D&D 5E Moving the Average

[Yunru]

So does anyone know why this happens?

I've been playing around in Anydice seeing where the average lies for various Xd6k3 combinations:
http://anydice.com/program/cafd

As you can see, going from 3d6 to highest or lowest of 4d6 moves the average by 2. Yet to move it further, the number of dice needs to increase by 2.

N.B. I'm also very bad at statistics, so plain english would be appreciated (algebra and whatnot I can get, statistical functions? Nooope).

 

[TwoSix]

Because as you add more dice, you're getting asymptotically closer to a value of 18. If the difference keep increasing linearly, you'd have an average of 18 at 7d6k3, which obviously doesn't make any sense. For comparision, the difference between, say, 19d6k3 and 20d6k3 is really small; you mostly roll 18s, and once in a great while might get a 17 or 16.

 

[Yunru]

Because as you add more dice, you're getting asymptotically closer to a value of 18. If the difference keep increasing linearly, you'd have an average of 18 at 7d6k3, which obviously doesn't make any sense. For comparision, the difference between, say, 19d6k3 and 20d6k3 is really small; you mostly roll 18s, and once in a great while might get a 17 or 16.

I guess the same is true for going the opposite way, because it's the same thing, just taking the lowest numbers,

 

[TwoSix]

I guess the same is true for going the opposite way, because it's the same thing, just taking the lowest numbers,

Yes, it's absolutely the same for keep lowest. It just approaches 3 instead of 18.