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I wrote a program that runs 100,000 shots from various weapons vs. various armor types.

* Edit : You can access this at http://uma-musado.com/cgi-bin/mathHammer.cgi

Double post.

Why did the Pulse laser
Times fired : 100000
Total Shots : 194422

Should it not have been total shots :200000

Just wondering

jbunny wrote:Why did the Pulse laser
Times fired : 100000
Total Shots : 194422

Should it not have been total shots :200000

Just wondering

If the pulse laser destroyed its target on the 1st shot, the 2nd shot is not fired.
That is done to prevent overkill from skewing the numbers and showing more deaths than it should. Imagine if both shots from the pulse laser destroyed the target, you would only want to count one kill. Not rolling the 2nd shot duplicates this effect
That is why multi-shot weapons roll less dice than one would think at first.

Alright i was just confused when I first saw it.

I am very interested to see how weapons stack up against living metal. Only suggestion I can make is the final numbers output should be to adjust percentages to an easier to read number. Remembering how many decimal places to move is difficult on occassion. But good work here as I see it.

Living metal only effects Melta's at half range, Bright Lances, and Assault cannons. All other weapons are uneffected.

Bright lances and Melta's would be treated as a Missle launcher for results (with the +1 to damage result exception for the AP1)

How come damage results 5 & 6 happen less than 4 & 5?

Shouldn't they be equal?

Furthermore, the computer program is flawed in that when you entered in BS3 at the beginning, it hit as if the shooter was BS4.

I'm a little curious as to why this is necessary. The math can be done without a finite number of individual trials. I don't really see what's being gained.

bonekrusher wrote:How come damage results 5 & 6 happen less than 4 & 5?

There will be more results for 1-4, save for melta weapons. That is because glances do 1-4 on the chart.

Ailaros wrote:Furthermore, the computer program is flawed in that when you entered in BS3 at the beginning, it hit as if the shooter was BS4.

I know there is a lot of data there, check again. You will find the time the shooter was hitting closer to BS 4 was when they were using a twin-linked gun. What I find odd is that I always thought a twin linked gun at BS 3 gave a 75% average hit roll, but for some reason its less.

Ailaros wrote:The math can be done without a finite number of individual trials. I don't really see what's being gained.

To test multiple scenarios without needing to run new math. Once you have built an engine that lets you run tests, you can just plug in any numbers you like and get the results. Once you have an engine built you can expand it to test squad vs. squad results.

But you can create a spreasheet to calculate the exact percentages, so you can also create a modifyable program to also calculate the exact percentages.

Furthermore, if you do that, you can also calculate the exact percentage to Wreck a vehicle no matter what the results are (i.e. taking into account cumulative Damaged results.) Perhaps a configurable number of times you are allowed to shoot at the same vehicle and have the Damaged results still stack.

Hooray for the Law of Large Numbers!

Not a bad beginner's programming exercise, though, since you can validate the results against the Mathhammer [or vice versa].

LMoE

labmouse42 wrote:What I find odd is that I always thought a twin linked gun at BS 3 gave a 75% average hit roll, but for some reason its less.

It is precisely 75%. BS3 means you hit 50% of the time. Re-rolling misses, you hit on 50% of the remaining 50% (50% of 50% being 25%). You therefore hit 75% of the time with TL BS3. So the program is faulty - my guess is that it may be calculating the rerolls using a different BS (a BS 3 original shot with a BS 2 reroll would give your results).
Alternatively, it may not be rerolling all of the misses.

DaveL wrote:

labmouse42 wrote:What I find odd is that I always thought a twin linked gun at BS 3 gave a 75% average hit roll, but for some reason its less.

It is precisely 75%. BS3 means you hit 50% of the time. Re-rolling misses, you hit on 50% of the remaining 50% (50% of 50% being 25%). You therefore hit 75% of the time with TL BS3. So the program is faulty - my guess is that it may be calculating the rerolls using a different BS (a BS 3 original shot with a BS 2 reroll would give your results).
Alternatively, it may not be rerolling all of the misses.

It is 75% chance to hit total for the weapon per shot but it is really two independent 50% chances that average to a 75% total. Labmouse' results look off because it is not rerolling if the shot hit on the first attempt. For example, if the computer rolls a 4, 5, or 6 on the first attempt the reroll does not occur. The program itself is accurate.

PanzerLeader wrote:

DaveL wrote:

labmouse42 wrote:What I find odd is that I always thought a twin linked gun at BS 3 gave a 75% average hit roll, but for some reason its less.

It is precisely 75%. BS3 means you hit 50% of the time. Re-rolling misses, you hit on 50% of the remaining 50% (50% of 50% being 25%). You therefore hit 75% of the time with TL BS3. So the program is faulty - my guess is that it may be calculating the rerolls using a different BS (a BS 3 original shot with a BS 2 reroll would give your results).
Alternatively, it may not be rerolling all of the misses.

It is 75% chance to hit total for the weapon per shot but it is really two independent 50% chances that average to a 75% total. Labmouse' results look off because it is not rerolling if the shot hit on the first attempt. For example, if the computer rolls a 4, 5, or 6 on the first attempt the reroll does not occur. The program itself is accurate.

Sorry, no. The way you're saying it should work gives a 75% chance of hitting in the end. I'll go into detail, and list each first roll hit with a "reroll" so that it adds up more easily for the kind of math you were trying to do. (Note, of course, that the actual value of the reroll doesn't matter if the first roll was a hit.)

First roll: Reroll: Hit?
1 1 N
1 2 N
1 3 N
1 4 Y
1 5 Y
1 6 Y

2 1 N
2 2 N
2 3 N
2 4 Y
2 5 Y
2 6 Y

3 1 N
3 2 N
3 3 N
3 4 Y
3 5 Y
3 6 Y

4 1 Y
4 2 Y
4 3 Y
4 4 Y
4 5 Y
4 6 Y

5 1 Y
5 2 Y
5 3 Y
5 4 Y
5 5 Y
5 6 Y

6 1 Y
6 2 Y
6 3 Y
6 4 Y
6 5 Y
6 6 Y

Number of hits: 3+3+3+6+6+6=27
Number of total possibilities: 6+6+6+6+6+6=36
27/36=.75 (75%)


Automatically Appended Next Post:
Rereading his post, though, I suspect that the actual problem with the program may be that he has the rerolls set up as if the firer had the default BS (4) instead of by misses, meaning that only 2/3 of the misses actually got rerolled.

DaveL wrote:Sorry, no. The way you're saying it should work gives a 75% chance of hitting in the end. I'll go into detail, and list each first roll hit with a "reroll" so that it adds up more easily for the kind of math you were trying to do. (Note, of course, that the actual value of the reroll doesn't matter if the first roll was a hit.)

DaveL is correct. BS 3 twin linked has a 75% of hitting.
In the program, this was being used to determine a reroll. if (($hitRoll > $neededRoll) && ($twinLinked)) { -- Reroll -- }.
The > should have been a >=

This has been corrected as shown in this thread
http://www.dakkadakka.com/dakkaforum/posts/list/302069.page

Or you can access the web version of this program directly
http://www.uma-musado.com/cgi-bin/mathHammer.cgi

Just wanted to say that I love this. Yes, you can in theory set up an Excel spreadsheet to do these calculations exactly, but due to the Law of Large Numbers the results will be almost identical. In fact, if you want greater precision, just increase the number of draws. This sort of procedure (called a Monte Carlo) gets used a lot in fields like Economics and Finance because it is often much easier to set up a simulation than, for example, calculate a probability because the exact calculation will require an integral, which may not have a closed form solution anyway.

Labmouse, if you were to add the ability to specify infantry targets as well as more than one weapon shooting (ie allow the comparison of 5 Fire Dragons to 5 Dark Reapers), this would be the only Mathhammer tool I think anyone would need.

I hereby 2nd the greatness of the tool. And, am anxious for the infantry page to be up and running, oh and gauss weapons, for us lowly necron players around here. Thanks!

Can you please fix your percentages? I don't like looking at 10,000 shots fired and seeing that 7000% of those shots we're Shaken results. That makes no sense to me.