quadibloc.com/other/bo0201.htm
>
> I note that one can manage, with a little extra effort, to use three
> identical plain six-sided dice to serve a great many purposes.

Interesting, though I doubt very many would use such a large table
during game play. If I wanted to simulate other dice using a d6, I
would try to avoid tables and complex arithmetic. Dice smaller than a
d6 can be simulated by rerolling (though you would probably use a d6/2
for a d3 instead of rerolling 4-6).

A d7 is more tricky. Here is one option:

1. Roll three d6s, one of which is of a distinct colour (or rolled
separately).

2. If the two same-coloured dice are different, the third die shows
the result. If they are both ones, start over from step 1.
Otherwise, you get a 7.

Since you reroll pairs of ones, you have 35 remaining combinations on
the same-coloured dice, five of which are pairs. 5/35 = 1/7, so this
works. The remaining 30 cases are split evenly by the third die, so
each value has probability 5/35 = 1/7.

You only reroll one time in 36 and it is fairly fast to read the
result from the three dice otherwise, so this should work faster than
using a table.

Torben

I suppose one could roll two ordinary dice, and get a d7 result most
of the time like this:

Interpret the total as follows:

8 - counts as 1
2 or 9 - counts as 2
3 or 10 - counts as 3
4 or 11 - counts as 4
5 or 12 - counts as 5
6 - counts as 6

A total of 7 counts as 7, unless you roll 1-6.

In that case, you take one of the dice, and roll it. If the result is
odd, it also counts as a 7.

If the result is even, you need to reroll.

John Savard