Preview: Brutal Ability

[Enaloindir]

3d4 doesn't give the same probability spread as a single die-roll. Instead of having a flat curve where you have highs and lows, you have a bell curve where you're going to roll the same 3 damage numbers a full half of the time.

Man, this whole discussion seems sooooo retro. Back in "ye olde days", they listed the range of possible results instead of the dice you needed to roll: 2-9 would be 1d8+1, but 3-12 could be generated using 1d10+2 or 3d4...

- Enaloindir

 

[Ginnel]

Wrote some interesting cool maths

Please can someone send this thread into xkcd it would so fit.

http://xkcd.com/393/
http://xkcd.com/244/http://xkcd.com/393/

Just picture it a barbarian stick man with an axe a label with D10 +2 on the axe and another in the other hand with D12 reroll 1's and 2's then another stickman explaining how they're both the same with a chalk board

would be pure win infact I might give it a go

 

[Stalker0]

It may over many rolls provide a +1 average damage.

But DnD combat does not work like that in 4E.

DnD combat would look more like a punctuated graph with damage spikes depending on how many dice are rolled. You are viewing it as a standard bell curve or flat curve that looks averages die rolled many times. That is not how DnD combat works.

In this particular case, this in incorrect.

In the vast majority of discussions that have happened on these boards, people talk about the average damage. But they neglect to speak about the variation. An easy example is 4d6 vs 2d12+1. The average damage is the same, but the variation is different. For this example, your concern would be correct. On any given roll, the chance of getting certain damage numbers are higher than others.


With the brutal mechanic this DOES NOT happen. In this case, both the AVERAGE and the VARIANCE are EXACTLY THE SAME. 1d12 brutal 2 and 1d10+2 are mathematically identical. The only difference is player perception, how they see that math carried out.

Now a difference comes about with 2[w] damage...but ONLY if we stick to how 4e has looked at damage so far. If 2[w] means 2[1d10+2] = 2d10+4, then 1d10+2 and 1d12 brutal 2 would still be identical. However, 4e uses this system, where 2[w]= 2[1d10]+2 = 2d10+2. So with this, 1d10+2 and 1d12 brutal 2 do have a difference.

 

[blargney the second]

I just realized that brutal weapons get even better on crits when they are magical - you get to reroll the +1d6s from the enhancement bonus as well. Same goes for the high crit property.

(I don't often engage in endgame speculation, but this feels like pipe dream time: epic minotaur with a large +6 vorpal executioner's axe and Axe Mastery would do 30+12d6 brutal 2 exploding 6 on a 19-20 crit. *boggle*)

 

[eamon]

I just realized that brutal weapons get even better on crits when they are magical - you get to reroll the +1d6s from the enhancement bonus as well. Same goes for the high crit property.

(I don't often engage in endgame speculation, but this feels like pipe dream time: epic minotaur with a large +6 vorpal executioner's axe and Axe Mastery would do 30+12d6 brutal 2 exploding 6 on a 19-20 crit. *boggle*)

Do magical critical bonus die count as weapon damage dice? I suppose they do, brr....

 

[blargney the second]

Actually, I could see arguments both for and against rerolling magic weapon d6s, but the high crit ones are definitely brutaled.

 

[FireLance]

Okay, let's try it again. Apparently, my earlier example using a d10 brutal 2 weapon wasn't clear enough. Consider all the possible outcomes of 1,728 (12^3) damage rolls with a d12 brutal 2 weapon. After the first roll:

144 (1/12) of them will be 12.
144 (1/12) of them will be 11.
144 (1/12) of them will be 10.
144 (1/12) of them will be 9.
144 (1/12) of them will be 8.
144 (1/12) of them will be 7.
144 (1/12) of them will be 6.
144 (1/12) of them will be 5.
144 (1/12) of them will be 4.
144 (1/12) of them will be 3.
288 (1/6) of them will be re-rolled and still undetermined.​

Now, consider all the possible outcomes of the 288 re-rolls:

24 (1/12) of them will be 12.
24 (1/12) of them will be 11.
24 (1/12) of them will be 10.
24 (1/12) of them will be 9.
24 (1/12) of them will be 8.
24 (1/12) of them will be 7.
24 (1/12) of them will be 6.
24 (1/12) of them will be 5.
24 (1/12) of them will be 4.
24 (1/12) of them will be 3.
48 (1/6) of them will be re-rolled and still undetermined.​

So, by the end of the first re-roll, all the possible outcomes are:

168 (14/144 or 9.72%) of them will be 12.
168 (14/144 or 9.72%) of them will be 11.
168 (14/144 or 9.72%) of them will be 10.
168 (14/144 or 9.72%) of them will be 9.
168 (14/144 or 9.72%) of them will be 8.
168 (14/144 or 9.72%) of them will be 7.
168 (14/144 or 9.72%) of them will be 6.
168 (14/144 or 9.72%) of them will be 5.
168 (14/144 or 9.72%) of them will be 4.
168 (14/144 or 9.72%) of them will be 3.
48 (1/36 or 2.77%) of them will be re-rolled and still undetermined.​

Now, consider all the possible outcomes of the 48 second re-rolls:

4 (1/12) of them will be 12.
4 (1/12) of them will be 11.
4 (1/12) of them will be 10.
4 (1/12) of them will be 9.
4 (1/12) of them will be 8.
4 (1/12) of them will be 7.
4 (1/12) of them will be 6.
4 (1/12) of them will be 5.
4 (1/12) of them will be 4.
4 (1/12) of them will be 3.
8 (1/6) of them will be re-rolled and still undetermined.​

So, by the end of the second re-roll, all the possible outcomes are:

172 (43/432 or 9.95%) of them will be 12.
172 (43/432 or 9.95%) of them will be 11.
172 (43/432 or 9.95%) of them will be 10.
172 (43/432 or 9.95%) of them will be 9.
172 (43/432 or 9.95%) of them will be 8.
172 (43/432 or 9.95%) of them will be 7.
172 (43/432 or 9.95%) of them will be 6.
172 (43/432 or 9.95%) of them will be 5.
172 (43/432 or 9.95%) of them will be 4.
172 (43/432 or 9.95%) of them will be 3.
8 (1/216 or 0.46%) of them will be re-rolled and still undetermined.​

As mentioned, there is an equal chance of getting each number from 3 to 12, which is essentially d10+2. 8 possibilities are still undetermined (you would have to do a third re-roll; this represents the 1/6 x 1/6 x 1/6 chance that you get a 1 or 2 on the initial roll, the first re-roll and the second re-roll), but hopefully it is obvious by now that those 8 re-rolls would still be distributed evenly between 3-12, with a small chance of a fourth re-roll.

 

[Celtavian]

re

Yeah.... look, Celtavian, math says you're wrong.

The easiest way to see it is to realize that there's an equal chance of any number from 3 to 12:

If you roll a 3 to a 12, you get what you roll. Chances are equal for any of those numbers.
If you roll a 1 or 2, you try again.
On the new try, if you roll a 3 to a 12, you get that roll. Chances are equal for any of those numbers.
If you roll a 1 or 2, you try again.
On the new try, if you roll a 3 to a 12, you get that roll. Chances are equal for any of those numbers.
Etc, etc, etc.

See? No matter what you do, you either receive a number from 3 to 12 with equal odds for any number in that range, or, you roll again. And on the new roll, the rules are the same.

You can imagine it as if it weren't numbers. Suppose you had to pick one door out of three. One has a car, one has a boat, and one has a sign that says "close all the doors, the game show host mixes up the prizes again, and you pick a new door."

Your chance of getting the car or the boat are 50/50 each. The extra result is irrelevant, since all it says is to pick again.

What part are you missing about retrying?

Do you get to retry with the d10+2? If you roll a 1 on a d10+2 do you have a number other than a 3?

I already said that yes, over a few thousand rolls you may come out the same. But that isn't how DnD combat works.

I'm saying the following with a reroll will occur:
1. More spiked damage that rises higher than a single die roll.

2. With the same average flat damage of 7.5

That makes the reroll slightly more advantageous.

Just because someone runs a thousand rolls on a random program that does not simulate Dnd combat well does not mean that d10+2 is equivalent to a reroll.

So what if you have an equal chance of getting a new number between 3 and 12. You still have to stick with the roll for d10+2.

What you are in essence saying is that reroll abilities are useless. And that over a few thousand rolls rerolling will equal the same as not rerolling. Fine, that is true over a few thousand rolls.

But DnD combat doesn't look like that. The chance for damage spikes is much higher with a reroll.

As I said, an analysis should be run like a series of DnD combats and not a thousand rolls as though that is how you would roll damage dice. Because it isn't how it would be rolled.

 

[FireLance]

But DnD combat doesn't look like that. The chance for damage spikes is much higher with a reroll.

This is incorrect. Your chance of getting a 12 with a d12 brutal 2 weapon is exactly 10%, the same as the chance of getting a 12 on a d10+2 weapon.

Your chance of getting a 12 on your initial roll is 1/12 or 8.33%, with a 1/6 or 16.67% chance of a re-roll.

Your chance of getting a 12 after a re-roll is (1/12 + 1/6 x 1/12) or 9.72%, with a 1/36 or 2.78% chance of a second re-roll.

Your chance of getting a 12 after a second re-roll is (1/12 + 1/6 x 1/12 + 1/36 x 1/12) or 9.95%, with a 1/216 or 0.46% chance of a third re-roll.

Your chance of getting a 12 after a third re-roll is (1/12 + 1/6 x 1/12 + 1/36 x 1/12 + 1/216 x 1/12) or 9.99%, with a 1/1296 or 0.07% chance of a fourth re-roll.

Mathematically, your chance of getting a 12 on a d12 brutal 2 roll is exactly the same as getting a 12 on a d10+2 roll.

 

[Dalzig]

Celtavian, you are just falling into the pitfall of probabilties.

Pick up a d20. What is your pecent chance to roll a 20? 5%. Go ahead and roll it. Got a 1? Reroll it. Your chance to roll a 20: 5%. Roll a 2? Reroll it. Your chance to roll a 20: 5%.

Previous rolls do not affect current or future rolls at all, except in your mind. If you get a hot streak of 20's, your mind will tell you that with every 20 you roll, the possibility of a lower number popping up increases. This is not true.

You have an equal chance of rolling a 3 on a d12 brutal 2 weapon as you do a 1 on a d10+2 weapon. Rerolls do not matter in this case. It is all psychological.