Preview: Brutal Ability

[Keenath]

The rerolling is powerful. More powerful than d10+2. If you roll a one or two on a d10+2 you get a three or four for damage. Wheras if you reroll a one or two with a brutal weapon you get a chance at higher than 3 or 4.

Yes, but a brutal d12 has a smaller chance of rolling a 1 to 2 than a d10 does.

That they're equivalent can be proven using many methods; you could produce a limit equation; you could use probability mathematics; I chose monte carlo -- I wrote a quick computer program to run ten thousand tests, rolling a d12 and rerolling any result of a 1-2.

The average damage output was, as expected, 7.5. A standard d12 roll has an average damage of 6.5, so that represents an average damage increase of +1, just like all superior weapons. (For example, a rapier is equivalent to a shortsword with a bigger damage die, which gives it an average +1 damage.)

The damage distribution was a straight line across 3 to 12 -- thus there is no bias towards a particular value*. An average 7.5 with an even distribution of values is identical to 1d10+2. It just IS. I'm sorry.

Think of it this way: If you converted all 1s and 2s into 3s, you'd have a 25% chance of getting the lowest possible damage for your weapon. That method would produce a huge bias towards small damage rolls.

When you reroll the d12, you have an equal chance of all the values coming up -- and if you roll a 1 or 2 again, you reroll again, STILL with an equal chance of all 12 values. That's mathematically equivalent to simply removing the 1 and 2 from the pool of possible values, effectively turning your d12 into a d10, and then adding 2 to the damage rolls.


* A single die roll has a flat distribution curve -- all values have an equal chance of coming up. Rolling more dice will produce a bell curve that becomes sharper with each additional die. For example, 2d6 is not an even distribution between 2 and 12; it's heavily biased towards the center of the range. You have a 45% chance of getting a 6, 7, or 8, and only a 16% chance of a 10, 11, or 12.

But for multidice powers being able to reroll every one or two is a pretty powerful advantage. It makes the axe better than any weapon in the game bar none.

Simply incorrect. I just can't explain any more clearly. You're wrong. It's exactly as powerful as a +1 average damage, or a +2 with a smaller damage die. They're mathematically equivalent, period. There's not even a variation in the distribution of values.

 

[Cadfan]

I think they did it for two reasons.

1. They wanted to keep [W] as just being a die, rather than a die plus modifiers. That means that multiplying [W] can be done by just increasing the number of dice rolled, rather than by multiplying out an equation like 3*(1d10+2)=3d10+6.

2. Its sad to roll a really big dice and see a low number, and fun to pick that dice back up and try again.

 

[Celtavian]

Yes, but a brutal d12 has a smaller chance of rolling a 1 to 2 than a d10 does.

That they're equivalent can be proven using many methods; you could produce a limit equation; you could use probability mathematics; I chose monte carlo -- I wrote a quick computer program to run ten thousand tests, rolling a d12 and rerolling any result of a 1-2.

The average damage output was, as expected, 7.5. A standard d12 roll has an average damage of 6.5, so that represents an average damage increase of +1, just like all superior weapons. (For example, a rapier is equivalent to a shortsword with a bigger damage die, which gives it an average +1 damage.)

The damage distribution was a straight line across 3 to 12 -- thus there is no bias towards a particular value*. An average 7.5 with an even distribution of values is identical to 1d10+2. It just IS. I'm sorry.

Think of it this way: If you converted all 1s and 2s into 3s, you'd have a 25% chance of getting the lowest possible damage for your weapon. That method would produce a huge bias towards small damage rolls.

When you reroll the d12, you have an equal chance of all the values coming up -- and if you roll a 1 or 2 again, you reroll again, STILL with an equal chance of all 12 values. That's mathematically equivalent to simply removing the 1 and 2 from the pool of possible values, effectively turning your d12 into a d10, and then adding 2 to the damage rolls.


* A single die roll has a flat distribution curve -- all values have an equal chance of coming up. Rolling more dice will produce a bell curve that becomes sharper with each additional die. For example, 2d6 is not an even distribution between 2 and 12; it's heavily biased towards the center of the range. You have a 45% chance of getting a 6, 7, or 8, and only a 16% chance of a 10, 11, or 12.

The reason it is more powerful than a d10+2 is not that it gives the same average damage of 7.5. It is more powerful because you get to reroll whereas you get a 1 or 2 on a d10 that becomes a 3 or a 4. As you stated here:

If you converted all 1s and 2s into 3s, you'd have a 25% chance of getting the lowest possible damage for your weapon. That method would produce a huge bias towards small damage rolls

It would be a huge bias towards lower damage rolls. Which by your own words indicates that rolling a d10+2 once would give more lower damage rolls than say a d12 reroll any 1 or 2. You only get to roll once, rather than rerolling each worse damage roll.

Since eliminating the 1 and 2 turns your d12 into a d10, you get to reroll with a better chance of getting a higher roll than accepting what is on a single rolled d10.

d12 has a smaller chance of rolling a 1 to 2 than a d10 does.

especially during multidie rolls where your chances of getting a 1 or 2 increase because of the number of dice used.

So though a d10 gives you a greater chance of 1 or 2, it also gives you a greater chance of a higher number very slightly. Difference is you don't get to reroll the d10 when you get a 1 or 2. You are set with it.

Simply incorrect. I just can't explain any more clearly. You're wrong. It's exactly as powerful as a +1 average damage, or a +2 with a smaller damage die. They're mathematically equivalent, period. There's not even a variation in the distribution of values.

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.

They don't hand out reroll abilities because they don't affect the damage of an ability. There are several encounter powers like Elven Accuracy that give a reroll when you make a bad roll. There are several paragon path abilities that allow for a reroll if you don't like the roll.

The fact that you get to chose the reroll increases your chance of getting higher damage. You choose to reroll when you roll the lowest possible damage.

The Brutal 2 ability does that for you. You're lowest possible rolls on a d12 are 1 or 2. So you get to reroll whenever you get a 1 or 2 giving you a higher chance to obtain a higher number.


This is great for a multidice power such as when you roll a series of 1s or 2s mixed in with a number of other higher numbers. It will in fact at times be better than a full reroll granted by powers because you will only have to reroll the lowest possible dice.

It will at times be better than a reroll power because this ability is in giving constant rerolls for a 1 or a 2 rather than having to accept the second roll as a power would.

Though that reroll over a long time could give a 3 or 4 and does average out to 7.5 damage. I would bet money that if you tracked individual damage spikes, you would see a tremendous advantage that far exceeds any other weapon in the game including a rapier or bastard sword.

When you roll a 1 or 2 on a d10+2, you get a 3 or a 4, period end of story 100% chance. When you roll a 1 or 2 on a d12, you get a chance at a 3 or 4, but you have just as much a chance of rolling an 11 or 12. Something you do not have when you roll a 1 or 2 on a d10+2 once.

Thus you have a chance of obtaining a much higher result than a 3 or 4 as you would with a d10 which you only get to roll once.

Though over the course of 100s of rolls, or 10,000 as you say, this may be true.

I think your analysis should be run as a numer of DnD combats. A number of punctuated rolls including powers that use multiple dice for average encounters. I think that would create a very spiky graph in favor of rerolling the d12.

I will run this analysis myself and get back to you. If I am proven wrong, I will admit it.

But I do not believe that the analysis system you are using provides an accurate picture of how DnD combat works. I think your analysis just looks at a d12 over ten thousand or so rolls rather than a Dnd combat where the number of dice rolled will often vary as will the number of times you roll per combat.

I personally think that powers like Elven Accuracy, the Halfling ability, and several paragon path powers would be very useless if a reroll wasn't more powerful than a single dice roll. The chance to reroll may not over a thousand rolls amount to much, but I know it will create damage spikes that will create superior damage in some battles and just average in others which is better than the constant average damage of d10+2.

It's like this to me.

Sure, over a few thousand rolls and d10+2 will be the same as a D12 reroll 1 or 2.

But in the course of DnD combats, d10+2 rolled once will not match the damage spikes of d12 reroll all 1s or 2s which makes d12 reroll 1s or 2s superior in some combats and the same as d10+2 in most combats, which ultimately results in d12 reroll 1s or 2s being better.

I know for certain that a Brutal 2 Executioner's Axe is well worth the feat and is the best 2h weapon in the game bar none. Nothing else can match it. And that is all for one feat. It is even better than the difference between a Greatsword and a bastard sword or a rapier and a shortsword, especially considering that High Crit is stacked upon Brutal 2.

I'm hoping what drove this is that the Greataxe has fallen out of favor with alot players, at least it has in my group. It is a staple of fantasy. If this gets more people using Greataxes, then I guess I'm for it. Even I'll admit the d12 is a frustrating dice because it does have less of a chance of rolling a good number just like it has less of a chance of rolling a 1 or 2 versus a d10 and especially versus 2d6.

This new Brutal 2 axe may be too good, but I'm all for seeing more two handed axe wielders. So I'll go with it. Even so, I still think the damae graph will have alot more spikes with d12 reroll 1 or 2 versus d10+2 rolled once. I will still roll this out for a series of combats with multidice powers and see if I can prove it statistically.

 

[Runestar]

Can anyone do the math to see how much it will be worth it to wield a large brutal axe to get 2d6/brutal2? This mechanic seriously has me intrigued, and I am interested to see how far it can be taken.

 

[Celtavian]

I think they did it for two reasons.

2. Its sad to roll a really big dice and see a low number, and fun to pick that dice back up and try again.

This is the single best reason for the ability I have read.

Alot of my players would not touch the greataxe because of the d12 and the frustration of rolling a 1 or 2 or some other low number. The d12 is a frustrating dice. So if this makes the Greataxe viable again, albeit for a feat and under a different name, then I'm going to go with it spiky damage and all.

 

[Ulorian - Agent of Chaos]

*bunch of faulty logic*

Wow... I don't know how many times people are going to have to tell you that you are wrong and explain why you are wrong before it finally sinks in. This thread has become strangely fascinating to me.

 

[Cadfan]

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.

 

[Stogoe]

Can anyone do the math to see how much it will be worth it to wield a large brutal axe to get 2d6/brutal2? This mechanic seriously has me intrigued, and I am interested to see how far it can be taken.

Well, the rolled damage is going to be 6-12, so 9 average damage, which I think is equivalent to 2d8's average.

 

[jadrax]

You can simply knock the brutal value of the Die type and then add it as a bonus, so 2d6 (brutal 2) is the same mathematically as 2d4+4.

 

[Keenath]

The reason it is more powerful than a d10+2 is not that it gives the same average damage of 7.5. It is more powerful because you get to reroll whereas you get a 1 or 2 on a d10 that becomes a 3 or a 4...

Incorrect. It is exactly the same power. Try it yourself. Roll 1d12 100 times, rerolling the 1 and 2, and then roll 1d10 100 times and add 2 to all the results. They'll be the same. You can choose not to believe me, but fortunately mathematics doesn't depend on your belief to operate.

It would be a huge bias towards lower damage rolls.

NO! God! No! 1d10+2 has NO BIAS towards ANY damage rolls! It has an equal chance of providing a 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12!

Now try it with a d12. You reroll all your 1s and 2s. There's a 1/6 chance of a reroll, plus a 1/12 chance each of a 3-12.

So, you have an equal chance of a 3-12, and sometimes you reroll. When you make that reroll, what do you have?
You have an equal chance of a 3-12, and sometimes you reroll. When you reroll what do you have?
You have an equal chance of a 3-12, and sometimes you reroll.

Do you see where we're going with this? No matter how many rerolls you make, you ALWAYS have an equal chance of a 3-12, and that's the DEFINITION of d10+2.

Since eliminating the 1 and 2 turns your d12 into a d10, you get to reroll with a better chance of getting a higher roll than accepting what is on a single rolled d10.

No. Each reroll has an equal chance of any value, just like the original d10 roll.

Remember, each die roll is totally independent. The die doesn't remember what it rolled last time. (Believing this to be untrue is known as the Gambler's Fallacy.) Each time you reroll, it's the same as the very first roll, and your chances of any value are exactly the same as always.

So though a d10 gives you a greater chance of 1 or 2, it also gives you a greater chance of a higher number very slightly. Difference is you don't get to reroll the d10 when you get a 1 or 2. You are set with it.

Yes, and then you add TWO to it! You never really roll a 1 on d10+2, you can only roll a 3 at the very lowest.

They don't hand out reroll abilities because they don't affect the damage of an ability. There are several encounter powers like Elven Accuracy that give a reroll when you make a bad roll. There are several paragon path abilities that allow for a reroll if you don't like the roll.

And they're completely different from what we're talking about here because those abilities don't allow you to continue to reroll when you get low values.

And I never said "rerolls don't affect the damage". They DO affect the damage. They effect it exactly as much as an average +1. I mean, geez.

Thus you have a chance of obtaining a much higher result than a 3 or 4 as you would with a d10 which you only get to roll once.

That is also true.

Interestingly, it doesn't change anything. They're still the same thing.

You have to keep in mind that the d10 has a narrower array of values. The chance of getting any given value is slightly better on a d10. A d10 gives you more 10s than a d12 gives you 12s. Thus you get more 12s on a d10+2 than a standard d12. The rerolls just fill out those extra probabilities.

Okay, look at it this way:
On a d10+2, I have a 10% chance of a 12.
On a d12 brutal 2, I have an 8.33% chance of a 12. But I also have a 16.66% chance of a reroll. And on that reroll, I still have an 8.33% chance of a 12, and a 16.66% chance of a second reroll.

Thus, the total chance of a 12 is the chance of a 12 on the first roll, plus the combined chance of getting to reroll AND getting a 12 on that reroll, plus the combined chance of getting a third roll AND getting a 12 on that third roll, etc. This is called a limit series, because it goes on infinitely, with each iteration getting less and less likely to come about. I'll just add up the first four iterations:

8.33% + (16.66% * 8.33%) + (16.66%^2 * 8.33%) + (16.66%^3 * 8.33%)
= 9.9875%

That's only off 10% by about 1 hundreth of a percent, or 1 roll in ten thousand, and it's only off by that much because I didn't take it out to an infinite number of iterations. If you keep doing that, the sum will eventually add up to 9.99999~%, which is actually 10% due to the weirdness of limit mathematics.

But I do not believe that the analysis system you are using provides an accurate picture of how DnD combat works. I think your analysis just looks at a d12 over ten thousand or so rolls rather than a Dnd combat where the number of dice rolled will often vary as will the number of times you roll per combat.

That doesn't matter. The analysis tells me how the die acts on every roll. It tells me that every single time, I generate a flat probability curve between 3 and 12. I can easily see that a 1d10+2 does exactly the same thing, so what difference does it make how many rolls I make or how many times I make them?

Sure, over a few thousand rolls and d10+2 will be the same as a D12 reroll 1 or 2.

But in the course of DnD combats, d10+2 rolled once will not match the damage spikes of d12 reroll all 1s or 2s which makes d12 reroll 1s or 2s superior in some combats and the same as d10+2 in most combats, which ultimately results in d12 reroll 1s or 2s being better.

Over a few thousand rolls or over a single roll.

What you're describing here would be the reason that, say, 3d4 isn't the same as 1d10+2. Over many rolls, they average out the same way, but 3d4 is more likely to hit in the middle of that range while d10+2 is a flat distribution.

But that's not the situation here. Because you throw out the old roll and roll anew with each 1 or 2, the average doesn't get altered by that 1 or 2.

I know for certain that a Brutal 2 Executioner's Axe is well worth the feat and is the best 2h weapon in the game bar none.

Your certainty is misplaced. It's just +1 better than a normal greataxe, and equivalent to all other superior weapons. Well, for a given value of "equivalent" -- I'm not convinced that, for example, a shortsword and a longsword are balanced against each other, but a longsword and a bastard sword certainly have the same benefit as a greataxe versus an execution axe.