2D6 and Dice Pools

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Following Lich Van Winkle's post about dee-five-six, I wanted to post about a realization I had that I'm sure others know but thought would be nice to record: 2D6+X where we take the sum PbtA-style approximates (X+1)D6 where we take the highest roll. Below is a table of result brackets:

Result Sum of 2D6+X Highest of (X+1)D6
< …6 1–3
= 7–9 4–5
> 10… 6

Below is a table of results with increasing X ∊ [0, 3] for 2D6+X:

2D6+X < = >
2D6 41.7% 41.7% 16.7%
2D6+1 27.8% 44.4% 27.8%
2D6+2 16.7% 41.7% 41.7%
2D6+3 8.33% 33.3% 58.3%

Below is a table of results with increasing X ∊ [0, 3] for (X+1)D6:

(X+1)D6 < = >
1D6 50.0% 33.3% 16.7%
2D6 25.0% 44.4% 30.6%
3D6 12.5% 45.4% 42.1%
4D6 6.26% 41.9% 51.8%

I think this is where we get the BitD and Trophy variations on the original PbtA roll, and I prefer that version because the results feel less obscure? Or just on the basis of pure vibes? I constantly go back and forth between using D20 or D6 pools in my home game, except that D20 feels quintessentially (lowercase) "d&d".

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