Beyond the necessary stepladder effect created by having a finite set of possible results (which I mentioned above and is always going to be a problem with dice), how is 4d6 not a Gaussian function? I suppose it isn't centered at 0. So fair enough, it's an offset Gaussian function.
I'm aware of the math. I did it, you may recall. There are a lot more than 27 people on these forums, and I guarantee the average number of characters per person here is somewhere north of 1. So if everyone here was rolling for hit points, we'd see someone roll that badly more than once. Now, obviously, the chance of it happening to a specific character is pretty small, but not nearly small enough for how badly it cripples the character. At least, so a lot of people would say. It comes down to risk-aversion. The probability may be pretty low, but the consequences are relatively severe, and the probability isn't nearly unlikely enough to wash that out for a lot of people.
@Jarrakul I don't understand why you keep pressing the matter, but please, can you explain how it is a Gaussian? Or an offset Gaussian. Because it doesn't fit the definition I've learned.
I'm not sure I can prove it, due to the errors created by the stepladder effect I referred to earlier, so I suppose I have to admit that I might be wrong about this. But a function of the possible sums of die-like probability distributions have all the necessary traits of a Gaussian distribution that I was ever taught (mean = median = mode, unimodal, symmetrical, steady but non-linear drop-off to 0 with a positive second derivative left of the mode and a negative second derivative right of the mode) within the limits of the resolution of the dice. As more dice are added, the resolution improves and the distribution narrows. But again, I don't actually know the math to prove it, so I suppose I might be wrong. Feel free to explain how, if I am, because I'd love to learn that.
@Jarrakul I agree, when the number of dice -> inf, we get a Gaussian. When the number of dice is finite, we are merely close to a Gaussian. Which was what I was trying to say.
I killed Ramazith at the top of his tower in one strike. I am a Mage PC generalist. My party is Imoen, Khalid and Jaheira, Ajantis and Yeslick. The rest of the party, with ranged weapons, killed Ramazith in a single round, before my Mage could even cast Magic Missile! It was like, "Hi!" BOOM. Dead. Then it was all over but the looting. I know what you mean about combats not lasting long.
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I'm aware of the math. I did it, you may recall. There are a lot more than 27 people on these forums, and I guarantee the average number of characters per person here is somewhere north of 1. So if everyone here was rolling for hit points, we'd see someone roll that badly more than once. Now, obviously, the chance of it happening to a specific character is pretty small, but not nearly small enough for how badly it cripples the character. At least, so a lot of people would say. It comes down to risk-aversion. The probability may be pretty low, but the consequences are relatively severe, and the probability isn't nearly unlikely enough to wash that out for a lot of people.