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.
I will roll a series of combats and go by that. I want to see if the spikes I think will occur happen.
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.
The math is not difficult to figure out. Neither the percentages or numbers. The reroll is what I think makes it better because it gives a chance at a higher number in each reroll situation versus a guaranteed 3 or 4 for a d10, not because over a thousand or so rolls it equals out the same.
No. Each reroll has an equal chance of any value, just like the original d10 roll.
I do not dispute this.
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.
I do not dispute this either.
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.
I do not dispute this. But you get that three and you have no chance for improvement as you do rerolling a d12.
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.
Yet they are powers and just as you stated, you have to keep that 1 or 2 on a reroll. But you do get to reroll a series of 3s or 4s. So the situations where Brutal 2 would be better would be those with a mix of high rolls and a few 1s or 2s mixed in.
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.
I don't dispute this. d10 is a much stabler dice than a d12.
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.
Not disputing this either. It seems to indicate that a d10+2 are the same.
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?
I guess no difference.
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.
You may be right. I'll see how it rolls in play. Theory is nice for theorizing. But I want to see it in play.
It seems like a no brainer two handed weapon that will make the Great Axe obsolete.
The d12 is a frustrating die. It has been around my table for a while. Player perception may skew that, but perception is more important than fact when it comes to choices. Player's at my table hate the d12. They would be fine with a d10+2 as the d10 is more stable die.
I do see what you're saying. d10+2 does appear to produce identical results.
I'm still going to roll it out. I'm less put off by this weapon than I was initially. It still appears to be the best 2 handed option in the game and player's do love to reroll over roll once with d10+2. That alone will make my players want to use it whether the advantage is perception or not. I've met few players that don't love the chance to reroll a bad roll.
Thanks for taking the time to outline the math behind it. It was illuminating.
I have some measure of understanding of statistical mathematics. I don't often use it at this point in life. But I did see the basic math and knew the difference between d10+2 and d12 reroll 1 and 2 wasn't great, but it seemed slightly more advantageous than a single roll.
But the limit series math you showed me seems to indicate it is the same. I can't much dispute that.
I'll still roll it out just to see what it will look in a series of combats. But I feel a bit better about the weapon, though I still think it is the best 2 handed weapon in the game and well worth the feat. But I don't think you're disputing this.
