Mathhammer: Predator vs. Dark Eldar

 

So I have a friend of mine that has picked up the new DE book and is making himself an army. He has already warned me that he is looking at bringing 10 or so raider/ravagers. So I got to thinking about what I'm goinng to use to get rid of them. I'll probably take some Long Fangs, but I'm afraid they are going to die quickly to poisoned attacks wyches, so I was considering a Predator, but which one? People have been talking about the destructor as it has so many shots, but then other people have been saying the Autocannon LasCannon is the way to go. So I pulled out my excell spred sheet to check it out.

Mathhammer: Blood Claws Blah

Stolen from Big Jim on the
Space Wolves Blog.

Stolen from Lexicanum.

So I've been painting recently and just finished up 26 Blood Claws. Now It may be that this has been a waste of time because I just don't think Blood Claws are worth it in the new book which is a switch, because in the old 3rd ed. supplement, I felt the say way about Grey Hunters.

The main reason for taking the Blood Claws in the old 'dex was that they were 3 points cheaper, oh, and GHers had to pay a point to get BP and a CCW, oh, and you can get up to 3 PFs in a squad not counting a Wolf Guard Leader, and you can have up to 15 dudes which mean a lot of ablative wounds for the PFs, OH! and they get 4 attacks on the charge!

Mathhammer: Coldblooded Leadership

So this week I was taking a look at coldblooded leadership. With this rule, whenever you take a leadership, you roll three dice and take the lowest two. Not surprising, this makes passing the leadership rolls much easier, but how much easier?

This was actually difficult for me to figure out with mathematics. The problem being, I can't just count up how many different ways there are for a person to roll a 6 on three d6 (33 different ways, fyi) but I had to count and differentiate the different rolls because 1,2,5 and 3,1,5 and 5,1,6 and 6,2,4 will all be the equivalent of a leadership roll of 6. I tried several different ways to make this easier on myself and I found that it was just a simple matter of listing out all 216 different ways you can roll three d6. Then I just went through them and figured out the sum of the two lowest dice.

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.

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%

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.