We are Viking Lumberjacks, not scientists. But, our Head of Ops, Zoe once was. We asked her to test our Wooden Dice using that strange, wonderful, unknowable thing they call science. So, onto her results.
To test the balance of our dice, we took a Chacate Preto D20 (similar weight to your typical plastic D20) and rolled it 1000 times. We also rolled a D20 made by one of the most popular plastic dice brands on the market 1000 times. You can see the roll results below in bar graph format. You may be tempted to draw some conclusions from this graph, but let's get into the nitty gritty.
First, some basic statistics: our Chacate Preto D20 had an average roll of 10.427 with a standard deviation of 5.6684, the plastic die had an average roll of 10.205 with a standard deviation of 5.5559. Already, these numbers appear like they won't have any statistically significant difference between them. But let's test that to be sure.
So, second, a quick, simple test: a two-tailed t-test gives us a t value of 0.37645. This is higher than your standard alpha cutoff, 0.05, so this tells us that there is no statistically significant difference between their averages, as we expected.
But let's go deeper... What about the rolls within each die? Does the wood or plastic die roll certain numbers more or less than any others? Performing an ANOVA, we get a p value of 0.3721. Again, this is higher than 0.05, so there is no significant difference across the roll results. There is variance, but no number appears more or less than another in a significant manner.
Finally, what about between one another? Is the roll distribution in the wooden die different from the plastic? Nope – and this is the most definitive result. With a p value greater than 0.9999 (from another facet of the ANOVA), there is no statistically significant difference between the two die's results.
From the ANOVA, we do also get coefficients of variation. The wooden die's was 17.99% and the plastic die's was 21.97%. As we already stated, there's no statistically significant difference between these two variations. It could be argued that the wooden die has less variation – the numbers are more evenly distributed in their chances – but it's insignificant.
DISCLAIMER: These are just two die. It is entirely possible that we could grab another plastic die and another wooden die and the results would be different (although it's pretty likely that the differences would still be insignificant). Unbalanced die can be produced, but to thoroughly test the likelihood of those existing, you would need to roll multiple, different die of the same manufacturer 1000 times (preferably on different surfaces, by different people). At the end of the day, though, our dice are virtually the same as your most popular plastic brands out there (balance-wise) and you shouldn't need to worry about your rolls!