Follow-Up: Testing Balanced Dice

When I wrote the previous blog on how to statistically test for balanced dice, I hadn't actually used the test on any of my own dice (as was requested in at least one comment). But shortly thereafter I started to get worried that I would be compelled by curiosity to (a) test all the dice in my house, and (b) wonder what testing dice-manufacturers use, if any, for quality assurance purposes.

For part (b), I'm broadly guessing that the answer may be "none" in any sense other than an eyeball-check. If anyone has other information I'd be interested in hearing it.

For part (a), I haven't checked all my dice, but I did check all my d20's, and the results were rather interesting. Again, the process outlined earlier is this -- roll 100 times, count the frequency of each face, subtract 5 and square each, then add them all up; at the end you have the SSE "sum-squared-error" (higher results indicating a more unbalanced die).

I started by testing all my "newer" sets (at least a couple years old), mostly translucent, pre-inked digits, with slightly softer edges (many by Chessex, I believe). The SSE results I got for them were 150, 148, 106, 100, and 98. Recall that we were going to reject a die as clearly unbalanced if the result was more than 150; the first two d20's I tested (which I was already suspicious about, because of prior in-game behavior) just barely squeaked through the test. The P-values for these dice would be 0.05, 0.06, 0.33, 0.39, and 0.42 (you can sort of think of these as the probability that each die is in fact balanced; that's not exactly correct, but a fair analogy for what P-values represent -- a higher value is better news for the "balanced die" hypothesis). For the first two dice, we've got at least moderate-level evidence that the die is unbalanced.

Now at the end, I tested what I presumed would be the weakest die in my collection: an older translucent red d20, with sharp edges, that I had to color in myself with a crayon. The other dice in this set still show the tab from where it was snapped off the molding sprue (although I can't see it on the d20 itself; these dice are probably from Gamescience). Well, unexpectedly to me, this d20 had the lowest error of the bunch: SSE = 80, significantly lower than anything else I had in the house, and clearly the fairest-rolling die of anything I tested (P-value = 0.66).

So my theory now would be that a die that has sharp edges is more likely to roll fairly than one that has rounded edges, even though I've been avoiding this "sharp-edged" set for years now because to my eye it looked less professional.

Back to item (b) above. Interested in seeing what, if anything, the dice manufacturers have to say about their QA process, I landed at the Gamescience website ( http://www.gamescience.com/ ). And the fascinating thing is that the home page has a couple of videos by the long-time owner Lou Zocchi, where he rants for a total of about 20 minutes on exactly this subject. Namely: (a) he intentionally produces dice with sharp edges, similar to requirements for casino gambling dice; (b) people complain about the cost, the lack of inked digits, and still seeing the sprue-tab, and (c) his competitors solve these problems by mass-painting the whole die and then throwing them into a tumbling sand grinder (removing excess paint, the sprue-tab, and rounding all the edges in an irregular fashion).

So I hadn't known about Zocchi's position before, and I hope I don't come off as a shill for Gamescience in this paragraph. (Zocchi doesn't use formal statistics in his presentations; he uses more user-friendly demonstrations, like stacking up competitors' dice and seeing that you get obviously different total heights from different directions). But at this point in time, I'm basically sold on that position; if I wanted dice that I really knew would roll in as fair a distribution as possible, I would go out of my way and get sharp-edged dice from Gamescience.

This is not to say there's no downsides. Frankly, their dice are more expensive. Moreover, I must say that the rounded-edged dice are a little more pleasant to look at and hold in the hand without the really sharp corners (and even more so to step on in stocking feet if you leave them on the floor; Gamescience dice are like deadly little caltrops).

But I'm glad I found Zocchi's videos, because an older gentleman devoting his life to fairly-rolling dice, and delivering a really angry rant about correct probability distributions, really warms and delights my heart.

I see on the Gamescience web site that Lou is selling the business at this time to Gamestation, Inc., which makes me a little sad, just at the time when I discover the advantages to his product. I'll salute Lou Zocchi for his years in the industry and hope that his dice stay available with the same level of quality in the future.