Last night I went to my weekly Dungeons & Dragons meetup. I had a particular 20-sided dice that I considered “lucky”, as it seemed to roll high numbers and natural 20’s fairly often. I was curious as to whether or not the dice was actually fair, so using my statistical knowledge, I decided to test it for myself.

The dice in question

I rolled the dice in question countless times over the course of last night’s adventure, tracking the results as I played, and plotted the results below.

Looks to be fairly random, but looks can be deceiving. As such, I wanted to look at something a little more measurable in determining how fair this dice is.

Using a Chi-squared test, I compared my hundreds of dice rolls to the null hypothesis: a uniform discrete distribution from 1 to 20. I ended up with a Chi-squared statistic of 0.03, and a p-value of 1.

Unsurprisingly, this means that my dice is pretty much fair, and my feeling of luck is just that: a feeling.

Nonetheless, I find it fun when I’m in a game or situation where statistical thinking can come in handy.