I am also frequently trying to break people out of their misconceptions and insisting to them that 5.5 is average

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I am also frequently trying to break people out of their misconceptions and insisting to them that 5.5 is average
this has driven me up a wall forever in the context of, eg, the expected value of a six sided die being 3.5, a result you can never actually get. it is an obscenity. i simply hate that it is true
As someone who does DM tabletop games, I'm much more at home with this when I rephrased it as "the average on a d20 is 10.5 and that's evil but it means 1-10 and 11-20 are a 50/50 split and that's nice"
anything past yes, no, and NO!!! is splitting hairs
You only need a single factorial sign, Eevee. 0! already equals 1 just like 0!! and 0!!! do.