Understanding Bell Curves at Age 11 - Math from D&D

I'd planned on writing some more about Call of Cthulhu this evening but a combination of family and homework have occupied my evening and necessitate a bit of a brief post tonight.

And it's homework that got me thinking about statistics and RPGs. Currently I'm taking a Statistics class as part of my Strategic Analytics Master's program at Brandeis University. I'm diving deep into data science. My current statistics course is less focused with performing various statistical operations (though that is part of it) but rather with how best to present them. 

The diagram I show above is a simple comparison of a bell curve and a linear distribution from the 1st edition of the AD&D Dungeon Masters Guide. I seem to recall picking it up in 5th grade or maybe the summer before 6th grade. And the curve was a bit of a mystery to me. It seems obvious now, but a probability curve was some heavy math for an 11-year old. After some heavy duty analysis (for an 11-year old) as well as experimenting with dice and then jotting down lists of combinations (I think I did indeed write out 216 entries) I finally got it. I thought it was the coolest thing how rolling multiple dice forced the likely roll towards the middle whereas rolling a single die would have all outcomes equally likely. I'd been playing for 2-3 years so I understood that intuitively but to finally get the math behind it was awesome.

Playing D&D helped me a lot as the math got more complicated in middle school. Needless to say, when the bell curve came up I was more than ready. It also helped me level up my geekiness. To this day I actually enjoy working through problems with probability, determining distributions, etc. Heck, when I help my kids with algebra homework I enjoy setting up the equations. It's only fair to point out the geekiness went full circle as in fall of 2015 I quoted The Dracula Dossier campaign in a data science class discussion...

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