Mathhammer: Wolf Guard with Mark of the Wulfen?

So I am planning on running a Space Wolf Scout Pack in my army. I love the fact that you can really trick out the scouts (although they can be a huge points sink). The thought of 10 dudes coming in from the back field with a melta, 2 power weapons and a MoW dude can be quite scary if your opponent leaves someone in the back field. Now what I am considering doing is attaching a Wolf Guard squad leader to come in with them, but I'm not sure what I want to outfit him with. I was thinking of Mark of the Wulfen because the only thing that really seems better than one crazy mother F'er is two! But I got to wondering if there were better options, that lead me to break out the old probability hammer and figure it out.

Now what I am looking at is pure close combat killing ability. I'm not worried about making this Wolf Guard capable of killing vehicles in the back field (with a PF, combi-melta, or meltabomb). This is all just, which weapon is better.

The reason I was leaning towards MoW as the best was the sheer number of rending attacks. The dude's attack characteristic becomes D6+1! Add in the extra attack for two CC weapons (assuming BPistol and CCW), and another attack because of charging, that is 4-9 attacks!

So I was thinking of how to do this, and it quickly became apparent that it was really impractical to see how the five different weapons I am looking at would do against every possible encounter, so I tried to pick some generic "dudes" that this crazy mother F'er might charge.

First out would be s S3, T3 and Sv 5+ guy, more commonly know as the Imperial Guard Guardsman. Attacking the Guardsman I came up with this table for the average number of unsaved sounds created.

Weapon	Wounds
MoW	2.17
Power Weapon	1.78
Power Fist	1.67
Frost Weapon	2.22
Twin Wolf Claws	2.96

Next I moved on to a basic Tac Marine. This gave me S4, T4, and a Sv 3+. This time I got the following.

Weapon	Wounds
MoW	0.90
Power Weapon	1.00
Power Fist	1.25
Frost Weapon	1.33
Twin Wolf Claws	1.50

Lastly, I looked at a Terminator to see what the invulnerable save would do to things.

Weapon	Wounds
MoW	0.54
Power Weapon	0.67
Power Fist	0.83
Frost Weapon	0.89
Twin Wolf Claws	1.00

So the MoW does well against the Guardsmen, but really starts to do poorly against anything "tougher," and it really loses it's punch when you toss in an invulnerable save. I was just about to wrap it up and say that the Wolf Claws were the way to go when I realized that I didn't take cost into account. A Wolf Guard with MoW costs 33 points. A Wolf Guard wtih Twin Wolf Claws costs 48 points. So the last thing I threw into the excel spread sheet was to devide the number of wounds by the cost of the weapon. When I ranked up the weapons I got something that looked like this.

IG	SM	Term
PW	PW	PW
MoW	FB	FB
FB	PF	PF
WC	MoW	MoW
PF	WC	WC

So it looks like, when you bring cost into it, the power weapon is the clear winner. Now with all that said and done, I'm pretty sure I'm going to outfit my scouting Wolf Guard with a power fist and a combi-melta. But I'm a math nerd, so I really don't consider the time I spent calculating this wasted.

Outfitting Wolf Guard

So Wolf Guard are an intricate part of any space wolf army. Or at the very least they are in my Space Wolf Army. Now Grey Hunters are great because they can take just about any type of war gear in the Space Wolf arsenal from Terminator Armor to combi weapons to power weapons, frost weapons, wolf claws and even thunder hammers with storm shields.

Now I don't tend to drop a lot of points into my Wolf Guard. Most of them get a power fist, and thats about it.

One of the things I really don't understand is that while, Grey Hunters carry bolters and bolt pistols standard, Wolf Guard carry only one or the other. So because most of my Wolf Guard will be toting power fists, I'm thinking I'll be slapping bolters on them. The bolt pistol won't add an extra attack in close combat, and the bolter adds an extra shot if you are out of charge range, or you are trying to draw a charge from the foes of the Emperor.

Guess its time to break out a knife and chop off some bolt pistols.

Mathhammer: 8th Ed. Casting

So with the new edition of WHFB coming out, we have new rules. All wizards are allowed to use as many dice as they like (suck it druchii) so you can have a level 1 Warlock Engineer throwing six dice at the Dreaded Thirteenth spell in order to get that 25+. And it might seem like a very good idea, I mean, who wants to miscast with your (possibly) very expensive level 4 wizard? The downfall of a miscast now is much more devastating that it was in 7th edition, so what are your odds?

When we look at rolling the dice and we look at rolling double sixes it is pretty easy to understand that when you roll two dice, the chance that you'll get a six on the first die is 1/6 and the chance you'll get a six on the second is also a 1/6. The rules of probability say that in situations like this, you multiply the two results, so the chances of getting an irresistible force/miscast on two dice is 1/36.

When you move on to three dice it becomes a bit more complicated. You could get a six on the first die, a six on the second and something other than a six on the third die. Those chances are 1/6, 1/6 and 5/6 respectively and this would give you a probability of 5/216. But this just tells you the probability of the first two dice being a six and the third being something else. We haven't accounted for getting a six, not six, and then a six, or even getting not six, six and six. Now the chances of each of these three separate situations occurring is 5/216, so because these three situations are the only ways you can get two sixes with three dice, these are the only ones we have to count. So probability becomes 15/216 or roughly 6.94%.

But this still does not cover what we need because we will still get an irresistible force/miscast if we throw three sixes so we have to add in that probability (1/216) for a total of 16/216 which is roughly 7.41%.

It becomes even more complicated with four dice as you have to account for rolling two, three or four sixes. Using what is called a cumulative density function (CDF) on a calculator I came up with the following table of values for the percent chance of an irresistible force/miscast depending on how many dice you throw.

Miscast CDF
Dice Used	Percent
1	0.00%
2	2.78%
3	7.41%
4	13.19%
5	19.62%
6	26.32%

Review: Blood Money

C.L. Werner is fast becoming my favorite Warhammer Fantasy authors. Blood Money is the first book of the Brunner the Bounty Hunter Omnibus. It tells the story, oddly enough, of Brunner the Bounty Hunter.

Talk about the quintessential anti-hero. This guy is a total D-bag, but I couldn't help but love him. This book is a series of short stories that tell of Brunner's adventures in Bretonnia and the Border Princes, penned by a writer from the Empire.

I like the use of the short stories with Brunner as they give us many views of how he plies his trade and all the different ways he can be a bastard.

I think that what I like the most about Brunner is that he doesn't appear super-natural like many of the fantasy heroes such as Gotrek, and he doesn't rely on magic. What he does is use his mind as a weapon along with his very prodigious fighting skills.

I am very much looking forward to continuing to the next story Blood and Steal.

I give this book four collected bounties out of five.

Mathhammer: Gets Hot! Part 1

So as the resident math nerd, I figure I'd do a semi-regular article on the probability behind some of the things we see in 40k and WHFB.

This time I'm going to look at weapons that "Gets Hot!" So what I looked at was the chance of surviving firing one of these weapons. So for a "Gets Hot!" if you roll a 1 on the to hit roll, the weapon has overloaded and the firing model suffers a wound.

So in essence, we're looking at what is the probability of rolling a 1 on a d6, which is 1 out of 6, and then finding out the probability of passing the armor save.

What I've done is figured this out for the number of shots fired, and then the different armor saves possible. What I came up with is this:

		Armor Save
		2+	3+	4+	5+	6+
Shots Fired	1	97.2%	94.4%	91.7%	88.9%	86.1%
	2	94.5%	89.2%	84.0%	79.0%	74.2%
	3	91.9%	84.2%	77.0%	70.2%	63.9%
	4	89.3%	79.6%	70.6%	62.4%	55.0%
	5	86.9%	75.1%	64.7%	55.5%	47.3%
	6	84.4%	71.0%	59.3%	49.3%	40.8%
	7	82.1%	67.0%	54.4%	43.8%	35.1%
	8	79.8%	63.3%	49.9%	39.0%	30.2%
	9	77.6%	59.8%	45.7%	34.6%	26.0%
	10	75.4%	56.5%	41.9%	30.8%	22.4%
	11	73.4%	53.3%	38.4%	27.4%	19.3%
	12	71.3%	50.4%	35.2%	24.3%	16.6%
	13	69.3%	47.6%	32.3%	21.6%	14.3%
	14	67.4%	44.9%	29.6%	19.2%	12.3%

So there you go, a model with a 2+ armor save has about a 67% chance of shooting 14 shots without suffering a wound, and a model with a 6+ armor save has about an 86.1% of surviving shooting once.

Now this of course really only applies to models with one wound. If you have multiple wounds you obviously have a higher probability of surviving. I'll be looking at that in Part 2.