Tuesday, September 18, 2012

A Quick Note on Shoving Scrimshaw Dice

Doth Computeth Spawn:

I'm in the lab this morning and will be focusing on all sorts of important science stuff shortly, but Roger's good-humoredly cranky post about dice caught my attention. He points to a Forbes article that points to a test of 2 d20s (Chessex and Game Science) rolled 10k times each by the folks at Awesome Dice Blog. They show that the Chessex die is less random than the Game Science die, but neither are perfect; in fact the little nubbin on the 14 of the GS die severely affects that die. Now I didn't read all the comments on the post, so maybe this has already been said, but the Chessex data indicates that it can't be considered a "lucky" or "unlucky" die in the sense of always rolling high or low. The problem with that die is that it's slightly ovoid rather than spherical, and the 1-20 axis is relatively long. Neither crits nor fumbles are likely with that die. You can see this by comparing the data they present on the blog.

The red line is the expected outcome of 500 rolls per face. It's obviously not random. In fact there's some interesting structure in the data: opposite faces tend to be equally likely to appear. Combining these frequencies we see this:

How do you like that? I don't have a d20 in front of me and the distribution of the faces on d20s vary by manufacturer, but my guess it that overall the die is a bit longer across the 1/20, 2/19, 7/14, 8/13 axis. So that reduces the likelihood of rolling at the extremes of the range and a couple chunks in the middle as we see above. The dip at 5 in this die may be from the little nubbin not being filed off. But I wonder if this ovoid shape has anything to do with rounding off the edges per se, as opposed to the problems with the shape of the mold or uneven shrinkage in the plastic as it sets (or whatever, I'm not a dice manufacturer).

So to Roger's point about lucky dice being loaded, if the pattern above is common, it seems unlikely that players are really holding dice that give them better chance to roll high or low. Even if you have the 20 on the short axis, the 1 will be there too, and so you'll have a die equally likely to crit and fumble more often than expected. With a squashed die, switching roll-high or roll-low mechanics to keep players on their toes may not mitigate the lucky/loaded die superstition. Well, if I remember I'll take some digital calipers home tonight and see if I can detect squashedness in my Chessex d20s.


  1. Good point ... but if it's squashed in an overall fair manner then it's not a "lucky die" either ;)

    1. Yeah, my guess is that truly lucky dice -- in an empirical sense -- must be extremely rare. I wonder if the convention of putting having opposing faces add to N+1 on a dN evolved from these sorts of problems.

  2. I love science! I hope you will do a squashedness test on some of your own d20s and report back.