Thursday, June 24, 2010

Stereoisomeric Dice

Just an example of how my brain clicks. I was reading an article last might that featured a picture of a D20 that is a twenty-sided die and I suddenly wondered who decided how the numbers on it are arranged. To make this simpler I'll drop down to a D6 that is a six-sided die.

Logically the probability of any of the numbers landing face-up is 1/6th non-logically the highest face should be furthest away from the lowest face. In terms of reality this makes sense for reasons I'll show with higher-sided dice. So the 1 face is positioned opposite the 6 face; using this logic the 2 face is opposite the 5 face and the 3 face opposite the 4 so each opposite pair of faces add to 7.

So far so easy. So what about that big word in the title "Stereoisomeric" well that's a fancy term for mirror-image, hands are mirror-images of each other. How does that apply to dice? Well examine the following two dice closely.

From our previous rules we know that the 3 is opposite the 4 so from this point of view and using the 1 face as our North Pole the numbers flow clockwise for the left-hand die and counter-clockwise for our right-hand die. One is a mirror-image of the other.

For a six-sided die this is barely noticeable, but let's go one step up to an eight-sided die a D8. Again our previous rules dictate that the 1 face is opposite the 8 face, but how should the other numbers be distributed?

So why not set it as 1, 2, 3, 4  around the top or even 1,3,5,7 in order? Well I mentioned that the highest value should be furthest from the lowest and the reason is that all dice aren't perfect. It's possible that some dice are slightly uneven either in terms of their sides or in weight. Putting all the low numbers in a cluster might mean that this die tends to produce low numbers or high numbers depending on how it falls. Distributing the numbers gives a potentially more even spread. Again though it should be obvious that a mirror-image also exists of this die.

Now this is just for D6 and D8s move up to a D12 or a D20 and this becomes more difficult. It seems there's no default method of arranging the numbers. I've seen a D20 with a 2, 8, and 14 surrounding the 20 face; and another with 13,16, and 19, and another with 7, 11, and 14occupying the respective positions.

So who cares? Well other than just being how I think there's also a case of 'luck'. Despite the nerd/geek science vibe that messing with 'odd' shaped dice brings it's interesting to note how many role-players consider some of their dice to be 'lucky' or 'unlucky' that is which ones tend to produce high numbers and which produce low ones. Other than superstition could there be a reality behind this supposition based on either stereoisomerism or distribution; or both?

Is a left-handed player throwing a particular left-handed D6 more likely to result in higher numbers than if a right-handed player rolled it?

Just a thought.