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elvinltl
09-08-2007, 14:37
Well, i did some calculation based on MathHammmer and got some interesting results... Maybe my Calculation isn't really correct but i'll post the calculation.

Imagine i got a infantry that hits on a 2+ and wound on a 2+ ignoring amour saves.
Probability:
To Hit = 5/6
To Wound and kill = (5/6)(5/6) = 0.69444

Now imagine 2 infantry of the same,
Probability:
To Hit = 2 X (5/6)
To Wound and kill = 2 X (5/6)(5/6) = 1.3888
Which is equals to multiplying the initial probability by 2.

So 3 infantry will mean probability of killing 2.0833

It is kind of strange, in practice 2+ to hit and 2+ to wound ignoring amour saves usually mean a very very high chance of killing that will bring it to roughly 0.8-0.9 probability and yet Maths hammer says otherwise. As the number increase the probability drops slightly.

Is there a miscalculation? Do we need to use some complicated formulae?

Giltharin
09-08-2007, 15:57
It seems to me that's a matter of decimals, 5/6 = 0,833333333333333, so 5/6 * 5/6 = 0,694444444444445. By taking 0.69444 you proxy it cutting out some decimals. When you then multiply you start seeing the effect of the missing decimals.

Cheers
Giltharin

Bunnahabhain
09-08-2007, 15:59
Your maths is fine, it's your perception of in game numbers that's faulty.

Find a situation where you have lots of rolls like this ( war walkers with scatter lasers vs Guard?), and actually write down the results. You'll find they'll come out close enough to the calculated results. i will work if you're rolling enough dice, but if it's only a few a turn, odd results can easily show up.

susu.exp
09-08-2007, 16:04
While 3 models have a mean kill rate of 2.0833, the actual probabilities for killing n models is:
0 kills: 2.85%
1 kill: 19.45%
2 kills: 44.21%
3 kills: 33.49%

So 2 kills is indeed the most likely, the probability of doing better (33.49%) is greater than that of doing worse (22.30%).
Complicated formula used: Binominal distribution. Probability for k kills out of n models firing, each idividually with a probability to kill of p: P=B(n,k)*p^(k)*(1-p)^(n-k)
with
B(n,k)= n!/k!(n-k)!

Elektroniczny Morderca
09-08-2007, 16:46
Probability of killing something with two shooters is 1 - (Probability of failing both shots)

Probability of failing both shots = (1-0.694444) ^ 2 = 0.093364

Probability of killing something with two shooters = 1 - 0.093364 = 0.90663

FigureFour
09-08-2007, 16:58
This might be a little off topic, but has anyone else ever thought of making a MathHammer program so that they can just plug in their army list and find out who wins?

I swear to god I'm going to do it some day, just to spite all you wannabe statiticians.

susu.exp
09-08-2007, 17:29
@FigureFour: Iīve thought about why it wonīt work: Terrain. Canīt solidly quantify it and it makes or breaks armies. Iīve stopped caring about the general MH attitude, at least I can teach the kids something about Binominal distributions. What Iīd like to do is a webpage that explains statistics and stochastics using examples of 40k. Might even go into game and decision theory. Which will help people to realize that 40k isnīt just numbers and hopefully keep them from realizing they are actually learning (gasp) how math works...

FigureFour
09-08-2007, 19:35
Hahaha. It's not supposed to work.

It's a jab at all those people who think that mean MEQs killed per turn means something about a units performance.

And if you want to start a thread about how binomial distrobutions and game theory applies to Warhammer, you will be my hero.

Isambard
09-08-2007, 22:54
I am really hoping one of my maths students wants to do their High School essay on the application of Math-Hammer. I have a couple of likely candidates, and if I can them to do it, I will try and post it here.

shin'keiro
10-08-2007, 01:19
maths hammer doesn't work... its simply impossible to predict what dice are going to do! - it's silly!

RapidKiller
10-08-2007, 01:47
Imagine i got a infantry that hits on a 2+ and wound on a 2+ ignoring amour saves.
Probability:
To Hit = 5/6
To Wound and kill = (5/6)(5/6) = 0.69444
good job this is the probibility of killing the other model

Now imagine 2 infantry of the same,
Probability:
To Hit = 2 X (5/6)
To Wound and kill = 2 X (5/6)(5/6) = 1.3888
Which is equals to multiplying the initial probability by 2.

now this is where your equation goes up a certain creek without a paddle.

you did:
To Wound and kill = 2 X (5/6)(5/6) = 1.3888
this means: 2 times the probability of hitting and wounding

what you should of done was:
(5/6)(5/6) x (5/6)(5/6) = .48225
which means: P(robibility) model 1 hitting and wounding X P. model 2 hitting and wounding = the P. of both models hitting and wounding

So 3 infantry will mean probability of killing 2.0833

actually it is more like = .33489 = the probability of 3 models hitting and wounding

It is kind of strange, in practice 2+ to hit and 2+ to wound ignoring amour saves usually mean a very very high chance of killing that will bring it to roughly 0.8-0.9 probability and yet Maths hammer says otherwise. As the number increase the probability drops slightly.

Is there a miscalculation? Do we need to use some complicated formulae?

yep your formula was wrong. you just gotta know how probability really works. math hammer works fine as long as you know Probibility Distributions, bell Curves and normpdf (or is it normcdf)

note: as you increase the number of models the chance goes down that all those models will kill each of their opponents. if you want me to calculate the chance of say, 2 models killing one or more enemy's, tell me.

P.s. i never realized Principals of math 12 would help me so much;)

zeep
10-08-2007, 02:41
maths hammer doesn't work... its simply impossible to predict what dice are going to do! - it's silly!

I don't think you quite understand probabilities. ;)

I would however like to see a set of efficiency variable in most formulas.. representing generalship, terrain, Pt's mismatch, etc.

RapidKiller
10-08-2007, 04:18
math hammer just says what should happen with statistics and probibility

Higgen
10-08-2007, 09:54
Elektronic has the most useful statistic. It means that those two infantry have a 90% chance of killing at least one model.

Nurglitch
10-08-2007, 10:01
susu.exp:

The roll of terrain in calculating events seems to be reducible to the effect of cover saves and moving through difficult terrain, impassible terrain changing the dimensions of the game board (affecting the options available to units rather than their success in acting on options). The values derived from calculating the likelihood of the various possible outcomes of any attack are based on the number of models involved, which in turn depends on the relative positions of the models to terrain and to each other. Calculating the likelihood of success depending on arbitrarily chosen values for any definition of success (say, the likelihood of killing x number of Orks, if y number of bolter attacks from Space Marines where x is necessary to ensure retaliatory fire will result in the advantage going to the Space Marines).

Whether to a unit should assault would depend as much on the number of models you could expect to get into assault, assuming some random variable was involved like difficult terrain to navigate through, as the effect of those models in an assault against the number of models they can engage (which is, incidentally, a function of how many models can engage).

It seems that what you can do is input any starting position for any unit relative to any position you want them to be in an calculate the possibility of it reaching that position in some number of turns. They say no plans survives contact with the enemy, and to a degree that's true when a plan has an incomplete game tree. In Warhammer 40k it's a simple thing to graph the game's game tree as having a number of branches equal to the actions that each and every unit in the game can attempt during each turn. As turns are ordered, the options available to units over the course of games may change as they are destroyed, pinned, broken, entangled, stunned, shaken, immobilized, etc. If there were three units with two options a turn then each turn we'd have something like: ({{{) that would describe behaviour in the movement, shooting, and assault phases. But as with information regarding material (models and weapons) information regarding time and space (turns and position) needs to be inputted by the player.

Giltharin
10-08-2007, 10:45
you did:
To Wound and kill = 2 X (5/6)(5/6) = 1.3888
this means: 2 times the probability of hitting and wounding

actually it is more like = .33489 = the probability of 3 models hitting and wounding

Rapidkiller,
Actually both figures are correct, they just mean different things:

- 1.38.. is the expected number of wounds that two models both hitting and wounding on 2+ would score in a single round, provided they have one attack/shot each
- 0.33.. is the probability that said models score 2 wounds

Cheers
Giltharin

Moriarty
10-08-2007, 11:00
Cogito ergo sum, sed esse est non cogitare et cogitabat postulat non erat.

I think, therefore I am, but thinking isn't everything, and isn't always called for?

elvinltl
10-08-2007, 11:53
Hey but look at this...
2+ to hit and 2+ to wound the probability is 0.6944444444444 for an infantry shooting which is highly untrue in practice. It's roughly a 70% killing power which does not seems to reflect in reality.

Well, i've been giving my Autarch Fusion Gun which hits on a 2+ and wound MEQ T4 on a 2+ and i swear throughout the game he didn't even failed to killed a MEQ once. Even if he did it's maybe just 1 out of 6 turns. This makes the probability nearing 90% which does not tally with 70%...

Yes when the number becomes greater MathHammer works. I calculated my Warwalkers mass shots and they fired an average of roughly what i've calculated. It seems like as the number gets smaller and smaller MathHammer seems to become rather rigged.

There is also the fact Killing is affected by shooting. They are Mutually exclusive...

FigureFour
10-08-2007, 12:44
Hey but look at this...
2+ to hit and 2+ to wound the probability is 0.6944444444444 for an infantry shooting which is highly untrue in practice. It's roughly a 70% killing power which does not seems to reflect in reality.

ell, i've been giving my Autarch Fusion Gun which hits on a 2+ and wound MEQ T4 on a 2+ and i swear throughout the game he didn't even failed to killed a MEQ once. Even if he did it's maybe just 1 out of 6 turns. This makes the probability nearing 90% which does not tally with 70%...

You don't understand statistics then. You shouldn't expect a single case to demonstrate your statistical distrobution.

Yes when the number becomes greater MathHammer works. I calculated my Warwalkers mass shots and they fired an average of roughly what i've calculated. It seems like as the number gets smaller and smaller MathHammer seems to become rather rigged.

This is a fundamental fact of statistics. The more tests you do, the closer your average result will be to the probable result.

The "average" die roll is 3.5 on a d6. Roll me a d6 and get a 3.5, go ahead, try.

There is also the fact Killing is affected by shooting. They are Mutually exclusive...
Killing and shooting are NOT mutually exclusive. I don't think you know what that means.

guillimansknight
10-08-2007, 13:08
well mathhammer definetly dosen't work for me.

But thats probably because i can lose a 5 man termie squad to 10 Kroot even after shooting 4 SB's and a AC at them for two turns.
Im very unlucky thats why i NEVER win with guard or get a tank to survive beyond turn 3.

FigureFour
10-08-2007, 13:57
well mathhammer definetly dosen't work for me.

maths hammer doesn't work... its simply impossible to predict what dice are going to do!

Just out of curiosity, how do you people expect MathHammer to "work"?

It's not going to change the outcome of the game, or tell you what's going to happen . . .
Most of the time it's just a way for someone with a bad understanding of statistics to claim that one unit is "better" then another by badly aproximating it's performance in a limited area.

Nurglitch
11-08-2007, 02:45
I think, therefore I am, but thinking isn't everything, and isn't always called for? My latin must be worse than I thought! It was supposed to be "I think therefore I am, but to be is not to think and thought requires no being." Your version seems to preserve the import though.