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Ragnos
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Ragnos

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PostSubject: ProbHammer   ProbHammer I_icon_minitimeMon Apr 08 2019, 15:00

EDIT: Visit me on www.probhammer.fun

Dear Archons,

as I really like the math behind 40k I use MathHammer extensively. Lately, I felt the need to get some more detailed information about the probabilities involved in 40k and decided to start a small project called ProbHammer (Probability Hammer).

I use Monte Carlo Simulations to calculate not only the expectation of the wounds like MathHammer does it, but also the probability distribution. Till now this was more a project for me alone, but I thought that I should share it with the community to get more input and suggestions.

Below is a screenshot to show you what I mean. The first graph shows the probability to do equal or more the wounds listed on the x-axis. The second graph shows the probability to do exactly the wounds listed on the x-axis.
ProbHammer Ice_sc10

Haywire and many other rules are still missing but should be added soon. What do you think? Who of you thinks this additional information could be useful?


Last edited by Ragnos on Sat Apr 20 2019, 12:31; edited 2 times in total
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Count Adhemar
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeMon Apr 08 2019, 15:46

That looks pretty good!

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dumpeal
Hekatrix
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeMon Apr 08 2019, 17:33

You should add disintegrator cannons
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Burnage
Wych
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeMon Apr 08 2019, 17:37

Definitely a useful tool from the looks of it - just working with expected value misses out on a ton of meaningful information.
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Ragnos
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Ragnos

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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeTue Apr 09 2019, 07:12

@dumpeal wrote:
You should add disintegrator cannons

You can calculate any weapons you want. Just put in the numbers into the text fields.

If you want you can download this early version from Dropbox.

The only problem is that you need the Matlab Runtime Environment which the installer will download for you. This is about 1.2 GB of Data.

EDIT: That's also a reason I would like to know if people are interested in this. If they are I could write the whole app in a different environment making distribution easier. But if this is just a project for me and my friends it's simply too much effort.
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dumpeal
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeTue Apr 09 2019, 16:51

I'm pretty sure people would be interested in it. You should make an app with a small add in the corner. You'd make some money. :-P
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Gelmir
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeTue Apr 09 2019, 20:48

If you made this into an app, I would totally download it!

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Faitherun
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeTue Apr 09 2019, 22:17

100% I would pay for this.

This is pretty awesome mate - nice work. When I have some more free time, I'll take a look deeper.

If you go the app route, I'd suggest having a free and paid version, with things like saving configurations etc in the paid.
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Myrvn
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeWed Apr 10 2019, 23:02

I like the idea, but I would probably use from my phone and the Matlab requirement would be a problem for me. These types of programs and reports from programs are pretty sweet.

Along these lines, I've been wondering about a simple assumption to use for math during a game. Calculating average damage is pretty easy, but with the whims of dice the average isn't a good way to estimate the number of shots to put into a target.

What do folks think of calculating the average damage for one point less of ballistic skill (or WS)? It isn't perfect, but it provides a ballpark for a "low end" of average.

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dumpeal
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeWed Apr 10 2019, 23:43

You could add an option to weight the effect of non-equal probability on the dice.

A guy empyrically tested the randomness of different set of dice and found that the 1's have a much higher chance to appear. You can read the complete test here.

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

Sorry for the link to another forum

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Ragnos
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeSat Apr 13 2019, 20:00

Thanks for the replies. I think I will port everything in a Java App. Started yesterday and it's taking shape by now. Managed to write the code for some bar plots and the basic simulation logic is in place.

As to the paid version I could think of free versions for PC and maybe apps for 1-2€ in the Google Play Store.

In any case, I will place a "donate" button somewhere to fund my coffee. ^^

I'll keep you up to date. I will probably need some testers soon.

ProbHammer Screen10
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Ragnos
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeSun Apr 14 2019, 08:42

@dumpeal wrote:
You could add an option to weight the effect of non-equal probability on the dice.

A guy empyrically tested the randomness of different set of dice and found that the 1's have a much higher chance to appear. You can read the complete test here.

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

Sorry for the link to another forum


As this is something that I could definitely do later on (I just need to alter the Dice class I use to create the random results), you came up with a good idea. I would like to change this thread a little bit, so everybody can post features she or he would like to have in the app.

Of course, I'm going to implement the stuff MathHammer has. The only thing I'm missing right now is all the mortal wounds stuff and dmg alteration like always subtract one or half the dmg.

Please everybody post your ideas and wishes. I'm not sure if I will be able to implement all of them, but I think this is a good start.

EDIT: I added a link to the current alpha build in the first post so everybody can test it.
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Ragnos
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeThu Apr 18 2019, 07:29

I uploaded a newer Version that should support most of our needs including direct comparison of different stats, re-rolls and mortal wounds.
EDIT: You can also switch between wounds caused and models slain.

ProbHammer Ice_sc11
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Creeping Darkness
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeSat Apr 20 2019, 12:17

Nice work, I love a bit of probhammer - definitely the distribution adds important information.

Out of interest, why use simulations for an approximate probability distribution when you could just calculate the actual probabilities? With 1m+ the simulations should be very similar of course...
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Ragnos
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PostSubject: Re: ProbHammer   ProbHammer I_icon_minitimeSat Apr 20 2019, 12:42

Thanks. I also made a small website www.probhammer.fun where you can download the program and find some small tutorial.

At the begining, I thought that I could do the calculation analytically, but then I figured out that it's not that easy. The re-rolls and special rules make it very difficult.

This is not a big problem if you are just calculating the average values, but for the probability distributions, this is a mess. The reason is that a single dice roll has an equally distributed result, but as you add more and more dice the distribution approaches a Gaussian (normal) distribution as described by the central limit theorem (law of large numbers).

This combined with re-roll and D6 values instead of deterministic values make it very difficult.

As for the simulations, 100k simulations should be enough for nearly any case. I tried to program efficiently by using only 1 Byte for each dice. If you have 20 dice for hit-rolls you have a memory consumption of 20*100k Byte ~ 2MB.
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