Wednesday, January 14, 2009

Super Simple 'Method 216'

Do not worry about your problems with mathematics, I assure you mine are far greater. - Albert Einstein

Today I'm going to explain to you a super simple method I've developed for quickly calculating how many of something you can expect to kill by shooting or close combat. I've named it 'Method 216' for reasons that will become very obvious to you when I'm done explaining how it works.

Before we get into 'Method 216', let's go over some very basic things about probability. Very often we are going to need to know how many sides of a D6 will give us a successful roll of the dice. This is quite easy to figure out. Let's say a Space Marine is shooting his bolter at a Necron warrior 18" away. The Space Marine needs a 3+ on a D6 in order to score a hit, so there are 4 sides of the D6 that will result in a successful roll, because a 3, 4, 5, or 6 will result in a hit. So if I were to ask you how many sides of a D6 will result in a successful roll in the previous example, you would say 4. The same would be true for rolling to wound, if a bolter with a S4 will wound a Necron warrior with a T4 on a 4+ then you would say 3 sides of a D6 will result in a successful roll.

Take note that in the case of your opponent making an armor / cover save it's a little different because a successful roll for your opponent is a failure for you. So because the Necron warrior needs a 3+ to make his armor save, then a 1 or a 2 will result in a successful dice roll for you. So if asked how many sides of a D6 will result in a successful dice roll for you when the Necron warrior rolls for his save, you would say 2.

Now then here is how the 'Method 216' works...

(H * W * S) / 216 = average number of kills

H = # of sides on a D6 that will result in a hit

W = # of sides on a D6 that will result in a wound

S = # of sides on a D6 that will result in your opponent failing his armor / cover save

Let's go over a few examples...

1) Space marine firing at a Necron warrior 18" away.

SM needs a 3+ to hit, a 4+ to wound, and Necron warrior needs a 3+ to save.

3+ to hit = 4 sides of a D6 to hit

4+ to wound = 3 sides of a D6 to wound

3+ armor save = 2 sides of a D6 to kill

Plug in the numbers and you get (4 * 3 * 2) / 216 = 0.111111

So the SM on average should kill a Necron warrior about 11% of the time, if you have a unit of 5 marines firing, then just multiply the .111111 by 5 to get .555555. Or in other words the 5 marines can expect to kill .555 Necrons per round of shooting.

2) 3 Necron Heavy Destroyers firing at a squad of Space Marines.

Necrons need a 3+ to hit, a 2+ to wound, and Space Marine does not get a save (S9 weapon vs T4).

3+ to hit = 4 sides of a D6 to hit

2+ to wound = 5 sides of a D6 to wound

no save = 6 sides of a D6 to kill

Plug in the numbers and you get (4 * 5 * 6) / 216 = .556

So each Heavy Destroyer should kill a SM 55.6% of the time, or as a squadron of 3, they should kill .556 * 3 = 1.667 Space Marines per round of shooting.

3) 12 Necron warriors shooting at a unit of Terminators less than 12" away.

Necrons need 3+ to hit, 4+ to wound, and Terminators need a 2+ to save. Necrons get double number of shots since they are within rapid fire range.

3+ to hit = 4 sides of a D6 to hit

4+ to wound = 3 sides of a D6 to wound

2+ armor save = 1 side of a D6 to kill

Plug in the numbers and you get (4 * 3 * 1) / 216 = .0555

24 shots * .0555 = 1.33 Terminators per round of shooting

Once you have done this a dozen or so times it should become very easy, and you should be able to figure it out during a game quickly using the calculator that comes with your cell phone.

That's it for today, hope this helps you crush your foes in battle, let me know if you have any questions. In the future I'll post some more advanced Mathhammer concepts.

- By the way, the number 216 that you divide by comes from the fact that to kill someone three dice rolls have to take place, hit, wound, and save. So 6*6*6 = 216. Chaos players might prefer to call this 'Method 666'.

6 comments:

  1. "Space Marine does not get a save (S9 weapon vs T4)."

    As far as I know this is not true as Instant Death only killes multiple wound models. They are still alowed a save in the case of strenght. They are how ever not allowed a save due to the AP value of the weapon.

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  2. This is interesting and useful. I'm more of a fantasy player myself but I can see this would work in the same way. One question I have is how would you go about quickly working this out in your head? The h*w*s I can do, but dividing by 216 is an issue. On top of that multiplying by the number of models in the middle of a game makes it even worse, and I'm not the sort of person who whips out his phone for a few quick calculations during a battle.

    I figure I can get away with dividing by 200, which makes it a bit easier. Any tips for doing this in your head?

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  3. Just divide by 2, then move the period over twice.

    EX: Necrons need 3+ to hit, 4+ to wound, and Terminators need a 2+ to save.

    4x3x1 = 12

    12/2 = 6

    Move the period over twice because of the 200, you get .06 which the full answer above was .0555555555 so it's a quick in the head way of doing it.

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  4. It's funny that you make probability more complex by dumbing it down.
    216 is indeed just 6*6*6. What you did is joining the top part of the fractions.
    I just use calculate each chance into a simple fraction.
    For example with the Space Marine shooting the necron warrior.
    2hit: 4/6= 2/3
    2wound: 3/6 = 1/2
    Failed save: 2/6 = 1/3
    If you now multiply those the actual math becomes easy.
    2/3 * 1/2 * 1/3 = Simpifie to= 1/3 * 1/3 = 1/9 = 11,11%

    I prefer this method as it can be applied to any number rolls you need to make (even RR's) and makes you appreciate what part of the roll is the most difficult to make.

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