Find the error in my assault cannon math

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**Flavius Infernus**

Well one thing I notice off the bat looking over this thread is that in some cases I'm mostly looking at the odds of the weapon doing *anything* at all--that is getting a glance or pen or whatever. But some of the numbers here show only the chances of the weapons getting a "destroyed" result. I agree that it feels like ACs should get more pens, and therefore more "destroyed" results overall. I'm looking more at the chances of even just shaking the target vehicle.

Thank you, Mr. Economics, for new information. What you describe as the difference between 10d10 and 1d10X10 is something I've been trying to put a name to for years. Is there a name for it?

**Phryxis**

Six of one or a half dozen of another. 118 pennies or 118% of a dollar

Well, not exactly. You said the percentage listed was "the chance of a single shot/volley of 4 shots resulting in a glance/pen."

Thus, 118% would be more than a certainty of a Pen, when in reality it is not.

What you actually were providing is "the average percentage of 1 glance/pen created."

**labmouse42**

I am not the best on high end statics. I am good at programming though, and I wrote a perl script to simulate 100000 shots from a weapon If you want a copy of this, pm me and Ill email it to you. Otherwise I am planning on moving it to a web interface when I get some free time.

I have attached the actual combat results as a quote so you can see how the program flow works. You will notice how the AC did not fire 400000 shots. Thats because if the LR was destroyed on the 1st, 2nd, or 3rd shot the 4th one no longer was fired. That was done to prevent overkill.

100,000 assault cannon shots on AV 14

(10:49 AM)[labmouse42@] ~/Desktop
./mathHammer.pl
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
WELCOME TO THE WARHAMMER NUMBER TESTER!!

This program will guide you through the process of
testing your favorite weapon vs. your favorite armor
in the wonderful world of Warhammer 40k!

How do you want to crack some armor today?
1 : AssaultCannon
2 : AutoCannon
3 : BrightLance
4 : KrakMissle
5 : LasCannon
6 : MeltaGun
7 : MultiLaser
8 : MultiMelta

Please Enter Your Weapon of Choice : 1
Excellent choice sir! I'm a big fan of the AssaultCannon

What is the BS of your gun-wielding bunny? (4) : 4
I bet it a chaos marine! Scum!

Is the weapon twin linked ? (N) : Y
Two guns are better than one!

What is the AV of your target ? (12) : 14
Land raiders, true machines of war!

How many shots are you taking ? (10000) : 100000

Do you want the play by play ? (N) : N
Fine, close your eyes, coward...
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Times fired : 100000
Total Shots : 390797
Total Hits : 325550 83.3041195300885%
Total Misses : 65247 16.6958804699115%
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Total Plinks : 289074 73.9703733651998%
Total Glances : 18137 4.64102846234746%
Total Penetrates : 18339 4.69271770254122%
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Shaken Hits : 12106 12.106%
Stunned Hits : 5974 5.974%
Weapon Destroyed : 6066 6.066%
Immobolized Hits : 6148 6.148%
Destroyed : 3134 3.134%
Exploded : 3048 3.048%

100000 LasCannon shots

./mathHammer.pl
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
WELCOME TO THE WARHAMMER NUMBER TESTER!!

This program will guide you through the process of
testing your favorite weapon vs. your favorite armor
in the wonderful world of Warhammer 40k!

How do you want to crack some armor today?
1 : AssaultCannon
2 : AutoCannon
3 : BrightLance
4 : KrakMissle
5 : LasCannon
6 : MeltaGun
7 : MultiLaser
8 : MultiMelta

Please Enter Your Weapon of Choice : 5
Excellent choice sir! I'm a big fan of the LasCannon

What is the BS of your gun-wielding bunny? (4) : 4
I bet it a chaos marine! Scum!

Is the weapon twin linked ? (N) : y
Two guns are better than one!

What is the AV of your target ? (12) : 14
Land raiders, true machines of war!

How many shots are you taking ? (10000) : 100000

Do you want the play by play ? (N) : N
Fine, close your eyes, coward...
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Times fired : 100000
Total Shots : 100000
Total Hits : 83523 83.523%
Total Misses : 16477 16.477%
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Total Plinks : 55550 55.55%
Total Glances : 14020 14.02%
Total Penetrates : 13953 13.953%
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Shaken Hits : 9256 9.256%
Stunned Hits : 4750 4.75%
Weapon Destroyed : 4677 4.677%
Immobolized Hits : 4685 4.685%
Destroyed : 2317 2.317%
Exploded : 2288 2.288%

2 AutoCannon shots so you can see the logic

./mathHammer.pl
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
WELCOME TO THE WARHAMMER NUMBER TESTER!!

This program will guide you through the process of
testing your favorite weapon vs. your favorite armor
in the wonderful world of Warhammer 40k!

How do you want to crack some armor today?
1 : AssaultCannon
2 : AutoCannon
3 : BrightLance
4 : KrakMissle
5 : LasCannon
6 : MeltaGun
7 : MultiLaser
8 : MultiMelta

Please Enter Your Weapon of Choice : 2
Excellent choice sir! I'm a big fan of the AutoCannon

What is the BS of your gun-wielding bunny? (4) : 3
We are not afraid of Guardians!

Is the weapon twin linked ? (N) : N
No matter, we will do the job with what we have!

What is the AV of your target ? (12) : 11
Cracking some rhinos eh?

How many shots are you taking ? (10000) : 3

Do you want the play by play ? (N) : Y
You like to see the action ... I like it! weaponChoice = AutoCannon
BSskill = 3
targetAV = 11
targetShots = 3
Running the shots now
Dakka Dakka : Shot number 1
Shooting the AutoCannon
Shots from each weapon tap : 2
Min roll to do anything : 4
DAKKA! Shot 1 fired!
Random Shot Rolled : 6
HIT!
What is the armor we are shooting at? : 11
Is our weapon a lance? : 0
Is our weapon a melta? : 0
We dont need no fancy weapons to do the job...
What is our base damage roll : 1
How strong is our weapon ? : 7
What is our total damage roll : 8
Plink.....
DAKKA! Shot 2 fired!
Random Shot Rolled : 5
HIT!
What is the armor we are shooting at? : 11
Is our weapon a lance? : 0
Is our weapon a melta? : 0
We dont need no fancy weapons to do the job...
What is our base damage roll : 5
How strong is our weapon ? : 7
What is our total damage roll : 12
Oh, who's your daddy? Thats penetration for you
Rolled a 5 ... lets check results
DESTROYED!
Done with that shot, good shooting tex
Dakka Dakka : Shot number 2
Shooting the AutoCannon
Shots from each weapon tap : 2
Min roll to do anything : 4
DAKKA! Shot 1 fired!
Random Shot Rolled : 1
Doh....we missed the target sir!
DAKKA! Shot 2 fired!
Random Shot Rolled : 6
HIT!
What is the armor we are shooting at? : 11
Is our weapon a lance? : 0
Is our weapon a melta? : 0
We dont need no fancy weapons to do the job...
What is our base damage roll : 6
How strong is our weapon ? : 7
What is our total damage roll : 13
Oh, who's your daddy? Thats penetration for you
Rolled a 2 ... lets check results
Vehicle is STUNNED!
Done with that shot, good shooting tex
Dakka Dakka : Shot number 3
Shooting the AutoCannon
Shots from each weapon tap : 2
Min roll to do anything : 4
DAKKA! Shot 1 fired!
Random Shot Rolled : 3
Doh....we missed the target sir!
DAKKA! Shot 2 fired!
Random Shot Rolled : 1
Doh....we missed the target sir!
Done with that shot, good shooting tex

#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Times fired : 3
Total Shots : 6
Total Hits : 3 50%
Total Misses : 3 50%
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Total Plinks : 1 16.6666666666667
Total Glances : 0 0
Total Penetrates : 2 33.3333333333333
#-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=#
Shaken Hits : 0 0
Stunned Hits : 1 33.3333333333333
Weapon Destroyed : 0 0
Immobolized Hits : 0 0
Destroyed : 1 33.3333333333333
Exploded : 0 0

**Flavius Infernus**

Thanks for the numbers, labmouse.

From your simulation, it looks like what I would expect from each weapon shot. Individual assault cannon shots bounce off of armor 14 about 92% of the time, including misses. Individual Lascannon shots bounce off of AR14 only 72% of the time. Compared one-to-one, lascannon shots are more likely to do something--and I suspect that fact would carry through to AR12 and 13 as well.

The factor I don't know how to account for is the fact that you get 4 times as many shots with an assault cannon. Does the increase in damaging results from having 4 shots compensate for the much lower effectiveness of each individual shot?

Also, the simulation shows what I'd expect with the damaging results--that the AC is more likely to score a kill or immob result when it does get through the armor.

**labmouse42**

Flavius Infernus wrote:The factor I don't know how to account for is the fact that you get 4 times as many shots with an assault cannon. Does the increase in damaging results from having 4 shots compensate for the much lower effectiveness of each individual shot?

Yes, that is what happens. In the simulation, 4 shots are fired from one AC. That is what gives the AC its advantage.

As I show in the other thread, both of those percentages are pathetically small compared to melta guns.

**Dracos**

Flavius Infernus wrote:Also, the simulation shows what I'd expect with the damaging results--that the AC is more likely to score a kill or immob result when it does get through the armor.

Not entirely correct, they both have the same chance to get those results *when they get through the armor". What the results show is that the assault cannon is more likely to get through the armor

**Airmaniac**

Flavius Infernus wrote:The factor I don't know how to account for is the fact that you get 4 times as many shots with an assault cannon. Does the increase in damaging results from having 4 shots compensate for the much lower effectiveness of each individual shot?

Say a single Assault Cannon shot has a 5% (or 0.05) chance to glance or penetrate an AV14 Vehicle. The chance that at least one of the four shots will glance or penetrate is now:

1 - 0.95^4 = 0.1855 (or 18.55%)

So basically, you need to determine the chance that none of the shots will glance or penetrate, which is equal to failure chance for a single shot to the Nth power, N being the amount of shots fired. Substracting this chance to do nothing with all shots from 1 will give you the odds that at least one shot will glance or penetrate.

**Nurglitch**

All you need to do now is factor in range. Outside of 24" the Lascannon beats Assault Cannons hands down at everything. Likewise getting a Multi-Melta into the 12" range required for its Melta effect to make it useful does things to the numbers that are difficult to represent statistically.