Wednesday, 27 March 2013

A question for (potential) diemakers

If the probability of rolling each of the individual results on a given die is influenced by the weight of material removed from each face to create the specific pips or numbers that face has, why not:

a) cut seven pips in each face to a three-by-three grid then ink only those pips actually needed, or

b) cut the pips or numbers on different faces to different depths, i.e. cut the one six times deeper than the six, to equalise the weight of each face?


M. Jared Swenson said...

Coopdevil said...

B is effectively done on Asian dice where they have a very big 'one' spot. Always coloured red for some reason.

Porky said...

Well, that surprised me. Not so much that someone has thought of it or even implemented it, but more the fact the KS is only a week and a half old. I saw that die ring campaign a while back, but not this one and I haven't read anything complaining about die balance in a while. As far as I can tell, what set me off this time was Marc Pavone's recent post on geomorph dice. Maybe there's something in that noö-braner idea after all.

I wonder how much this KS will set a new standard, whether the big firms will feel a need to match the accuracy more closely, or even to pay lip service to it. The seven-pip approach might be a cheaper way to go, maybe even the only way with more standard materials, but it's also less aesthetic, so I can't see it catching on.

Something to be said for KS is the size of the bang it offers, for warning shots to existing firms, to get them digging into any excess capacity they have, and for boosting a sense of just what's possible and what can reasonably be expected among a large group of people.

Coupled with the big red spot idea, it also makes me wonder how much scope there is for continued incremental progress in the d6 and dice in general. Can it reach effective perfection, as in a stage beyond which rising expectations and the technologies will no longer meaningfully push? If so, where does the spirit then turn, in the sense of where do dice go next? My thinking still follows the lines in the deeper dice series, the networked die set taking the strain and possibly playing us.

Marc Pavone said...

I know casino grade dice are prepared to be as perfectly balanced as possible. The manufacturer will drill out the pips to a given depth then fill the holes with a contrasting color resin of the same density, thus effectively replacing all the material they drilled out. Their dice aren't polished in rock tumblers, which seems to have a bigger effect on the fairness of a die than the pips removed. I have handfuls of six sided dice that are obviously not cubes. I have run some short tests (100 throws or so) and the dice will clearly favor certain numbers over others.

If you were to go and drill dice out (yep, done that myself) and then collect the shavings you'd see that the differences in volumes of material is so tiny it's almost negligible.

For common play, cubic perfection is more important than balance or center of gravity.

Marc Pavone said...

Hey, me again.

Just read the guy's case for his dice on his Kickstarter page and I have a few points (pips?) I'd like to bring up.

We all know opposite sides add up to 7, so it seems like the pair of opposing sides with the least difference in pips would be the most balanced side. So the 3,4 pair has a difference of 1 while 5,2 has a difference of 3 and 6,1 has a difference of 5. So the center of gravity should be closest to center of the cube along the 3,4 axis. On the 1,6 axis it would (on less precise dice) would be closer to the 1. On by a hair really. So the center of gravity (off the top of my head) should be closer to the vertices where the 1,2,3 sides meet.

With the 3,4 sides having the least difference in weight we should see 3 and 4 show up on average the greatest number of times, with works out to the 3.5 mathematical average.

Even then, while dude is drilling the dice so the material removed balances out as perfectly as possible, the 6 still has more surface area removed and spread out, while the 1 has a single (duh) pip that is deep. That little balancing game could still influence the die, as anybody who has carried a full tray of plates with one arm will tell you. On top of that, those multiple ridges on the 6 face make for more edges to offer friction and resistance during the roll.

The beveled edges of the metal dice will allow the dice to roll easier, thus influencing the roll. I'm starting to sound like I work for Lou Zocchi.

To make his metal dice as fair as possible he'd have to drill the pips in such a way that the edge of the pip closest to the center of gravity is deeper while the further edges are shallow.

Pardon my mad science rambling, but if you want nearly perfect d6 dice, buy them from a casino. They have spent the most money making sure their dice are as fair as possible. It's in their best interest.

Porky said...

I agree on that related balance problem, the distribution of the weight removal across the face. The casino die remove-and-replace is one solution, but the only alternative I've come up with is option a) in the post, that each face be drilled the same number of times. If the weight of the ink is a concern, all of the unused pips can be inked too, but the same colour as the die material.

Interestingly, the KS page does mention something akin to the remove-replace approach, specifically "a very slight conical rise of material in the center of the pip", but it's difficult to see exactly how that looks in the images, and how relatively low the amount of material removed is overall.

One other point of interest given the switch to metal is relative expansion due to heat for the various materials dice can use.

On the subject of result spread, I recently made up around three dozen pick-up characters for an old school RPG campaign, which meant rolling around 650 d6s for attribute scores alone. In doing that and building up a range of natures and careers on the back of the scores, I got the distinct impression that certain results scame up with greater frequency and there was a general bias down in the totals. Of course, the roll count has to be very high to iron out bumps, but even the impression of irregularity can be a distraction at the table. That said, the irregularity can be woven into the nature of the game, as the fabric of the world say, fate or similar.

I lean heavily on dice in a lot of the gaming I do and I really do want as even a spread as possible, but at the same time I'd like to retain the feel of the roll casual dice have. A slightly greater overall weight would be a bonus. I think we're moving in the right direction, with greater awareness and discussion and more options.