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Old 14 May 2010, 19:48   #1 (permalink)
Shas'Vre
 
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Default advanced mathhammer

its always bugged me that while we can always find the most likely occurrence in any given situation by using mathhammer the probability of any given result (8 kills for example) always offered more challenge than we could prove we could handle (I have seen people with 'big computers' which could apparently calculate these things but I frankly doubt thier accuracy)

over the past week I've been working out a general formula for calculating the probability of a given set of results, which I've gone on to use to generate a general formula for hits, wounds and failed saves.

I'm using pascals triangle as part of this formula, nCr on your calculators. to understand any of this you'll need As maths or equivelent, I can explain it but not on this thread. pm me or try a revision website. I'll be using x^2 to mean x squared as well.

firstly the general formula:

when rolling (a) dice, with a success probability of (s/6), the probability that (b) wounds would be caused is:

aCb x (s^b)/(6^a)

this figure is exact so the possibility of, for example, 8 or more hits would be the sum of the probabilities of 8, 9 or 10 hits.


still following?


general formula for calculating the chance of a specific outcome when firing a unit of like weapons against identical targets

ALL letters must be known

when firing (a) shots the percentage change to cause (b) hits, (c) wounds and (d) unsaved wounds; with a hit chance of (h/6), a wound chance of (w/6) and a save chance of ((6-s)/6) is equal to:

100 x aCb x (h^b)/(6^a) x bCc x (w^c)/(6^b) x cCd x (s^d)/(6^c)


while in reality a, h, w, s and d are the only required values removing the others from the equation is almost immpossible and not really neccecary.

to calculate say, the possibility of 8 kills from ten shots all possibilities must be calculated separately (which I would define as an embuggerance) for this example that would be 10 hits, 10 wounds, 2 saves OR ten hits, nine wounds and 1 save OR 10 hits, 8 wounds and 0 saves OR 9 hits, 9 wounds and 1 save OR 9 hits, 8 wounds and 0 saves OR 8 hits, 8 wounds and 0 saves.

you get the idea.

I would write out an example but, frankly, I can't be bothered as I know I will be asked to work out specific so I leave it up to a race!!

the first example to be posted in full detail (unit A fires at unit B) will be calculated by me using the above method, including any overheats, heavy weapons and wierd and wonderfull things. I have gaurd, tau, chaos and various space marine codecies.

please bear in mind that this may take a while.
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Old 15 May 2010, 04:35   #2 (permalink)
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Default Re: advanced mathhammer

A worthy endeavor, though you should probably be aware that you are not the first...

A good primer and discussion on Probability Mathhammer can be found on the Advanced Tau Tactica forum. I'm fairly sure there are similar articles/threads here on TO.
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Old 15 May 2010, 06:41   #3 (permalink)
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Default Re: advanced mathhammer

I just tend to slap together the averages in my head. Gives me a good idea of what my units can do if I can't feel it for whatever reason.

*shrugs*

http://www.heresy-online.net/combatcalculator/
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Old 15 May 2010, 08:56   #4 (permalink)
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Default Re: advanced mathhammer

the heresy online calculator is a traditional mathhammer calculator and, while good, doesn't generate this type of data. it treats, for example, 20 s4 shots at Bs2 (6.6 hits) as being the same as 10 s4 shots at Bs4 (6.6 hits again)

this method would factor in the possibility that the 20 shot unit will hit with more than ten models, or the general reliability of the Bs4 unit.

the advanced tau tactica method appears to be very similar to mine, using both nCr and algebraic powers and responding well to simple working checks. I'll see whether it gets the same results as mine does, if it does its simply a different way of writing mine
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Old 15 May 2010, 14:57   #5 (permalink)
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Default Re: advanced mathhammer

Somewhere I have an excel probability mathhammer calculator, allowing you to put in Weapon Strength, BS, armor saves, etc., and get both an average and the probabilities of the # of kills. For the life of me, I don't know where I found it.
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Old 15 May 2010, 16:08   #6 (permalink)
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Default Re: advanced mathhammer

Heresy's calculator also shows the perecentages for any given result (i.e. chance to kill 1 guy, 2, 3, bla bla bla all the way up to the max # of shots). For example, ten marines firing on ten marines:

Wounds:Chance
0 : 9.483%
1 : 23.708%
2 : 28.153%
3 : 21.115%
4 : 11.217%
5 : 4.487%
6 : 1.402%
7 : 0.351%
8 : 0.071%
9 : 0.012%
10 : 0.002%

If you want to know the percentage of killing, say, at least X marines, just add up all the percentages from that number up.

Edit: This is my post 1111. Hee hee. :funny:
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5th edition stats (W/D/L)
Deathwing: 14/6/3
Tau: 5/0/3
Blood Angels (NEW): 10/1/3
Blood Angels (OLD): 27/5/10
Eldar: 10/0/1
Death Guard: 1/0/0
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Old 15 May 2010, 21:01   #7 (permalink)
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Default Re: advanced mathhammer

@unusual suspect: I'd really like to see that excell calculator, the old ones tend to iether be totally untested or false positives. for an example scroll down ;D

@crazyguy832: heresy's calculator is unfortunately a dud, the true value for 10 kills is: 2.868x10^-10 (which I calculated with old mathhammer as if I'd used my own formula it would have been my word against thiers) this is the probability of a hitXwoundXkill all to the power ten ((1/9)^10)

this is the problem when you can't see the working, which you can't with most computer programs performing this kind of advanced maths. checking some answers on paper is always advisable.


EDIT: as far as I know it is immpossible to put nCr into excell, rendering all spreadsheet based calculators flawed.

EDIT2: I have made an excell calculator that can do all the formula can which I can extend to make everything even quicker but you do have to insert nCr manually. if somone can run me through number-letter conversion or refference tables or something I can build a functioning formula
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Old 16 May 2010, 00:01   #8 (permalink)
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Default Re: advanced mathhammer

I mathhammer a lot, but I can't see myself using this. It goes to far. All I want to know is the % chance unit A will defeat unit B and how many turns that will likely take. And whats better, assault or shooting. Really thats what I am looking for.


The chance that 10 marines kills 5 marines... sorry, but doesn't interest me :-\. It doesn't seem useful in games. Knowing that statistically 10CSMs champ PF, 2 meltas will kill 7PMs champ PF 2 meltas in shooting or hand to hand gives me information I could use in battle. Knowing that I have a 1%(example) chance of killing 5 guys in one round of shooting is somewhat interesting but really not that useful. I guess what I'm trying to say is that I want to know what is most likely to happen.... not what the chances of one particular outcome are.

For instance. I don't care what the chances of rolling a 4 to hit a LR, then a 6 to pen, and then exactly a 5 on the dame chart is. I just want to know my overall chance of popping it.
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Old 16 May 2010, 07:54   #9 (permalink)
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Default Re: advanced mathhammer

thing is, this will tell you the overall chance of popping it while old mathammer won't.

say you fire 4 lascannons at it, you can kill it on 4 hits, 3 hits, two hits or 1 hit, or you can fail to pop it. only with this method can you work them out and adding them together is the only way you can work out how likley it is that you will destroy it
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Old 16 May 2010, 20:44   #10 (permalink)
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Default Re: advanced mathhammer

This will also show you how truly un/balanced some armies are for their points.
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