First up, who hates mathhammer? Personally I'm not a big fan of the usual mathhammer so you're not going to see it here.

But even if you prefer experience over maths (as I do) there are some things I generally accept.

For example, I accept the probability of rolling a 6 is 1/6, or flipping heads is 1/2. If you're not comfortable with this kind of maths then I don't think you'll get a lot out of reading this post.

There are many varieties of space marines so I can't cover all the options, but I decided to show you guys some probability maths on falcons. Rather than saying "you will kill 1.829 falcons with this unit if you shoot for 6 turns", I'm going to say "you have a 0.109 chance of killing a falcon if you shoot this unit at the falcon".

I hope you can see the difference. The way I'm going to state these probabilities, "you have X chance of killing that falcon", it's exactly the same as saying "you have X chance of rolling a 6". So if you're not comfortable with mathhammer, but are comfortable with knowing there is a probability of rolling a 6, and a probability of not rolling a 6, then you should be fine with what I do here. I'm not going to say you are going to do the physically impossible and kill 0.256 falcons.

Ok, onto the usual suspects.

A marine squad shoots a lascannon at a falcon. What is the chance of killing that falcon?

The chance of killing the falcon is 0.0494, or 4.94%.

Now if you don't like maths turn away for a moment, I'm going to explain how I got that number. I took the chance of hitting the falcon, 2/3, multiplied it by the chance of glancing the falcon, 2/3, then multiplied it by the chance of immobilising or destroying the falcon, 1/9.

Ok now lets line this up with a nice looking list of weapons and probabilities:

Weapon - Probability

Plasma Cannon - 0.0247
TH Plasma Cannon - 0.0370

Missile Launcher - 0.0370
TH Missile Launcher - 0.0494

Autocannon - 0.0487
TL Autocannon - 0.0648
TH Autocannon - 0.0727

Lascannon - 0.0494
TL Lascannon - 0.0658
TH Lascannon - 0.0617

Assault Cannon - 0.0485
TL Assault Cannon - 0.0642
TH Assault Cannon - 0.952

So the clear winner here is the tank hunting assault cannon. Surprisingly, a lascannon is better than an autocannon, but not if they have tank hunters.

But this is not the whole story. What about the chance of doing nothing? The chances of each weapon doing nothing is obviously important because at the very least you don't want that falcon shooting.

Weapon - Probability

Plasma Cannon - 0.778
TH Plasma Cannon - 0.667

Missile Launcher - 0.667
TH Missile Launcher - 0.556

Autocannon - 0.605
TL Autocannon - 0.495
TH Autocannon - 0.444

Lascannon - 0.556
TL Lascannon - 0.407
TH Lascannon - 0.444

Assault Cannon - 0.624
TL Assault Cannon - 0.527
TH Assault Cannon - 0.366

Meltagun/Multimelta are the same as missile launchers, and within melta range are the same as a TH lascannon. Plasmagun is the same as a plasmacannon, and within 12" is the same as an autocannon.

Again that lascannon appears better than the autocannon. I believe there are many of you out there that still believe autocannons are better than lascannons when shooting at falcons.

You are all wrong.

Shooting an autocannon at a falcon is like trying to roll a 4+. Shooting a lascannon at a falcon is like trying to roll a 3+. Except we're using D10000's instead of D6's and the difference is smaller.

But you are still preferring trying to get a 4+ than a 3+ and that's just silly.

Let me make this clear. Rolling the D6 three times, to hit, to glance, and to destroy, is exactly the same as rolling one very large dice once (physically impossibly large).

Shooting a lascannon at a falcon is exactly the same as trying to roll a 9507+ on a 10000 sided dice.

Shooting an autocannon at a falcon is exactly the same as trying to roll a 9514+ on a 10000 sided dice.

So what do you prefer, a 9507+, or a 9514+? This is not on average, this is constant. You are always trying to roll that 9507+ with a lascannon! Always trying to roll that 9514+ with an autocannon!

Just to complete the analysis, lets use the same idea for the chance of doing nothing. With a lascannon, you need a 5560+ to do something. With an autocannon, you need a 6050+.

Ok I've done the weapons now I'm more interested in actual units. For example:

Question: A unit of terminators with 2 assault cannons and tank hunters shoots a falcon. What is the chance of killing that falcon? What is the chance of doing nothing?

Answer: 0.181 (18.1%) chance to kill the falcon, 0.134 (13.4%) chance to do nothing.

Question: A dreadnought with a twinlinked lascannon and a missile launcher shoots a falcon. What is the chance of killing that falcon? What is the chance of doing nothing?

Answer: 0.100 chance to kill the falcon, 0.272 chance to do nothing.

Question: A unit with 4 tank hunting heavy bolters shoots a falcon. What is the chance of killing that falcon? What is the chance of doing nothing?

Answer: 0.138 chance to kill the falcon, 0.243 chance to do nothing.

Ok that's enough of that, if you want to check how good your own units are against a falcon, keeping in mind that you should build your lists with the possibility of facing a falcon in mind, then read the following:

Vehicles

Vehicles can only die once. The mistake people make when calculating the probability of killing a vehicle is to double count the probability of killing it twice.

For example: Two Tau crisis suits with BS4 and twinlinked missile pods (autocannons) shoot at an open topped AV10 skimmer that's moved fast.

The mistake: Probability of killing the skimmer is:

#(shots)*P(hit)*P(glance)*P(destroy) = 4*8/9*2/3*1/2 = 1.19

This is wrong.

Correct way to do it:

1 - {1 - [P(hit)*P(glance)*P(destroy)]}^#(shots) = 1 - {1 - [8/9*2/3*1/2]}^4 = 1 - [1- 8/27]^4 = 0.755

That number again: 1 - {1 - [P(hit)*P(glance)*P(destroy)]}^#(shots)

Thanks for reading and good huntin'!