Saturday, December 26, 2020

The distribution of mixed polyhedral dice rolls

In a recent post, Kevin McCall wrote,

We might compare [a particular hypothetical distribution of IQs] to rolling all 5 Platonic solids: one 4 sided die, one 6 sided, one 8 sided, one 12 sided, and one 20 sided, which would have a completely different distribution from rolling five 6-sided dice.

And I commented,

Would rolling a mix of polyhedral dice really result in anything significantly different from a normal bell curve. I haven’t done the calculations, but my assumption is that it would not.

Then I almost immediately retracted this statement ("Never mind. I've checked it, and my assumption was totally wrong!") because I'd put the possible rolls of three dissimilar dice (a d4, a d6, and a d8) into a spreadsheet and it had given me a histogram that looked nothing like a normal distribution.

But now I have to retract that retraction and reaffirm my original assumption. The weird-looking histogram is an artifact. Rolling the three dice mentioned yields one of 16 possible values, from 3 to 18, but the spreadsheet software (Google Sheets) for some reason made a histogram with only 13 bars. Most of the bars represent a single value, but 3-4, 9-10, and 15-16 are grouped together, which is why those three bars are abnormally tall. Making a 16-bar histogram by hand, I find that rolling mixed dice does after all yield a normal bell curve.

The moral of the story: If it comes down to trusting either your own instincts or the basic competence of Google programmers, go with your own instincts every time!

But you already knew that.

1 comment:

No Longer Reading said...

Thanks. It looks like that wasn't a good metaphor after all. But I don't mind because it was interesting to learn this.

There is a statistical theorem called the Central Limit Theorem which says that if you have independent and identically distributed experiments, then over time they will converge to a normal distribution, but polyhedral dice aren't identically distributed, so I will have to think about why this happens.

Sync: Odin at the door, DD lemniscates, sideways eyeballs

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