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POwell0
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PostSubject: Math-hammer??!!   Fri Nov 25 2011, 06:11

Hi all,

So i have been reading through lots of posts and threads over the last few days and one thing seems to crop up a lot an thats Math-hammer.

Now it may just be me being stupid but can someone please explain to me why it is so readily used. I understand the mechanics of it but not the justification of it. To me the game we all know and love is dice based so it is therefore inherently random, and thats what is exciting and fun about. So saying that I dont really see much point in it.

Do people math-hammer out there whole armies for Uber optimisation? Would people not take a unit because the Math-hammer says it wont kill much?

Its a topic that intrigues and confuses me!
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Local_Ork
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 06:23

Indeed, people use mathhammer for über-optimisation, however also because most people suck at math.
This exactly how casinos get they money - if "players" would know odds, they would pick "lucky" games (or, frankly, none).

Would You consider taking 2 Ork Warpheads? People say they suck, I love that combo (odds of rolling 1 Zzap (36" S10 Melta autohit) are... 60%. Add pretty much auto-pass LD tests, easy pen roll and You can wreck Land Raider in 1 shooting phase (Orks can't do that, right? BZZZZZ, wrong.). I killed every single LR they saw, most from range. How that can be bad?)

[edit]
Also, zombies (number 4)


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Evil Space Elves
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 06:23

Math-Hammer is the only way to play 40k on the internet without actually playing a game Laughing
Seriously, it really is a way for people to demonstrate through basic statistics what is most efficient and theoretically best to use. I totally agree with your point that add dice+random crap that happens in the game and you get whatever happens.

I've never seen a formula for how to have the most fun playing a game either... tongue

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Thor665
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 07:09

You have issues with math but seem to understand that dice are used in this game. Via the math of probability it is indeed possible to predict dice rolls and narrow down the chances of a given roll. For example, get yourself 100 six sided dice and roll them - I'm willing to bet about 50 (or somewhere quite close to that number) of the dice came up 4+ Huzzah, math at work.

Yes, there will be statistical bell curve outliers, but mathammer is an excellent way to predict the expected effect of a given matchup.

If you don't care about using units that are "better" than others than you can happily ignore the mathammer and pick via what looks coolest or is the cheapest to buy or makes you giggle with joy when it's on the table top. Some people have enjoyment from building finely honed precision armies - others do not - both have fun with the hobby.
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 12:50

Mathhammer is not the solution to every problem, but one of the few that can be discussed and argumented about, becaus it is based on facts.
If someone wants help with his list, the only other, obvious and I'll admit, most of the time probably true answer would be: "learn to play!"
But if we assume, that the other is a good general the only thing we can argue about is his list composition.
On the other hand, a good tailored list can level the difference between the opponents or even tip the scale in favor of the inferior player.

@POwell0 wrote:
To me the game we all know and love is dice based so it is therefore inherently random, and thats what is exciting and fun about. So saying that I dont really see much point in it.
You are right insofar as that the dice roll is random, but the rules around are not. 40K isn't based on inherent randomness, but weighted probabilities, or it wouldn't work.
Let's look at humble guardsmen arming their trusted lasguns and firing at a talos. What would happen? The dice roll is completely random, true, but lasguns can't hurt a Talos, whatever you roll. So the rules diminish the random factors. Sometimes the rules give us a clear and solid 100% chance, like in this case, but more often they give us a probability.
If, for example some space marines used their bolters to shoot a talos, what would happen? Of course they actually can hurt the talos, but is it likely? If it was completely random, it would be as likely to happen, as not, but the probability here is 1/6.

As LocalOrk seaid, we humans have problems to understand and judge probabilities. So often units or weapons get missjudged, because we base our judgement on biased information, when for example someone tells us, how awesome/crap it is, we remember that. When someone tells us, that some unit or piece of equippment delivers a totaly mediocre, worth it's points, but nothing extraordinary performance, we either forget it instantly, or wonder why the hell he mentioned it.

This gets even more complicated, when we factor in points.
So marines produce 0.15 wounds per attack on whyches, while Wyches produce 0.05 wounds per attack on marines. So, is that good, bad, something else?
Fact is, that a wych costs 10pts, and a marine 16pts, so the wych is obviously cheaper. Additionally, the wyches strike first, so every wound they cause means they will suffer less retaliation; they have more attacks; fleet; etc., etc.

I often use mathhammer to see, if a unit can actually (or at least is likely to) perform, what I want it to do.

Of course it can neither predict outcomes of a game, nor tell us how fun it will be, I think that is good, since I want to play and not only calculate games, but for me it is part of the hobby, like painting and modeling are.

edit:typo

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misfratz
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 13:05

@Thor665 wrote:
..Via the math of probability it is indeed possible to predict dice rolls and narrow down the chances of a given roll. For example, get yourself 100 six sided dice and roll them - I'm willing to bet about 50 (or somewhere quite close to that number) of the dice came up 4+ Huzzah, math at work.

Yes, there will be statistical bell curve outliers, but mathammer is an excellent way to predict the expected effect of a given matchup....

Thor's post is exactly my problem with Math-hammer - it concentrates exclusively on the mean result, and *not* on the spread of the probabilities - which is a very important factor when considering reliability.

Let's take Thor's example of 100 D6 coming up with 50 4+ results. I used a random number generator in a computer program to simulate this test 10,000 times [this is called a Monte-Carlo test, something that would take ages with real dice!].

The overall average of dice coming up with 4+ is indeed very close to 50 [50.0146 in my test], however, the number of trials where exactly 50 came up with 4+ was only 787, or 7.87%. More than 90% of the time your Math-hammer assumption of 50 4+ will be wrong. With Math-hammer you have no idea of how wrong.

Where probability is used in risk analysis, people will want to know something like, what number of 4+ results will I roll more than 67% of the time? In Warhammer terms this equates to how reliably will you cause that 1 wound you expect. For Thor's example, my test tells me that about 69% of the time you would expect to roll 47 or more 4+ on 100 dice, and 97% of the time you would expect to roll 40 or more 4+ on 100 dice. So, Thor's average of 50 is quite reliable - this is because he is rolling 100 dice and the Law of large numbers decrees that you will tend to get much closer to the average with a larger number of tests. However, Warhammer does not often involve that many dice.

Let's take something more concrete from the Dark Eldar codex, say a Venom with two splinter cannons firing at tactical marines. We can all agree that the average number of wounds you would expect is 1.33, as the probability of a wound is (2/3) [probability of a hit] * (1/2) [to wound] * (1/3) [failed save] = 1/9 and you have 12 shots = 12/9 wounds. So most people expect at least one dead space marine, and will end up feeling aggrieved if it doesn't happen. But how likely is it?

Using a computer program to simulate it 10,000 times [or for a simple example one can use binomial maths to work it out], I can see that the probability of the Venom causing zero wounds is about 25%. I reckon that probability is a lot higher than most people would expect, so traditional Math-hammer sets people up to be disappointed, The probabilities are 35% for 1 wound, 25% for 2 wounds and there's a roughly 15% probability of 3 or more wounds. Go Venom!

Where it gets interesting is where you compare that to something else - say the blaster and blast pistol wielded by the kabalite warriors in that Venom. On average they will cause 10/9 wounds - slightly fewer than the splinter cannons on the Venom. However, the probability of them causing zero wounds is actually lower - about 20%, vs 25% we had earlier.

I want to repeat this, because it's important, and I think counter-intuitive. Two dark light shots cause fewer wounds on average than two stationary splinter cannons, but are more likely to cause at least one wound.

So there are at least two factors to consider. There's the average, which dominates internet Math-hammer discussions. Then there's a notion of reliability, which is ignored completely. There's also a third aspect - potentiality - where there's the potential of something brilliant happening [as with our Venom causing 3+ dead space marines].

I think that if you rely on the Math-hammer average too much you will be disappointed too often when the dice appear to go against you, because you are ignoring the large range of outcomes that are reasonably likely. Those "statistical bell curve outliers" happen a lot more frequently than people expect.

If people want to go all-out Math-hammer, then they should try to consider all three aspects: the average, the low-end and the high-end probabilities. Only then will they have a good understanding of the frequency distribution. Of course, one can also gain an intuitive understanding of this by testing out units in the game itself...

Sorry for the rant - it appears that numbers are something I take a bit too seriously...(!)
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 15:39

Mathhammer is more of a way to see on average what your should be doing. Its a good rough idea of how competitive your force is, and what you should be expecting from its output. Sure there is a range, and sure you dont always get what you wanted, but its just used as a rule of thumb for effectiveness.

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POwell0
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 20:31

I dont have issues with maths,i just dont think its a worthwhile venture in 40k terms. I was just asking why a lot of stock is put into math-hammer when it only takes into account what a given unit should be doing on average in a perfect world, using something that cant really be predicted IRL ie dice rolls. You can work out averages and use computer programs etc to tell you these things but so many variables are not considered.
If you want to go down the science root then factors such as the weight of the dice, the hardness and smoothness of the surface they are being rolled on, any imperfections in either the dice or the surface. Even air temperature and moisture can effect the outcome. Also maths doesnt take into account the most important thing, the actions and army build of the opposing player and the gaming board itself ie terrain, size etc.

You can work out that your squad of Wyches should kill X amount of marines in an assault, but if that unit gets killed before it assaults or ends up walking across the board and doing nothing of much value then all that work math-hammering out your army was wasted.





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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 21:10

[censored] happens, we can't help it.


Still, math (proper one) is best we can use to compare units before we field them. Also it IS more or less right most times.
Also, like someone pointed out more rolls mean more "accurate" results - and exactly on this my "perfect" army rely (cheap-spam foot IG). We also are one "accurate" race.

Also, math is context of unit - this is exactly why I always take NS and FF on any flyer. And NOT take any of those on Ravagers. Or bitch about Succubus beeing easy to kill. Or seriously think about Blast Pistol (and Blaster) on 5 man Warrior squad.
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 22:10

Its not about what they did in the perfect world, but what they will "most likely" do in the real world. Its like saying statistically 1 in every 400 kids have diabetes. That doesnt mean everytime you get 400 kids together, 1 is going to have diabetes. You might end up with 2,4, or even none, yet we as a race use statistics to define problems and show how things effect us as a people.

The same could be said about mathhammer. Knowing my venom statistically should do 4 wounds, and kills 1 marine a turn doesnt mean its going to do it every turn. Sometimes it does 3 wounds, and kills 2 marines. Other times it does 8 wounds, and doesnt even kill one. Its how the dice fall, but knowing what it should do made the venom an easy choice for me.

Mathhammer is also used to compare units. Take for example Mandrakes. They are terrible right??? Why so??? What made you decide that they are terrible??? Did you run them??? Have you tried everything you can possibly do with them??? Who has time for that. Run the math and you can see their shooting output is outdone by a venom, or even warriors, and their offense is overdone by wyches. Both of which are troop choices and have less contenders for a spot than mandrakes do. It easily shows what a unit can possibly do if given an average cercumstances. A mandrake squad has the ability to whipe a tact squad out in one turn, but it will almost never happen.

Also yes stuff can happen to your squads and wrenches can be thrown. Remember the saying the best laid plans of mice and men, 40k is no acceptions. Stuff like placement and battle plans cant be hammered out, and even the worse army can beat the best if they have a good general and the dice are on their side, but its a game, and you have to take that also into consideration. Mathhammer isnt the end all be all, but it helps when making a competitive list and seeing what you expect from each unit, so you can see your army as a whole and where things work together.

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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 23:15

I think this is my main problem with Math-hammer. People completely disregarding units as unusable just because the maths says so.
Now i will take your example of Mandrakes....Yes things can potentially do what they do better but until i have tried them out and seen them in action for myself, i wont disregard them just because a few numbers go against them. I will try them out over 2 or 3 games and see how they do. If they dont work for me then i will move on or give them a rest until i think of a different way of using them on the tabletop.
IMHO experience is better than a calculator any day.
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PostSubject: Re: Math-hammer??!!   Fri Nov 25 2011, 23:24

Agreed. I give every unit a try atleast twice, did that for the first 7~8 months to codex was out. What I can tell you though is there are some units that you just cant help.

Take mandrakes for example. They are suppose to be an assault unit, the problem is look at their price, and see what you get. for 2 more points than a wych you get a weaker save and +1 S, you also arent scoring, and cant get a special weapon with your sarge. You also compete in a slot that is overfilled with good units (incubi, trueborn, bloodbrides, and even grots) But what do you get??? outflank. Ok... but an outflank unit is suppose to be able to take care of back row tanks and devs. Well they cant beat devs in combat constistantly, and they can barely glance tanks.

Ok, so they cant do that, well what about their shooting??? Its actually decent, but they need to get a pain token first, which means combat, or haemie. Ok, so I drive a haemie up there, drop him off, and bam!!! Now I have a S4 shot shooting at a tank wall (if you pop said tank, then awesome. Shoot away!!!) But then you have to look at the price of said unit. You could get 2 and 1/2 venoms for the same price (bare haemie included) and do almost the same thing, from a safer distance.

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PostSubject: Re: Math-hammer??!!   Sat Nov 26 2011, 00:13

Yes i agree some units are just plain bad, but they still have a legitimate place in a codex even though they are out performe. They may fit better into someones playstyle or army Synergy better than something that is mathematically 'better'.

The way i see it with math-hammer is that a lot of the codex gets overlooked due to a few numbers:
As an example:
Unit X can kill 2.2 marines whilst Unit Y can kill 2.25 marines so forget Unit X and go with Unit Y, even though Unit X may work better in their army and/or playstyle.
It seems a bit backwards to me that one would math-hammer an army then have to develop a playstyle around it, whereas I believe it should be the other way around - build a list around your playstyle
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PostSubject: Re: Math-hammer??!!   Sat Nov 26 2011, 01:34

@misfratz - I don't get disappointed by figuring out the averages.
About half the time I perform below average, and about half the time I perform above average. You sound more like you're discussing people not understanding what averages are, and I guess that could lead to frustration - but whether or not that's true has very little to do with why people do mathammer. Even all your examples were mathammer assessing probability as opposed to averages, yet both sets of numbers are true it's just a question of what you're using them for.

I thought your issue was lack of understanding why people even used mathammer? Or are we discussing whether or not it is often used well?

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POwell0
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PostSubject: Re: Math-hammer??!!   Sat Nov 26 2011, 01:37

Both to be honest thor
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PostSubject: Re: Math-hammer??!!   Thu Dec 01 2011, 22:20

Frankly at levels that mathhammer demonstrated its not all that usefull for 40k.

Yes would be optimisers will show you most likely possibility, assuming there is vast numbers of dice throws, but they will also show exact same probabilites for say atacks involving far less throws (i.e. low amounts , ignoring armor saves) as if they thrown vast numbers of time.But they dont.

You dont really care about average if you use something once a game , it does not matter , you cant use that average.

And results shown for such units are simply unusable in the game , cause it have far more dispersion and results are shown as propabilities not mathematical expectation.

I.E. typical mathhammer will likely tell you that this unit/atack will kill on average 2 marines. But that mathhammer wont tell you what are probablities that same unit kill 1 or 3 marines. And are those probablities different for different kind of atacks/units.

It isnt demonstrated at that level cause its little more timeconsuming and difficult to calculate.And result isnt actually accurate, its variable.It have variety of roughly same probability results.

Long story short - if you see mathhammering for something regarding torrent atacks , armor saves like venom shoots or normal wyches torrenting marines results guys posting are fairly accurate and you can use them.

If they say each volley will kill about 2 marines - well thats about it 2 marines will die.Results that 3 marines will die or 0 marines will die are far more unlikely.

For other power atacks for example that average is not all that usable as you will notice from experience.And that does matter.

If venom volley is highly unlikely to kill above or below expectation , say several agoniser can vary in results more.Lower results are possible and higher as well.There is a place for ingame decision here, a bet , a risk.

Thats why vehicles are so bitch to kill , you have to push through Balistic Skill - Armor Penetration - Cover - Damage Table Result. It is more likely tp provide fairly accurate statistical output - and thats why meta changed to accurate statistical damage as well (auto cannons , scatter lasers , mass of missile launchers , psycannons etc...mass). When say powerweapon bitchy strikes target she have To Hit , To Wound. Thats it. More variable results because of lack of throws. Cant use accurate statistic here. Thats good and bad at the same time.

If rumours of the 6th edition turn out to be true and in Balistic Skill - Armor Penetration - Cover - Damage, Ballistic Skill and Cover will lose its weight i expect meta shift towards more destructive , less rate of fire AV weapons. More free variable space for lucky lascannons.

So regarding torrent atacks that cause armor saves - you can use em. Everything else - you better just experience yourself , your brain will calculate accurate probablities without your attention after long enough experiments , it is capable of learning without your effort.
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