Chi-square tests of GameScience dice
Summary: almost all the GameScience dice I looked at passed chi-square testing fine, with one exception: the “D16 Transparent Ice Blue Gamescience Gem Die”, which failed miserably.
I ordered this stuff from G2 Collectibles and Hobbies:
1 x Gamescience Precision RPG Dice Set Opaque White 7pc () = $9.99
1 x D16 Transparent Ice Blue Gamescience Gem Die () = $5.99
1 x D10 Opaque Green Gamescience Precision Die () = $1.39
1 x D4 (8 Sided) Opaque Red Gamescience Die () = $1.99
1 x D5 (10 Sided) Opaque Blue Gamescience Die () = $2.99
And subjected them to chi-square testing– rolling them N times, computing the chi-square critical value, and using http://stattrek.com/Tables/ChiSquare.aspx to look up the corresponding cumulative probability.
| Description | N | df | CV | P(X^2 < CV) | Stat. sig.? |
|---|---|---|---|---|---|
| Die #1: white d4 | 100 | 3 | .48 | .03 | |
| Die #2: white d6 | 120 | 5 | 4.4 | .51 | |
| Die #3: white d8 | 160 | 7 | 12.5 | .92 | Yes |
| Die #3: white d8 | 80 | 7 | .6 | .001 | No |
| Die #3: white d8 | 80 | 7 | 4.0 | .22 | No |
| Die #3: white d8 | 120 | 7 | 7.7 | .64 | No |
| Die #4: red octahedron labeled 1-4; a "d4 on a d8" | 160 | 3 | 3.6 | .69 | |
| Die #5: white d10 labeled 00-90 | 70 | 9 | 11.1 | .73 | |
| Die #5: white d10 labeled 00-90 | 200 | 9 | 6.2 | .28 | |
| Die #6: white d10 labeled 0-9 | 70 | 9 | 5.7 | .23 | |
| Die #6: white d10 labeled 0-9 | 200 | 9 | 7.0 | .36 | |
| Die #7: green d10 labeled 0-9 | 70 | 9 | 10.6 | .69 | |
| Die #7: green d10 labeled 0-9 | 100 | 9 | 4.8 | .15 | |
| Die #8: blue d10 labeled 1-5-- a "d5 on a d10" | 100 | 4 | 2.5 | .36 | |
| Die #9: white d12 | 120 | 11 | 14.0 | .77 | Marginal |
| Die #9: white d12 | 120 | 11 | 5.4 | .09 | No |
| Die #10: ice blue d16 | 120 | 15 | 24.0 | .94 | Yes |
| Die #10: ice blue d16 | 160 | 15 | 27.2 | .97 | Yes |
| Die #11: white d20 | 200 | 19 | 13.8 | .21 |
The white d8 gave me a bit of a scare, but retesting seems to indicate that first result was, in fact, just bad luck. The d12 didn’t really need a retest, but I did one anyway; it passed fine. The d16 is unquestionably broken. Examining the raw data showed (among other things) that it rolled fourteen only seven times out of two hundred and eighty; examining the die itself showed (A) a not-unexpected minor sprue mark on the one side, and (B) a significant burr sticking out of the three side, directly opposite the fourteen. (The die may be reparable– but that’s a separate question.)