Average Damaged By Different Dice?

[Pielorinho]

No.

1 + (12 - 1) / 2 = x
1 + 11 / 2 = x
1 + 5.5 = x
6.5 = x

I see that you get the right result -- I just don't see why.

With (1+12)/2, I understand: in any system of integers 1 to n, in which a number is chosen randomly, the mean chosen will be (1+n)/2. That's because 1+n, the lowest and highest values added and averaged, equals 2+(n-1), the next lowest and next highest values averaged, and so on until you reach the middle of the series.

But how does 1 + (n-1)/2 work?

It's been nearly 10 years since my last math class, so go easy on me and use words!

Daniel

 

[Pielorinho]

But how does 1 + (n-1)/2 work?

I just realized the two expressions are equivalent, I think:
1+(n-1)/2=
1 +n/2 - 1/2=
2/2 + n/2 - 1/2=
1/2 + n/2=
(1 + n)/2

which is what i suggested using as an equation.

Okay, now I understand why your equation returns the right result. Why on earth use it, though, when theres an equivalent, much simpler equation?

Daniel

 

[CRGreathouse]

Personally (for adb), I use:

(a / 2) * (b + 1)

Still, all of these systems are the same. If you want some complicated computations, though, i'll post the formula for 1dx-y when it has a minimum of 1.

 

[ConcreteBuddha]

"Why on earth use it, though, when theres an equivalent, much simpler equation?"

--Daniel


Why use English when there are so many simpler languages out there, like Esperanto?

Seriously, though, my mind doesn't think in learned equations, it thinks in logic. In logic, you simplify to the smallest possible parts.

Example: 1d6 + 7

In my mind this looks like:

8 + median {a set of numbers from 0 to 5}
8 + median {0, 1, 2, 3, 4, 5}
8 + {2.5}
10.5
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.
.
Oh, I also tend to see "big rollers" use 1dX's while "conservatives" use 2dX's.

Big rollers like the big hits of rolling big damage while forgetting the "1's". Conservatives, on the other hand, like the comfort that average damage brings.

Same goes for threat ranges: x3 and 19-20/x2

Of course, I could just be biased...

 

[Mustrum_Ridcully]

It believe sometimes it is easier to just say: Add lowest "rollable" number two hightest rollable number, divide result by 2...

The results are all the same ...

A Greatsword is slightly better than a Greataxe - but I wonder if .5 points of damage will every make the difference...

Mustrum Ridcully

 

[ConcreteBuddha]

I actually think a Scythe is better than a Greatsword or a Greataxe. (Not consistent, but more fun...)

Keen + Improved Critical

Yummy!
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.
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Disclaimer: I didn't mean to get into a "My daddy is bigger than your daddy" argument. Yes, a lot of things are immune to crits. Yes, it does less average damage. But it sure is fun!

 

[Pielorinho]

Why use English when there are so many simpler languages out there, like Esperanto?

C'mon, that's apples and oranges. You use English because:
1) It has a much large pool of speakers, so you'll communicate with more folks;
2) It has many more words, so you can communicate a greater range and subtlety of concepts; and
3) You speak English more fluently than you speak Esperanto, so you're likely to be more accurate in what you're trying to say.

WIth an equation, what's the benefit of a complicated one over an equivalent, simple one?

Seriously, though, my mind doesn't think in learned equations, it thinks in logic. In logic, you simplify to the smallest possible parts.

Example: 1d6 + 7

In my mind this looks like:

8 + median {a set of numbers from 0 to 5}
8 + median {0, 1, 2, 3, 4, 5}
8 + {2.5}
10.5
.

Interesting. Again, in my mind, the simple way to handle this is:
1d6+7
(1+6)/2 + 7
7/2 + 7
3.5 + 7
10.5

Why bring medians into it? And how does this relate to the first equation?

I'm not trying to be snarky; I'm really confused on how you got to that first equation, something like 1 + (n-1)/2

Thanks!
Daniel
.
Oh, I also tend to see "big rollers" use 1dX's while "conservatives" use 2dX's.

Big rollers like the big hits of rolling big damage while forgetting the "1's". Conservatives, on the other hand, like the comfort that average damage brings.

Same goes for threat ranges: x3 and 19-20/x2

Of course, I could just be biased... [/B][/QUOTE]

 

[Plane Sailing]

Okay, quick question I hear people talkign about average damage rol swhen doign character calculations and sayign a d8 is an average roll of 4.5 and what not. So I was wondering the difference between a 2d6 weapon and a d12 weapon for average rolls.
Thank you.

Since nobody else has explicitly mentioned this aspect, I might as well bring it up.

When rolling 2d6 your chance of getting minimum damage (or maximum damage) is 1 in 36. i.e. two 1's or two 6's respectively. With 1d12 on the other hand your chance of getting minimum or maximum damage is 1 in 12.

Thus the single die as a greater chance of getting to one of the extremes of damage.

In fact, with a single d12 there is an equal chance of any of the numbers from 1 to 12 coming up (1 in 12).

With 2d6 you get a "distribution curve". There is one way of rolling 12 (6 & 6), two ways of rolling 11 (6 & 5 or 5 & 6) through to six ways of rolling 7 (6&1, 5&2, 3&4, 1&6, 2&5, 4&3). The 2d6 weapon has a significantly higher chance of getting its "average" damage on any particular roll than of getting its maximum (or minimum) damage.

The more dice which are rolled, the harder it is to get the maximum. The chance of getting 60 damage from a 10d6 fireball is astonishingly tiny (unless you use Maximise )

--- People still talk about a d8 having an average of 4.5 (for the calculated reasons given above) because over a period of time the total number of d8's that you roll will tend towards a middle number. If you rolled 10d8 you would be much more likely to get a number near 45 than near 80 (for the reasons I explained in the 2d6 example above). Talking about average damage in this way is shorthand for saying "over the length of a campaign when you are rolling a d8 all the time your average roll would be about 4.5 if you added them all up and averaged them".

Incidentally this is a practical reason why on critical hits you roll and add the damage for the multiplier rather than just multiply your initial roll. Otherwise an Orc that critically hits you would have a 1 in 12 chance of doing 42 points damage! Since he has to roll each d12 separately he actually has only a 1 in 1728 chance of doing that (three 12's in a row).

Cheers