Anyone play with alternative dice?

[woodelf]

woodelf,
That page is wrong. There are an infinite number of other shapes that are fair; we just don't know what they are.

How do I know?

Imagine a pyramidal die with a square base and four triangular sides such that the four triangular sides are the same. If the height of the pyramid is very large compared to the dimensions of the square base (i.e. it's long and thin), it will land on any given triangular face more often than on the square base. If, on the other hand, the height of the pyramid is very small compared to the square base (i.e. it's low and almost flat), it will land on the square base more often than any given triangular face. Somewhere in between these two extreme pyramids, there is, in theory, a pyramid of a particular height to base ratio such that it lands on its square base exactly as often as it lands on any given triangular face. This theoretical pyramid would be as fair a die as a regular tetrahedron (i.e. a standard d4), cube (d6) etc.

There's fair, and then there's fair. Yes, it seems plausible that, given a pseudo-random initial toss, such a design could have equal chance of landing on each face. But it also might not be possible to find such a happy medium. And, it'll never behave like a truly fair die. It'll have to use a difference in face surface area to compensate for the difference in inter-face angle and the difference in distance from the center of mass, but in some circumstances some of those factors matter more than others--such as once it has hit the table and is rolling. If you really want a die that behaves fairly and has a number of faces otherwise not achievable, make a faceted log that's long enough that it can't land on the ends (and/or round the ends).

~~~
Here's a summary of the variously shaped dice in my collection, excluding ones that are double/triple etc-numbered (such as a cube numbered 1 to 3 twice). The number in parentheses is the number of different shapes I have for that particualr d#:

d2 (2)
d3 (2)
d4 (8)
d5 (3)
d6 (too many to count! Probably more than 12)
d7 (3)
d8 (2)
d9 (2)
d10 (3)
d11 (1)
d12 (3)
d13 (1)
d14 (1)
d15 (1)
d16 (1)
d20 (2)
d24 (1)
d30 (1)
d32 (1)
d34 (1)
d50 (2)
d100 (1)

Now, that's just not fair. You're gonna have to elucidate on the unusual ones--at least describe their shape and, if possible, where i can buy one.

 

[(Psi)SeveredHead]

A friend of mine owns "sex-sided" dice. Each side has a picture from the Kama Sutra.

We've actually found uses for it like when two characters fall down a shaft! Fortunately none of my characters had it inflicted on them.

 

[Saeviomagy]

There's fair, and then there's fair. Yes, it seems plausible that, given a pseudo-random initial toss, such a design could have equal chance of landing on each face. But it also might not be possible to find such a happy medium. And, it'll never behave like a truly fair die. It'll have to use a difference in face surface area to compensate for the difference in inter-face angle and the difference in distance from the center of mass, but in some circumstances some of those factors matter more than others--such as once it has hit the table and is rolling. If you really want a die that behaves fairly and has a number of faces otherwise not achievable, make a faceted log that's long enough that it can't land on the ends (and/or round the ends).

You're dealing with (more or less) a linear relationship between the height of the pyramid and the chance it'll land on a triangular side compared with the chance it'll land on a square side. At some point, that's going to be 50%. There's not really any complexity to this problem, and therefore the chance that it is unsolvable is vanishingly slim, and certainly not 1.

With an infinite number of possible dice, and a non-1 chance that they'll be unfair, that leaves us with an infinite number of fair dice...

 

[Zander]

Now, that's just not fair. You're gonna have to elucidate on the unusual ones--at least describe their shape and, if possible, where i can buy one.

Some of them are pictured in my album at the Dice Maniacs' Club. My album at the site is titled "Alexander's Dice". Others I will take pics of when I have the time.

You might want to head over to Kevin Cook's site at http://www.dicecollector.com . He has pics there of every die in his collection, the largest in the world. Most, though not all, of the strangely shaped ones I have, he has too.

If there are any that particularly interest you, please let me know and I will either describe them here or post a pic at the Club.

 

[diaglo]

Some of them are pictured in my album at the Dice Maniacs' Club. My album at the site is titled "Alexander's Dice". Others I will take pics of when I have the time.

You might want to head over to Kevin Cook's site at http://www.dicecollector.com . He has pics there of every die in his collection, the largest in the world. Most, though not all, of the strangely shaped ones I have, he has too.

If there are any that particularly interest you, please let me know and I will either describe them here or post a pic at the Club.

i have more dice than he does.

i just don't have as many unique ones.

 

[woodelf]

Some of them are pictured in my album at the Dice Maniacs' Club. My album at the site is titled "Alexander's Dice". Others I will take pics of when I have the time.

You might want to head over to Kevin Cook's site at http://www.dicecollector.com . He has pics there of every die in his collection, the largest in the world. Most, though not all, of the strangely shaped ones I have, he has too.

If there are any that particularly interest you, please let me know and I will either describe them here or post a pic at the Club.

I poked around there, and Alexander's site, for quite a while, but i might've missed some of these, so perhaps explicit picture links, or just descriptions?

d4 (8)
This one in particular: i'm familiar with tetrahedron, wedge, octahedron, dodecahedron, and "log" 4s--that still leaves 3 shapes to go. Oh, wait, didn't you say excluding dice that were "standard" shapes but numbered funny?--That'd leave out the octahedron and dodecahedron.

d5 (3)
I'm assuming rhombic decahedron and then a couple variations on a triangular prism?

d6 (too many to count! Probably more than 12)
These, i'm really wondering about ,too. I can immediately come up with: cube, sphere, log, and the crystal caste-style truncated rhombic hexahedron. That still leaves 8 or more unknown to me.

d7 (3)
Anything more interesting than a log or pentagonal prism?

d8 (2)
Anything wierder than crystal caste + octahedron?

d10 (3)
Well, i can come up with two: "standard" d10, and crystal caste d10--what's the third?

d12 (3)
Just dodecahedron, rhombic dodecahedron, and crystal caste?