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Hello all.

Recently, I played a game where I charged a Furioso Dreadnought with Blood Talons into a squad of Mega Armored Nobz. The Nobz had been weakened by shooting, and if I remember correctly, consisted of 4 models, 3 of which had been wounded. I expected to clean up, did a total of like 2 wounds, and was annoyed when the 1 penetrating hit rolled a 5.

So, I started wondering how bad my luck was. It's pretty easy to calculate the average number of unsaved wounds for a Blood Talon attack by using the formula for the sum of a geometric series. Since you hit on a 3, and wound 35 times out of 36, it seems like you should average 1 / (1 - 2/3 * 35/36) = 3 total attacks per initial attack, due to the re-rolls, which works out to 12 total attacks or 8 dead on average.

However, there is a buried assumption, which is that it's always possible to keep attacking until you fail to cause an unsaved wound. This isn't true, as you might simply kill the whole squad. It also doesn't tell you how common it is to kill everything.

So, I set up a simulation in Excel to crunch some numbers for me, which I've attached in a spreadsheet so the numbers don't look like crap. I've calculated the average number of unsaved wounds, and the percentage of times that the enemy get wiped, both when charging and getting charged for both Furiosos and DC Dreadnoughts.

Here are the enemies I consider: 10 Tactical Marines, a blob of 21 Guardsmen with a Commissar, 7 Plague Marines, a Tervigon, 10 Wyches, 5 TH/SS Terminators.

First, note that the Tactical Marines cover most situations, as there isn't any difference between them and most infantry. The DC and the Furioso mainly differ in the number of attacks, but I also take into account their differences in WS.

I think it's interesting that you can't expect to wipe stuff out all that often. Even with the fifth attack, a DC Dread will only wipe out a Tac squad equivalent around a quarter of the time. Thus, hidden Power Fists will always threaten you a bit. Obviously, a Furioso doesn't worry as much. A Furioso looks like a particularly good solution to the proverbial mob of 20 Boyz. Yes, you only kill about 6.5 on average, but that works out to 11.5 dead after No Retreat, and the 3 PK attacks you get back only average .25 glances and .25 pens. Unless you get somewhat unlucky, you'll run down the squad after 2 rounds of combat.

It's also striking how badly a BT Dread will do against TH/SS Terminators. There really is no easy way to kill those things, short of a C'Tan I guess (really risky though). You pretty much have to win via attrition.

I didn't put it in the table, but on average, you wipe out the Mega Armored Nobz described above 70.5% of the time. So I was quite unlucky.

The Wyches seem to be more resilient then they appear to be at first glance.

Wow the witches are almost as hard to kill as 5 TH/SS Terminators. That's ridiculous! I never thought that 10 Wyches could be so deadly. It seems like it'd be better to shoot at the Wyches from afar rather than let them obtain their 4+ saves in close combat.

Thanks for all of the math hammering!

All wyches should be carrying haywire grenades, so it's doubly a problem for cuisanart-dreads.

On the bright side haywire grenades aren't quite as good vs dreadnoughts as they are vs vehicles that they might hit on a 4+ or automatic.

Grenades of any kind are a poor choice to fight dreads with. I've tried several times with haywire wychs (with and without shardnets) to take down dreads, and more often then not they simply tarpit the dread and then die. Kans are especially bad for wychs.

Overall haywire should be used more as a tool of opportunity against non-walker vehicles or to force them to move and perhaps forgo shooting. Against a dread, they give the wychs a small chance to do something, but will most likely won't.

Its funny, but both sides would rather shoot the other than assault. I've seen witches bog down a furioso dread from turn 2 until the end of the game at turn 7. By that point the dread had no arms and the witches were down to 3 models, it was a rather boring combat.

With the Wyches, Haywire Grenades are a problem. Even though they hit on a six, odds are good that you'll get hit by at least one, and that means a good chance to lose an attack the next round, not to mention the risk of losing an arm.

I still think charging Wyches is a somewhat better idea than TH/SS, as you have a good chance to make them test at -1 or -2. You probably won't catch them, but making them fall back might be enough. Charging the TH/SS is complete suicide, which is a pity because there isn't anything in a typical mech BA list that can really deal with them.

If you want hard numbers, I worked on this problem a while back.

Each Blood Talon attack has the following expected value

EV = P * ( 1 + P * ( 1 + P * ( 1 + P * ( and so on, infinitely) ) ) , where P is the probability of landing an unsaved wound.

Multiplying it out, this is:

EV = P + P^2 + P^3 + P^4 + ... P^infinity

This is a geometric sequence, whose value is easy to compute:

EV = - P / ( P - 1 )

For example, verus a WS3-, T4- opponent a blood talon has a 35/54ths chance to wound, so the EV is - (35/54) / (35/54 - 1) = about 1.84 - you can expect to cause a little less than 2 wounds, on average, every time you roll a Blood Talon attack. This is a huge improvement!

If you want to find the probability that one attack will cascade into x number attacks, you just have to consult a geometric distribution. Luckily enough, there is a formula for this - the cumulative density function. In this case, it's defined as:

CDF = (1/P)^(-x-1)

For example, the probability that a single blood talon attack causing four wounds (or more!) against the above opponent is (1/(35/54))^(-4-1) = about 11.4%, or roughly 1 out of every 9 rolls.

Now, this isn't a very useful calculation, as you'll rarely roll only one attack. Ususally, you're rolling 3, 4 or even 5 of them. What's the probability that 4 attacks will cause at least 10 wounds? Conveniently, the sum of multiple geometric distributions is represented by another distribution - the Negative Binomial Distribution, with the probability = 1-P and N=number of attacks. Inconviently, the CDF of the negative binomial uses a beta function and that thing is a mess to explain. Luckily, online calculators exisit so you don't have to deal with it.

CDF = 1 - BetaRegularized[1 - P, N, 1 + x], where x is number of successful wounds (or more)

Pluging this into Wolfram Alpha:

http://www.wolframalpha.com/input/?i=%281+-+BetaRegularized%5B1+-+P%2C+N%2C+1+%2B+x%5D%29+where+P+%3D+35%2F54+and+N+%3D+4+and+x+%3D+10

Gives us about 21%, so the Dread will roll up a Tactical squad about 1 in 5 times. Play around with the numbers and see what else you can figure out!

Interesting that my IG CCS of 5 manage to defeat 8 wychs charging them (In 2 combat rounds). Only the Officer's left with 1 wound, but 2 wychs were sent running.
Guess I never appreciate how lucky I was!