Interesting mathematical dice rolling I came across.

[Muad'dib Pendragon]

Check out this AnyDice comparison. While the means may be comparable, that's about it.

 

[Evenglare]

Check out this AnyDice comparison. While the means may be comparable, that's about it.

Again I disagree. A single d20 has a flat 5% chance of hitting any number while the middle of 3d20 creates a parabolic curve. This resembles a bell curve much more than a flat 5% chance. I dont understand how you can say only the means are the same when the distributions are completely different.

 

[prosfilaes]

Check out this AnyDice comparison. While the means may be comparable, that's about it.

If they were identical, there would be no reason to use the middle of 3d20 instead of 3d6. The fact that several dice rolling system share this mean of 10.5 and the same or roughly the same range means that certain things can be tweaked easily. Certainly replacing 1d20 with 3d6 is not completely unheard-of among D&D players; this shows how to do that without changing the range. The fact it's a flatter curve may or may not be a desired effect.

 

[Muad'dib Pendragon]

Again I disagree. A single d20 has a flat 5% chance of hitting any number while the middle of 3d20 creates a parabolic curve. This resembles a bell curve much more than a flat 5% chance. I dont understand how you can say only the means are the same when the distributions are completely different.

That's part of my point. In terms of 3d6 vs your suggested 3d20 take the middle method, the distributions are different. In addition, the curve generated by your suggested method is much flatter than 3d6. Your suggested method also varies much more...

Take a look at Troll.

For 3d6, the syntax is "sum 3d6"
For 3d20 take the middle, the syntax is "largest 1 least 2 3d20"

3d6: spread (2.9580), deviation (2.4167)
3d20 take middle: spread (4.4814), deviation (3.7625)

That said, if those differences are acceptable to you and give your group a better playing experience,, then by all means go for it.

 

[Evenglare]

Hold on now. You said that only the means were comparable. I simply stated otherwise, your initial post indicated that other than the mean they are in no way comparible.
However they are much more similar than a flat 5% chance roll on a d20. This is the desired effect of the middle roll system, you WILL get around a 10 much more than rolling a single d20. The fact that your rolls are skewed towards a 10.5 similar to the 3d6 roll is the desired effect. Of course the deviation is difference because you are ranging in numbers between 1-20 and getting the score a different method other than adding. I agree it isnt -exactly- like a bell curve , but much more than a flat percentage .