Testing D20

As promised, I finally got some Game Science dice today and immediately set out testing them to see if they're fair, then compared the result against the black D20 that came with my old red box Basic Set and I've had since god-knows-when.  Ready for the results?



Figure 1:  Histograming results initially suggests that the black D20 likes to produce a result of "18."



The inital results are shown in figure 1.  After rolling each die 100 times, I then applied the chi-squared test to estimate the likelyhood of such a result, given the differences between the observed and expected distributions. 

The net result!  The observed distribution of my Game Science D20 is about 80% likely given the expected distribution of a fair die, while the observed distribution of my black D20 is about 5% likely (see figure 2). 

Figure 2:  Chi-squared test probability of the observed distribution given the expected distribution of a fair D20.

If the observed distribution is 80% likely given the expected distribution of a fair die, then I'd bet that the die is fair (or at least as close to fair as is easily observable).  Therefore Game Science die passes the test of fairness fairly well.  The Black D20, however, is a lot more problematic.  I will be testing more of my dice to see if I observe similar results.  In the mean time, however, I think the black D20 will be the designated "hit the bad guys" die.