Monday, May 18, 2009

Ordnance Armour Penetration, 2d6 Highest Roll Statistics, and the Melta Gun

One of the positive points about taking ordnance weapons and tank-mounted ordnance weapons such as vindicators is their special rule that they get to roll two die and pick the highest score. This means that they're probably going to penetrate a target quite often. But what are the statistics on "2d6 and pick the highest?". How does a demolisher cannon stack up against a melta gun at close range?

"2d6 and pick highest statistics".
These statistics apply to other situations apart from penetrating armour with a demolisher cannon - such as moving through difficult ground and so forth.

There are 36 possible combinations for rolling 2d6. I'm going to be incredibly dull and list them all here. I'm also going to detail the highest die roll (i.e. the outcome!) alongside them.

(1,1)= 1 (1,2)=2 (1,3)=3 (1,4)=4 (1,5)=5 (1,6)=6
(2,1)= 2 (2,2)=2 (2,3)=3 (2,4)=4 (2,5)=5 (2,6)=6
(3,1)= 3 (3,2)=3 (3,3)=3 (3,4)=4 (3,5)=5 (3,6)=6
(4,1)= 4 (4,2)=4 (4,3)=4 (4,4)=4 (4,5)=5 (4,6)=6
(5,1)= 5 (5,2)=5 (5,3)=5 (5,4)=5 (5,5)=5 (5,6)=6
(6,1)= 6 (6,2)=6 (6,3)=6 (6,4)=6 (6,5)=6 (6,6)=6

So, the final probabilities for each roll are:

Prob(1) = 1 in 36 = 0.028
Prob(2) = 3 in 36 = 0.083
Prob(3) = 5 in 36 = 0.139
Prob(4) = 7 in 36 = 0.194
Prob(5) = 9 in 36 = 0.250
Prob(6) = 11 in 36 = 0.306

Or, put another way, the cumulative probabilities are:

Prob(2+) = 1 - 0.028 = 0.972
Prob(3+) = 0.972 - 0.083 = 0.889
Prob(4+) = 0.889 - 0.139 = 0.750
Prob(5+) = 0.750 - 0.194 = 0.556

That means that you've got great than even odds of rolling a 5+ on "2d6 and pick the highest".

Demolisher Cannon vs. Melta Gun.
Here's the probabilities to penetrate a given AV using both a demolisher cannon and a melta gun at close range:

AV: Prob(Demolisher), Prob(Melta)
AV=10: 1.000, 0.972
AV=11: 0.972, 0.917
AV=12: 0.889, 0.833
AV=13: 0.750, 0.722
AV=14: 0.556, 0.583

Hence, the demolisher cannon is superior at penetrating all targets except AV=14, where a close range melta gun has the upper hand by a slim margin.

But the second major difference between ordnance and a melta gun is that a melta gun is a melta gun. What do I mean by that? Melta guns get a +1 on the result of the armour penetration roll since they're AP=1; conversely, at AP=2, demolisher cannons are worse at destroying vehicles. This is ultimately why meltas are so useful in 5th edition.


suneokun said...

It's preference really. Useful stats, but we're really dictated by how close you can get you ordnance or meltaguns. I'm keen on the Vanquisher Cannon, it's quite cheap and gives you the 2D6 penetration at 72" - the problem is that it doesn't add anything to the 'to kill' factor with only AP2.

eriochrome said...

Remember that there are lots of ordnance weapons other than just the demolisher cannon. Battle cannons and Earthshakers also get the pick high but start with the lower Strength value. The ordnance affect is also helpful on things like Monoliths and waveserpeants which deny melta's their extra die but do not affect the ordnance rule.

dverning said...

@erichrome: Actually, Wave Serpents specifically ignore the extra d6 for Ordnanace in the rule.
I believe the Monolith removes the extra d6 also, though it isn't specifically FAQ'd anymore.

eriochrome said...

It is not a extra d6 it is roll 2 and pick highest so they are not ignored unless specifically called. It is not a bonus die or a flat bonus to penetration. I know that monolith living metal does not ignore it. I cannot quote on the wave serpants.

Farmpunk said...

Mmmm MathHammer.

I'm actually eager to try out the new IG medusa Str10 Ap1 small blast with the extra D6 Armor Pen.

it's sounding like a good Anti-tank option. Of course, the regular shells at 36" are good as well.

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