Saturday, June 9, 2018

Spinning Down (dice testing)

Today I bought what will very likely be my last set of Chessex dice. As I've pondered the games I might run over the summer (and hopefully into the fall), one of the things that I've considered has been the dice required for each. AD&D 2nd Edition, as well as my vivisected Basic Fantasy rules set, use the standard complement of polyhedrons. White Box, in addition to being available for free or at low cost (much like Basic Fantasy), is so minimalist that players need only d20s and d6s; it was these that I bought today, such that up to four players can use a d20 and a rounded spot d6 of the same color. (I might even give these as small gifts to the players, if they choose White Box and prove committed.)

As much as I'd like to, I will not be running Dungeon Crawl Classics at this time; the extra dice are out of my price range at the moment, and I haven't spent enough time with the rules to be confident as a Judge. Which is too bad; their "Road Crew" program is pretty neat, even if it is blatantly commercial in nature.

Apart from my nice, pointy metal dice, the ones that I think I will be using going forward are Gamescience dice. I already have two of them that I plan on using (a d4, and a d20 numbered 0-9 twice - both "Jumbo" sized, and hand-inked by me), and the Jumbo Polyhedra set they sell will do perfectly for me (since I need another d10 anyway, for quick percentile rolls). It's too bad the set doesn't include any d6s, but at least they aren't too expensive to add on. Much like John Higgins explained in this post, I actually like the idea of carrying only as many dice as I need.

A die I own that I will not be using? One of the nicer-looking ones I own - a d20 designed for use as a counter in Magic: The Gathering. I ran a quick test on it, rolling it a total of 80 times and recording the results on the following chart:

Yeah... Looks like you were right, Simon and Tardigrade. It may not cluster around high or low numbers, but it sure isn't as even as it should be. (I realize that only 80 rolls isn't exactly scientifically rigorous, but since even this little experiment disproved my hypothesis, I'll take the results at face value for now.)


  1. If you have access to Dragon Magazine #78 from October of '83 there is an article about testing dice entitled "Be thy die ill-wrought?" which describes how to perform a chi-squared test on a die to decide if it is statistically biased. According to the author you would need at least 100 rolls on a d20, ideally 200, to reliably analyze the fairness of your die.

    The procedure is to tally the number of times you get each result (as you have) then sum the squares of the difference between that tally and the expected occurrences. With 80 rolls of a d20 you would expect a perfect die to yield each result 4 times. Take the the sum of the squares of each difference (97 in your sample) divide it by the expected value of 4 and compare this to a chi-square confidence table (someone with more background than I have might be able to explain this). Your set yeilds 24.25 which is under the 27.204 required by the test to be reasonably assured the die is fair. The number would have to be over 36.191 to be reasonably sure it is biased. In between you might go again with a larger sample.

    So, despite the pattern your mind detects, you die appears to be fair.

    1. Good point. I also need to try the saltwater test on it, and a second rolling test couldn't hurt (as long as it's done on a day when my wrist is in better shape).

      I remembered hearing about an article in Dragon, but couldn't remember which issue it was; thanks for pointing me to it!