Quote from: Doom;426854Hey, that's a clever way to get around the whole "add a 0.5" silliness.

Next to a discussion about police riding unicorns, this is probably the 2nd best fun-but-pointless gaming board discussion I've seen for 2010.

Think we could make a list? Rule is it has to get to the third page.

Quote from: Bloody Stupid Johnson;426836Or can't you???

Going the other way 1d6+3, rerolling any 1s gives an average value of exactly 7.
(all values possible on the d6: 2,3,4,5,6 = 20, /5 possible results = average value of 4)

If you do that then the only difference becomes the distribution, no change in average damage between the d6+3 and the 2d6 at all.

woooo smart!

Quote from: Cranewings;426947woooo smart!

Go me!! Though maybe its kinda cheating since it really turns the d6 into a d5.

Quote from: ggroy;426864Wonder who (in rpg gaming) pays attention to kurtosis and skewness.

I had to google those, but best use of weird distributions I can think of goes to Gary?
Whoever set up random encounter tables for D&D to use d8+d12 knew what they were doing: all the numbers from (IIRC) about 9 to 12 are equally likely, so you get a "truncated bell curve", a distribution that when you graph it looks like a hill with the top cut off. Good use of this since it makes all the "common" encounters equally likely.

But other than that, I don't know why someone would be deliberately trying to make a skewed distribution?? A mechanic like Tunnels and Trolls' "roll 2d6, doubles roll up" would I think give you a weird probability curve when drawn out (either a fat tail, or maybe a series a progressively smaller bulges like the spine of an iguana ?) but that's probably unintentional on the part of the designers.

To answer the original question as best I can:

Those who pointed out the importance of armor absorption are absolutely right. That needs to be nailed down in order to proceed.

Secondly, the typical amount of hit points of the target are also important. Reason: the more hit points the target has, the more individual hits it's going to take to kill them. (Duh.) That means, at some point, you're summing enough hits that the standard deviations of the sums start to look similar. And that means that the mean & standard deviation in # of hits to kill the opponent will be about the same.

I mean, if the opponent has 20 hp, you'd figure it'll take "about 3" hits to kill them. That means in one case you're rolling 6d6 (mean 21.5, sd 4.58), and in the other you're rolling 3d6+3X (mean 10.5+3X, sd 3.24). In relation to the range of results, these standard deviations are about 15% and 20%/

If the opponent has 40 hp, you're looking at "about 6" hits to kill. The standard deviations are then 6.48 and 4.58, respectively. While these are larger numbers, they're smaller in relation to the range of results--about 11% and 15%, respectively.

If you turn this around and look at this in terms of the mean and standard deviation in "# of hits to kill", you'll see that two methods basically converge as the target damage goes up.

Third, there's the question of how long you have to take out the opponent. If you're facing someone who has a high chance of killing you in one or two rounds, then you'd want a damage roll that's got at least a chance of doing the same to him, even if it offers a lower mean. So here, you'd probably go for the 2d6 because of the higher standard deviation. You don't care that it might dink him for 2-3 points; what you care about is that it can wallop him for 11 or 12 points.

Quote from: Doom;426716It's stunning how many people think all there is to a distribution is the mean.

Sorry. I mis-spoke.

I was looking at the distribution range and not the exact values. Naturally a linear addition of 3.5 cannot give a total distribution the same as the bell shape of 2d6 (even if you could add a half point). Basic mathematics.

With 2d6 you get 36 combinations that form a bell shape. With 1d6+something you get a simple linear shape. My point was that the "typical" roll for each would be similar.

2d6 is actually a wedge curve. Each number is 1/36th more likely than the number before it until you hit the mid point, and then each number is 1/36th less likely until you get to the final number.

That being said, which is better depends on what I am being asked to do. If I am expecting to fight Orc warriors and Goblins who only have 4 hit points, I'd rather do d6+4 or even a d6+3 damage. If my opponents have 8 hit points, then I would rather do a d6+4 (6/12 kill) than 2d6 (5/12 kill), and rather do 2d6 than d6+3 (4/12 kill). If my enemies are gnolls who have 11 hit points, I would rather do 2d6 than a d6+3 or even a d6+4. The d6+3 does half a point less on average than 2d6 and the d6+4 does half a point more. Furthermore, the 2d6 has a higher chance of doing an average amount of damage, but it also has a higher chance of doing extreme edge damage. If I am happier to roll an extreme high edge case than I am sad to roll an extreme low edge case (such as when the enemy has a large number of hit points), then I want the extra dice. If I am sadder to roll very low than I am happy to roll very high (such as when the enemy has very few hit points), then I want the extra fixed bonus.

By the way, if we go to 3d6, we could have the same average on 3d6 or 1d6+7. And then if the enemy had 11 hit points we seriously wouldn't care either way - it's a 50% chance to drop the enemy regardless. But if the enemy had 10 hit points we'd rather roll d6+7 (67% drop instead of 63%), and if the enemy had 12 hit points we'd rather roll 3d6 (38% drop instead of 33%).

-Frank

Frank, I think you've just convinced me that weapons should never do more than one die of damage.