The issue is *die roll variance* vs *stat range*. 3d6 has less variance than 1d20, but so does 1d10.

1d20 has standard deviation of 5.77

3d6 has standard deviation of 2.96

1d10 has standard deviation of 2.87

1d6 has standard deviation of 1.71

It's a question of the standard deviation of the roll versus the stat difference between master and weakling (i.e. Strength mod between Conan and a kobold, for example).

In terms of system design, you can get a less swingy system by any of (1) reducing the size of the die like using 1d10 instead of 1d20, (2) replacing the die with more smaller dice for a tighter bell curve, like 3d6 instead of 1d20; or (3) increasing the range of the stats. It's not like the only choices are 65% or 99%.

This means the system has less swing and is more stable.

A difference of +-1 in modifiers has a huge weight in comparing 1d20 to 3d6.

And I will not continue arguing about rolls because I have read all of you do it before and you just don't get it, some of you even argue that a single die has a bell curve.

I agree with you that 3d6 has a bell curve while 1d20 has a flat distribution. But the point is that 1d20 and 3d6 aren't the only choices. 1d10 also has less variance than 1d20. So let's look at real systems.

In D&D5, let's consider a Contest of Strength between a kobold (Strength mod -1) and Conan (Strength mod +5). So the kobold rolls 1d20 and subtracts 1, compared to Conan's 1d20 plus 5. There is a 73.75% chance that Conan will win, a 3.5% chance of a tie, and a 22.75% chance that the kobold will win. (Note that there was a previous claim that the kobold only had a 9% chance of winning, but I don't think that's right.)

Let's look at Interlock instead, which is the system for the Cyberpunk RPG (from R Talsorian). Here Strength goes from 2 to 10, with average 5. In a contest, each character rolls their stat plus 1d10. So the equivalent to a kobold would be Strength 4, while Conan is Strength 10. So here, there is a 90% chance that Conan will win, a 4% chance of a tie, and a 6% chance that the kobold will win.

That's a system with much less swing in it, despite not having a bell curve.

A bell curve 3d6 also has less swing than 1d20. Let's take GURPS. It's a little unclear what Conan's strength would be in GURPS -- there isn't a strict maximum and disagreement about what is a standard human max, and I don't have the GURPS Conan books.

This thread rated him as ST 17, though. If we take GURPS as Conan with 17 ST compared to ST 9, then a quick contest of Strength will result that Conan has an 94.6% chance to win, a 1.56% chance of tie, and the kobold has an 3.8% chance to win.

If you adjust for the draws, the probabilities for d20+mod and 3d6+1/2mod are pretty much the same. (At least within the range of values we're interested in.)

I haven't checked all of them, but those numbers seem reasonable. I mentioned that the standard deviation of 3d6 is about half that of 1d20. I don't know where you're getting those mods from, though. I think it's more concrete to use real RPG systems.