Hey sorry Zarlor I was working on my reply before your post showed up.
So here is how I see it. What his saying is that 3d6 will have the same average as 1d18. Which is technically true. In both cases your average is going to be about 9 or 10 or whatever. But what matters most for players from my experience is not being flogged with the flat curve. They want to avoid the negative outiliers. So with 3d6, they want to avoid rolling a 3. And 3d6 would be better for this than say, determining a number between 3-18 via percentile dice or something.
I’ll post some hard numbers on this later when I have time to do a bit more coding, (and I’m sure you know this already but bear with me as I restate the obvious), but basically a bell curve result such as you get from 3d6 means that most of the die roll results you are going to get are going to be in the middle range, 8-13. If you add up the number of results you get from rolling 3d6 10,000 times, something like 2/3 will be in that middle range, while the higher and lower results will be about 1/3. The chart above matches that ratio I think.
This gives you the experience of having far fewer outlier results. The curve skews toward the middle.
With the ‘advantage’ system as you call it (though I am loath to do so!) the curve skews more and more toward the top, and increasingly diminishes the chances of a ‘critical failure’ That is what matters most in my experience especially for your more tightly wound or angry players (like one or two people in your group): NOT getting a critical fail. The baseline with a 20 sided die is about 20% chance (around 4% in my test but that is because I used a small sample, it evens out the more iterations you do).
Rolling two dice reduces that critical fail chance already to about 2.5%, which helps (that is half of the normal risk), but 3 dice reduces it to 1%, a big improvement (a fifth of the normal risk). At four dice the chances are one quarter of one percent. This allows those players who can’t stand to get a Crit Fail to really avoid them if they are willing to spend the dice (or manage to min-max the situation to arrange for enough extras). The average die roll also goes up, but kind of gradually, as does the chance of a crit success, but still not to the point that it becomes routine (it becomes around a 1 in 8 chance based on my last test, though I think it ends up being about 1 in 6 or 7).
So this is what solves my problem. Skewing the numbers higher, as an option which players ‘pay’ for in one way or another. Some people like to gamble, and don’t mind the flat curve. Others can never get used to it, they feel like something is wrong and I’d say there is. Your chance of dropping a sword really isn’t one in twenty if you are paying attention to what you are doing. Especially if you are experienced. That’s why it feels off.