Dice testing [Discussion]
Hello,
I bought a relatively expensive D20 because it's engraved in crystal. I rolled it 907 times and recorded the results.
For numbers 1 to 20: (44, 39, 56, 36, 50, 54, 36, 41, 42, 34, 46, 57, 37, 49, 61, 57, 35, 43, 53, 37).
Applying a chi-square test, the statistic gives me 31.46. This means I reject the hypothesis that the die is balanced at the 5% significance level (the critical value is 30.14).
Not happy with this result, I start to think: if the die is unbalanced, we should observe an imbalance in opposite face pairs. In other words, we theorize that we uniformly and randomly draw a random variable from ten Bernoulli variables with probabilities pᵢ. If the die is unbalanced, then one of the pᵢ is large.
It seems that under this analysis, the die appears a bit more fair.
Now more generally, we can also assume the die is unbalanced in a physical sense: that one side of the die is heavier than the other. This justifies the following reasoning:
Let's create a mapping that sends each face to itself and adds the adjacent rolls. This should highlight more subtle and discrete imbalances in the die.
What do you think of this type of reasoning?