average damage for traps [Archive] - Wizards Community

average damage for traps [Archive] - Wizards Community

Post/Author/DateTime Post
masterlinktm
04-24-08, 07:01 PM I was reading the info on traps in the DMG when I read that the average damage for 1d4 is 2.5 the average for 2d8 is 9 and for 3d6 its 10.5. I have been thinking long and hard and can't think of the formula that would give these numbers.

Would someone mind telling me how these averages are achived?

In addition could someone tell me how to "hide" text in the spoiler option, I can't seem to find info on it. :(
ciaran
04-24-08, 07:18 PM The formula for the average result is:

(The highest number possible to roll with the dice + the number of dice) divided by two.

3d6:
3 X 6 = 18
18 + 3 = 21
21 / 2 = 10.5

1d4
1 X 4 = 4
4 + 1 = 5
5 / 2 = 2.5

2d4+2d6 (falchion and sneak attack) :)
(2 X 4) + (2 X 6) = 8 + 12 = 20
20 + 4 = 24
24 / 2 = 12
masterlinktm
04-24-08, 08:11 PM Thank you so much, I would have never thought of that. :embarrass
Edymnion
04-24-08, 08:19 PM Um, don't think I've ever quite seen it done that way.
As for how to find the average, you just need to find the average, basic elementary school math.

How do you find an average? Add up all the possible outcomes, and divide by the total number of outcomes.

So, 1d6 is (1+2+3+4+5+6) / 6 = 3.5

And, as it turns out, all of the dice will always have an average of 1/2 their max value, plus .5. So, a d20's average roll is 1/2 its max, 10, plus .5, for 10.5.

Then you just multiply the average times the number of dice. So, the average of 3d6 is 3*3.5=10.5. Which, mathematically, is the same average as 1d20. Which is why many times in other systems you will see a roll of 3d6 instead of 1d20, since the mathematical average is the same, but having multiple dice means you get a bell curve with less randomness.
ciaran
04-24-08, 08:34 PM I already know the average roll per die in my head, but thats a simple formula I wrote out. Maybe yours is faster for you. The way that my brain works, the one I have shown has fewer steps. I just wrote out the longhand version to demonstrate.

The point is, masterlinktm, that they both work. If you understand the principle, you can do it whichever way is best for you.

I would like to note on your comment regarding bell curves and randomness.

Some skill checks I see the rediculousness of the d20. Even someone with a +0 in jump will make a 20 foot leap sooner or later. Crazy, huh? But what the heck. Its a simple method and its fits into a high risk adventure game.
Edymnion
04-24-08, 09:51 PM The point is, masterlinktm, that they both work. If you understand the principle, you can do it whichever way is best for you.Which is why I typed it out that way, as I believe that doing it the long way like that shows the idea of the math behind it in an easy to follow manner.

Its rather like in school.
In high school, they teach you these god awful long ways to figure a problem out so that you'll understand why it works, then in college they show you how to solve the same equation in two lines.

Gotta know how to get there before you start taking shortcuts. We can get it even shorter than what you have as well. For any series of linear numbers starting at 1 and going to X, the average will always be X/2 + .5.

1d37? 1+2+3+4...+37 = 703 / 37 = 19. Which is the same as 37/2 = 18.5 + .5 = 19.

Sure, it makes it quick and easy, but if you want to know WHY it works, you gotta do it the long way.

Post/Author/DateTime	Post
masterlinktm 04-24-08, 07:01 PM	I was reading the info on traps in the DMG when I read that the average damage for 1d4 is 2.5 the average for 2d8 is 9 and for 3d6 its 10.5. I have been thinking long and hard and can't think of the formula that would give these numbers. Would someone mind telling me how these averages are achived? In addition could someone tell me how to "hide" text in the spoiler option, I can't seem to find info on it. :(
ciaran 04-24-08, 07:18 PM	The formula for the average result is: (The highest number possible to roll with the dice + the number of dice) divided by two. 3d6: 3 X 6 = 18 18 + 3 = 21 21 / 2 = 10.5 1d4 1 X 4 = 4 4 + 1 = 5 5 / 2 = 2.5 2d4+2d6 (falchion and sneak attack) :) (2 X 4) + (2 X 6) = 8 + 12 = 20 20 + 4 = 24 24 / 2 = 12
masterlinktm 04-24-08, 08:11 PM	Thank you so much, I would have never thought of that. :embarrass
Edymnion 04-24-08, 08:19 PM	Um, don't think I've ever quite seen it done that way. As for how to find the average, you just need to find the average, basic elementary school math. How do you find an average? Add up all the possible outcomes, and divide by the total number of outcomes. So, 1d6 is (1+2+3+4+5+6) / 6 = 3.5 And, as it turns out, all of the dice will always have an average of 1/2 their max value, plus .5. So, a d20's average roll is 1/2 its max, 10, plus .5, for 10.5. Then you just multiply the average times the number of dice. So, the average of 3d6 is 3*3.5=10.5. Which, mathematically, is the same average as 1d20. Which is why many times in other systems you will see a roll of 3d6 instead of 1d20, since the mathematical average is the same, but having multiple dice means you get a bell curve with less randomness.
ciaran 04-24-08, 08:34 PM	I already know the average roll per die in my head, but thats a simple formula I wrote out. Maybe yours is faster for you. The way that my brain works, the one I have shown has fewer steps. I just wrote out the longhand version to demonstrate. The point is, masterlinktm, that they both work. If you understand the principle, you can do it whichever way is best for you. I would like to note on your comment regarding bell curves and randomness. Some skill checks I see the rediculousness of the d20. Even someone with a +0 in jump will make a 20 foot leap sooner or later. Crazy, huh? But what the heck. Its a simple method and its fits into a high risk adventure game.
Edymnion 04-24-08, 09:51 PM	The point is, masterlinktm, that they both work. If you understand the principle, you can do it whichever way is best for you.Which is why I typed it out that way, as I believe that doing it the long way like that shows the idea of the math behind it in an easy to follow manner. Its rather like in school. In high school, they teach you these god awful long ways to figure a problem out so that you'll understand why it works, then in college they show you how to solve the same equation in two lines. Gotta know how to get there before you start taking shortcuts. We can get it even shorter than what you have as well. For any series of linear numbers starting at 1 and going to X, the average will always be X/2 + .5. 1d37? 1+2+3+4...+37 = 703 / 37 = 19. Which is the same as 37/2 = 18.5 + .5 = 19. Sure, it makes it quick and easy, but if you want to know WHY it works, you gotta do it the long way.