The 2/3 Rule

When mathhammering one common problem we run into is how to deal with cover saves. Should we assume that units are completely in cover in the time? Or maybe it’s better to assume that they are out of cover all the time? Arguments can be made for both sides. While it is important to know how your units perform in and out of cover, it’s pretty difficult to come up with a good rule to use to judge longer range statistics, such as how many transports you can expect your Lascannons to take down in the first two or three turns of the game.

For these type of situations we turn to the 2/3 Rule. This rule, simply put, is to assume that units will be in 4+ cover two-thirds of the time. Given the abundance of 4+ cover saves and the relative rarity of its weaker and stronger brethren in 40k, this should hold true for most games. And mathematically it works out really well - just add a 5+ cover save to all your calculations(except when dealing with AP6 and AP5 weapons)! If you don’t believe me run the numbers for yourself and see what happens.

However the 2/3 Rule isn’t perfect, as is the case with all approximations. We know this but for the sake of gaining access to several turn statistics we find that using the 2/3 Rule is worth it. So let’s see an application!

I have two lascannons (S9, AP2) in my 1000 point Space Marine army. How many transports, on average, could I pop in the first two turns with them?

Assumptions:

Both lascannons are able to fire at an undamaged transport for the first two shooting phases

Both lascannons are being fired at BS3

All shots are against an armor value of the front armor of an average transport – AV12

‘Pop’ means immobilize or better

The 2/3 Rule

Calculations:

So in two shooting phases you should get 4 total shots.

Given a BS of 3, 2 of those shots should hit.

Rolling for penetration against AV12 we should get averages of 1/3 glancing and 2/3 penetrating

Applying the 2/3 rule, the 5+ cover save gets 2/9 glancing and 4/9 penetrating hits

Rolling for an immobilized result or better with a glancing hit is 1/6 thus 1/6*2/9=1/27

Rolling for an immobilized or better result with a penetrating hit is 1/2 thus 1/2*4/9=2/9

1/27+2/9=7/27 or .26

What does this mean? In the first two turns of the game if you fire both your lascannons at AV12 you will, on average, immobilize or better about once every four games. So in other words you might not want to depend on just two lascannons to have to pop enemy transports. Luckily for the Space Marines, they don’t have to. This is a perfect example of how mathhammer should influence your strategy.

Rule #1

Mathhammer is just one skill in a large skill set that a player must have to be a good player. In fact it isn’t even the most important one. I don’t claim to know all the skills that make a good player but I would rate mathhammer pretty far down on the list, trailing such things as knowing what your army and the enemy army is capable of, knowing the rules, tactics, strategy, deployment, etc. However, mathhammer can be used to influence or shore up deficiencies in almost all of these. If you find yourself facing a new opponent you can sit down and crank out a few numbers before the game to give you a rough idea of what you might be expecting from that opponent. If you aren’t quite sure how to deal with a threatening flanking unit, a quick number crunch can show the unit that is most likely to be able to deal with it. Being quick on your mathhammer feet can help a lot of aspects of your game and point you in the right direction, but it isn’t everything.

We can look at it in another way – good mathhammer is a good way to make up for lack of experience. Veteran players just ‘know’ what units can counter which units from watching and playing countless games. However we don’t all have the luxury of years of experience and the next best thing is a good application of mathhammer.

Unfortunately there are many, many bad applications of mathhammer out there, mostly due to unrealistic assumptions or missed assumptions. Such things as: enemy terminators are going to come charging coverless at my plasma, assaulting troops are going to stay a leisurely 12 inches away from my gun line for two turns, and my heavy weapons won’t have to move or won’t be engaged the whole game are all completely unreasonable things to assume. Any conclusion is only as good as its assumptions. Bad mathhammer can actually hurt you, making you believe something that just isn’t true.

So for all of you out there thinking that you don’t need mathhammer, unless you’ve seen every combination of every unit and every strategy out there I can guarantee that a proper application of mathhammer can up your game. And for those you wading exclusively in mathhammer and wonder why you’re still losing most of your games, try getting some other important tools in your toolbox. And always, always, always know and check your assumptions when mathhammering! In fact, that’s Rule #1 of mathhammer, the most important one.

Welcome!

Welcome to Advanced Mathhammer. Our goal is to push the envelope of mathhammer by exploring new, practical ways of applying mathhammer to Warhammer 40k game play and army development. This is a site for people who:

-love Warhammer 40k

-sometimes think they get a ‘buzz’ off of mathhammer

-enjoy math and/or statistics

-know how to debate without resorting to ad hominem attacks

This isn’t a site for people who:

-want to have an intellectual pissing contest

-don’t understand basic mathhammer

-like to make sexist, homophobic, racist et al. comments

Not sure if Advanced Mathhammer is for you? We aren’t either. Please take our welcome quiz to find out.

Is Advanced Mathhammer for me?

Welcome to Advanced Mathhammer. Not sure if this site is for you? We aren’t either. Try taking our simple five-minute quiz to find out.

1.) A unit of twelve Fire Warriors (BS3) equipped with Pulse Rifles (S5, AP5, Rapid Fire) fires on a unit of eight Space Marines (T4, 3+) eight inches away. On average how many marines will die?

A.) 8/3

B.) 4/3

C.) 2? Maybe 3?

D.) None! I always make my Armor Saves on my Space Marines!

E.) How can a third of a marine die? Mathhammer is so dumb.

2.) After some brilliant tactical maneuvering and much gnashing of teeth you manage to get your unit of six Fire Dragons with their Fusion Guns five inches from the enemy’s Land Raider. You open fire and get three penetrating hits. Assuming the Land Raider has three weapons, what are the chances of destroying or exploding it?

A.) 87.5%

B.) 75%

C.) Pretty good.

D.) 100% - My land raider always gets killed by stupid Melta’s. It’s not fair!

E.) 50%. Either it dies or it doesn’t!

3.) You move of your Infantry Platoons of ten members including a Veteran Sergeant (Ld 8) to block line of site to your Leman Russ’ side armor. The enemy tries to wipe them out of the way but only kills four. You have to take your break test. What are the chances of your platoon heading for the hills?

A.) 5/18

B.) 5/12

C.) Not that good? Leadership 8 is pretty good.

D.) With me probably 100%. I’m so bad at taking leadership tests.

E.) I don’t care my Leman Russ is totally going to KILL YOUR FACE NEXT TURN OMG!!!11!!!

4.) When you see ‘mathhammer’ on the internets what is your first thought?

A.) Groan. Let’s see what they got wrong this time.

B.) Let’s pull out the old calculator.

C.) Eh. I hope my brain doesn’t hurt too much this time.

D.) I don’t get it.

E.) What’s going on? So many numbers… YOU GUYZ ARE SO LIEK TOTALLY NERDS!!11!!!!

If you answered mostly…

A – This site is for you. You’re a top notch mathhammerer. Please feel free to contribute and comment as much as you want.

B – You’re almost there, but not quite. Best have someone check over your calculations before posting too much.

C – Your head’s in the right place but you aren’t. Go learn some basic mathhammer and come back when you are ready for more.

D – You don’t get Mathhammer. You will get very little (besides headache and frustration) from reading this site. If you’re interested in learning mathhammer, this isn’t the place.

E – Yes I’d like fries with that.