# Probability distribution for 3d8 (keep one)

#### The Crimson Binome

##### Hero
I was thinking about probability distributions for core resolution mechanics, and I don't like how the D&D 5E Advantage/Disadvantage system converts a linear distribution into a weighted one. I was thinking that a mechanic where you roll three dice, then keep one of them depending on circumstances, would be more palatable in this regard; but I can't intuit what the distribution would actually look like, off the top of my head. What's the chance of rolling a 2 or an 11, on 3d20 (keep low) or 3d20 (keep middle)?

Or more the point, for my own purposes, what's the probability distribution look like for 3d8 (keep low), (keep middle), and (keep high)? Does someone have a convenient calculator or article with that listed out?

#### Nagol

##### Unimportant
I was thinking about probability distributions for core resolution mechanics, and I don't like how the D&D 5E Advantage/Disadvantage system converts a linear distribution into a weighted one. I was thinking that a mechanic where you roll three dice, then keep one of them depending on circumstances, would be more palatable in this regard; but I can't intuit what the distribution would actually look like, off the top of my head. What's the chance of rolling a 2 or an 11, on 3d20 (keep low) or 3d20 (keep middle)?

Or more the point, for my own purposes, what's the probability distribution look like for 3d8 (keep low), (keep middle), and (keep high)? Does someone have a convenient calculator or article with that listed out?

anydice.com is what you are looking for.

*edit*

output [highest 1 of 3d8]
output [lowest 1 of 3d8]
output [middle 1 of 3d8]

#### Deset Gled

##### .
anydice.com is what you are looking for.

*edit*

output [highest 1 of 3d8]
output [lowest 1 of 3d8]
output [middle 1 of 3d8]

Very cool site.

Side note, I discovered while playing around that using [middle] with certain even/odd dice combos will skew higher than I original expected. I.E [middle 3 of 4d6] will return {6,6,6,1} as 18, not 13.

#### Blue

##### Ravenous Bugblatter Beast of Traal
Very cool site.

Side note, I discovered while playing around that using [middle] with certain even/odd dice combos will skew higher than I original expected. I.E [middle 3 of 4d6] will return {6,6,6,1} as 18, not 13.

Well, there is no clearly defined middle 3 of 4 dice. Bottom 3 (what you expected) and top 3 (what it gave you) are both equally valid.

Looking around, Anydice seems to figure out "middle" in descending order. So when it's unclear (where the number of dice on the top and bottom don't match) it will pick the higher option.

#### Deset Gled

##### .
Well, there is no clearly defined middle 3 of 4 dice. Bottom 3 (what you expected) and top 3 (what it gave you) are both equally valid.

Looking around, Anydice seems to figure out "middle" in descending order. So when it's unclear (where the number of dice on the top and bottom don't match) it will pick the higher option.

Anydice's method is completely valid, it just caught me off guard. I have been conditioned by D+D to use the "round down" rule. My original assumption was that the [middle] function would pick the lower option to match that rule, and it took me a minute to figure out the disconnect.

I don't see any simple way to change the way Anydice is doing to calculation.