I used to have a link to this message in my sig, but that link broke with the demise of the old forums. So it seems like it's time to revise my public service announcement for the new generation:
One of the first things gamers learn about dice is that the average roll on 2d6 is 7.* It's true and it's useful to know. But then, one day, your ARM 19 warjack is subject to some POW 12 shooting, and you think, "That's dice-7 for damage. 7-7=0. My Jack is safe." However:
2d6-7 is not 0.
We've all done it. But when we do that, we are wrong, wrong, wrong. That Jack is going to take a moderate beating.
I used to have a long and complicated explanation for this (and I still do; keep reading). But the simplest explanation is that 2d6-7 isn't zero because 2d6-12 is zero.
2d6-7 is actually approximately 1. Which means that your Mangler getting shot at by those Hand Cannons is actually going to take an average of one damage per attack, and probably going to lose a big chunk of its health.
Here, I brought you a graph:
So what's going on here?
In Warmachine, there's no such thing as negative damage. If you roll a 6, and subtract 7 because of ARM, the rules treat that result as 0 damage, not +1 health to the jack. This is why Dice-12 is 0, and not -5.
If your Jack suffers 36 attacks, it will take (on average):
5 attacks for 1 points of damage (rolled a 8)
4 attacks for 2 points of damage (rolled a 9)
3 attacks for 3 points of damage (rolled a 10)
2 attacks for 4 points of damage (rolled a 11)
1 attacks for 5 points of damage (rolled a 12)
Add all that together and you get:
And 35 damage over the course of 36 attacks works out to just about one damage per attack roll.
Ok, fine, but what if the example were an ARM 20 Juggernaut instead of an ARM 19 Mangler? Or an ARM 18 Nomad? That graph up there shows a nice curve, but it's kinda hard to read. What are the average damages for ARM-POW?
Here are the actual values:
You'll notice that the actual averages start diverging from what you might expect at "dice - 3". That's the first instance of the "zero damage floor" coming into play. If you roll snake-eyes, the rules turn that 'negative one' result into a zero. This continues as you go further down the chart.
The chart is actually fairly easy to memorize, if you round things a little bit.
"Bonus Damage" kicks in at Dice Minus Five, and proceeds from there. Even if you just remember that Dice Minus Seven is 1, you're in much better shape than you would be otherwise.
So the next time your opponent complains that "On average rolls, you shouldn't have done any damage, you lucksack!" just smile at him and know that you're winning through the power of math. Or hit him with a high-velocity tubesock-encased pewter bludgeon... whatever. You're justified.
-- EDIT --
"But wait," you cry!
"Dice - 7 does ZERO damage 58% of the time. The average is clearly not 1."
To answer this, we have to talk about the difference between two different types of averages: Mode and Mean.
The mode is the most common value in a group. And it's true, 2d6-7 damage has a mode of 0.
When you roll 2d6-7, you are more likely to roll a 0 than any other number.
What I'm talking about here is a type of average called the Mean, also known as Expected Value.
The mean damage for 2d6-7 is 1 (actually 35/36).
When you're figuring damage to Jacks, Beasts, Warcasters, and Warlocks, you can expect an average of 1 damage per 2d6-7 attack.
Half the time it will be higher, half the time it'll be lower, but on average, that'll be the damage dealt over the long term.
"WAIT! How much higher, and how much lower?!"
Good question, and the answer to that is another whole article.
* Yes, it really is 7. Don't be superstitious; it's bad luck.