Game mechanics of dice!

[Reality Aberrant]

Hi all,

I am new here so i am sorry if i am posting this in the wrong section.

I have been playing with the idea of creating a setting with it's own mechanics for a while now and i am really glad to have found this place.

My first question has nothing to do with my setting but with a doubt i have of Dice mechanics.

What is the statistical diference betweing rolling 2d20 as percentile dice or rolling 2d10 as percentile... in the case of the d20 you would use dice of diferent colors to represent the 100's and the 10's while the d10 usually come labeled as such.  a friend of mine was arguing that the d20's have a greater spread of permutations and as such they more acurately represent randomness in the roll, he also stated that the phisical shape of the d10 is not a natural poligon so it does not roll right.

I would like your help with this question. It is obvious that he is a simulationist, i think. i think i rather would enjoy more the Narrativist style but i will speak of that in another post.

Once again, thanks for having me.

Luis R. Rojas

[Paganini]

What is the statistical diference betweing rolling 2d20 as percentile dice or rolling 2d10 as percentile... in the case of the d20 you would use dice of diferent colors to represent the 100's and the 10's while the d10 usually come labeled as such.  a friend of mine was arguing that the d20's have a greater spread of permutations and as such they more acurately represent randomness in the roll, he also stated that the phisical shape of the d10 is not a natural poligon so it does not roll right.

Hi, Luis! Welcome to the Forge. I think your question is in the right place, although we don't get very many questions like it (dice mechanics outside the context of a given game).

First of all, your friend is correct that the d10 is not a natural polygon. However, I don't think I've ever heard anyone complain of this being a problem when rolling. In practical terms randomness means unpredictability. As long as all the faces on the die are identical in shape and surface area the die will perfectly random (meaning that each die result is just as likely as any other). In actual practice, dice are not machined that perfectly, being made of extruded or moulded plastic. But, they're generally close enough for RPGs. :)

As for comparing d10% to d20%, I'm assuming that your d20s are labled 0 - 9 twice. I would suggest *not* using this sort of percentile roll, because such d20s are a bit hard to come by these days. Most gamers I know do not have them. (I have only one of them that came with an old FASA boardgame.)

In terms of statistics, d10% and d20% are identical. The whole point of percentile dice is that each possible outcome from 1 to 100 has an identical chance of occuring. (That means you're just as likely to get 100 as you are to get 1, or 42, or any other number.) You can't change it by switching to different dice.

[Reality Aberrant]

thanks for your promt reply...

The d20% i was referring to where standard d20, subtracting 10 to the roll if it's grater than 10.

Thanks for your information, it was my understanding that from a statistical point of view all the numbers have the same chance of coming up but my friend insisted that the d20% has a biguer spread of permutation options and so it provides for a better random factor.

Thanks once again.

Luis R. Rojas

[J B Bell]

I think what your friend is trying to say is that, for example, if on your d20, the "red" 2 has not quite a .05 probability of coming up, the "black" 2 might make up for that.  That might be correct, but it's almost certainly not statistically significant except for a die that would be skewed enough in other ways to be an unfair die anyway.  Technically, since the grinding of the numbers takes out uneven amounts of plastic, thus skewing the center of gravity, no die with etched numbers is fair.  (You'll notice that casino dice use plugs of a different-colored plastic, but the same density.)

As for the "naturalness" of a d10, that is totally irrelevant--as long as every face is identical (or symmetric axially or rotationally), a perfectly-machined die of that kind would be perfectly fair.

For the obsessive, check out the fair dice site.

--JB

[Eric J.]

He was probably reffering to the mathematical truth of Polyhedrons.  4-sided figures, 6-sided, 8-sided, 12-sided and 20-sided are the only possible hexahedrons that are regular, I think... It's something like that. However, his point is mute as the sides are equal to the point of statistical accuracy.  If he needs more proof, then do surveys.  I'm sorry for the rambly tone of my post.  I'm listening to Amish Paradise...

[Le Joueur]

He was probably refering to the mathematical truth of Polyhedrons.  4-sided figures, 6-sided, 8-sided, 12-sided and 20-sided are the only possible hexahedrons that are regular, I think... It's something like that. However, his point is mute as the sides are equal to the point of statistical accuracy.  If he needs more proof, then do surveys.  I'm sorry for the rambly tone of my post.  I'm listening to Amish Paradise...

First of all the polyhedrons listed are the only possible regular, three-dimensional polyhedrons (polyhedrons which have regular polygons - 'same sides, same angles' - for all faces).  The tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron are also called Platonic solids because Plato is first on record for identifying them.

In terms of probability (provided that they have little facial variation¹), every face will have equal distribution because all faces have the same angle/shape related to the center of the polyhedron and to the center gravity.  Now the familiar '10-sided die' (which can be called a decahedron, even though it is not regular) also has equal distribution of probability for the same reason.

While not regular it is called (if I remember correctly) a spindle; since it is symmetrical both one point to the other and radially along its primary axis it will have even distribution.  Any number of even-numbered die can be created using the basic spindle shape; so you could have a 14-sider, a 18-sider, and so on.

When it comes to comparing a spindle decahedron with a regular icosahedron (a 10-sider to a 20-sider) you have to realize that if half the numbers on the regular icosahedron repeat, the probability is the same.  Follow: if all faces have the same probability in both, then the chance of a single face on a spindle decahedron is 1 in 10 and for the regular icosahedron it's 1 in 20.  If there are 2 of every number on the faces of the regular icosahedron, then the chance of any number coming up is therefore 2 in 20, or dividing - 1 in 10, the same as the spindle decahedron.

I hope that clears things up.

Fang Langford

¹ It has been shown that a six-sider with 'pips' drilled into it is not perfectly distributed.  (Six 'pips' take out six times the amount and weigh of material as one.)  However given an otherwise perfectly balanced die, in 10,000 rolls, the six will only have about 25 more appearances than the one.  Since that is less than a quarter of a percentage point difference, few people care.

One bit of trivia: the tradition in 'die numbering' is to put the numbers opposite in such a way that they total the same no matter how which pair is examined; on a six-sider the 1 is opposite the 6, the 2 opposite the 5, and so on.  This has no affect on the distribution because all faces are equal.

[Reality Aberrant]

Wow!!!!

Thank you all for the insightfull replies...
It was i was hoping for and more.

Once again, Thank You

Luis R. Rojas