MM3 on a business card, improved

[Yakk]

I'd guess that the variance on 2d12+37 is tiny compared to 10d6+15.

VAR(d12) = 143/12
VAR(2d12) = 143/6 = 28.83...
VAR(d6) = 35/12
VAR(10d6) = 175/6 = 29.16...

Hmm, not much different. So I'm wrong there. (smaller dice don't add up variance that fast)

But if you replace 10d6 with 1d6*10, we get a lot of variance
VAR(1d6*10) = 100*VAR(1d6) = 1750/6 = 291.66...

SD(2d12) =~ 5.37...
SD(1d6*10) =~ 17.08...

That is more than 3 times the standard deviation. Which means 2d12+37 is *actually* 39 to 61 damage in 95% of cases, an effective range of 22 points or 44% of the average damage. (2 standard deviation radius is a 95%+ interval)

1d6*10 + 15 is 25 to 75, an effective range of 50 points or 100% of the average damage.

In one case, rolling for damage is almost pointless. In the other, rolling for damage generates lots of information.

At low levels, rolling for damage has lots of information. 1d8+3 has an average of 7.5 and a range of 93% of the average damage. 1d4+5 has a range of 40% of the average damage. In one case, that damage roll really matters -- in the other, replace it with the average of the roll and nobody would really notice.