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Lord Squidar
16-01-2012, 15:06
Hi Guys,

Ok this is a question slash challenge.

I was walking to the store and just thinking about one of my favourite youtube videos, involving Leeeeeroy Jenkins.

Well he got the chicken in the end, hell yeah. BUT I was thinking about the extremely scientific way in which the dudes he interuppted were taking wow. Calculating points per second and so on.

So I was wondering, what is the ultimate math hammer army for 40k. the army that is mathmatically designed in all aspects to crush everything (MEQ).

I am no good at maths, I can hardly add 2+2 (3 right?) so was wondering if this has been done before, or is someone willing to take on the challenge?

maybe things to consider as well would be mission types and base size, profile of the models. Lets say the rules are must be a standard model from the box, no converting to get leopard crawling wraithlords and stuff like that.

Go forth mathlings and break the game (for fun and teh emperorz)

p.s. I am not going to build this list, i am an old softy when it comes to fluff :evilgrin:

Bunnahabhain
16-01-2012, 15:09
Dark Eldar. The whole army is almost designed to kill marines.

/end thread

inq.serge
16-01-2012, 15:14
Dark Eldar. The whole army is almost designed to kill marines. Basically everything

/end thread

QFT.

Just look at our tactica thread.

Righthandedtwin
16-01-2012, 15:22
Grab necrons and max your heavy on Doom scythes

/roll deathray
/game

Noobie2k7
16-01-2012, 15:31
I know there are already mathematical ways to look at things on W40K like all those ratingss like DLRPG and DMPS (dead land raiders per game and dead marines per shooting phase). Those are good ways of looking at how well your army can do against specific things. (i personally have not the foggiest how you work these things out though)

Lord Khabal
16-01-2012, 15:32
What?! Doom scythes are only good VS mechanized heavy armies...

bildo
16-01-2012, 15:33
gks all the way

Corvus Corone
16-01-2012, 15:35
Surely it depends how you mean 'mathematically best'?

Putting out most wounds?
Putting out most wounds with specific Ap?
Maneuverable (therefore most likely to postion for optimal effect)?
Most able to minimise effects of incoming attacks (shooting/melee)?
Or just able to roll the most dice??

It really depends what you mean by best. No one army will do all of the above. Specify.

The Marshel
16-01-2012, 16:08
you can't mathhammer wargaming like that. you can create a "best mathhammer" army but it's meaningless because you can't factor in terrain, movement, what your opponent brings etc

Corvus Corone
16-01-2012, 16:13
you can't mathhammer wargaming like that. you can create a "best mathhammer" army but it's meaningless because you can't factor in terrain, movement, what your opponent brings etc

Can you even do that? It depends what 'best' is, surely? There is no single mathhammer formula that says this army is an 8 and that one a 9 so that one is best. It has to be relative to something.

Scaryscarymushroom
16-01-2012, 16:40
I think the OP is giving us a really tall order.

Someone could math out an answer to the question, "Which is more likely to kill 10 space marines? 30 Ork Boyz or a points equivalent of Blood Claws?"

The trouble with coming to an answer is that so much depends on the roll-off for first turn; and then on cover. One could handle the issue of cover by assuming it is evenly spread, and assuming 30% of the table is covered in it. Then it would factor in to 30% of the movement phases and 30% of saves against (many) shooting attacks.

Of course, you would need to approach a project like this assuming that both hypothetical players are equally competent.

A while ago I saw a thread that proposed an idea for "diceless 40k." The whole concept revolved around averages. Does anyone have any experience playing that version of the game? I wonder how it affects the game balance?

xxRavenxx
16-01-2012, 16:55
A while ago I saw a thread that proposed an idea for "diceless 40k." The whole concept revolved around averages. Does anyone have any experience playing that version of the game? I wonder how it affects the game balance?

All diceless games are unbalanced, as you can then calculate the UNFAILING conclusion of a fight.

If the game starts and I can go, right, so my 10 guys do this, then you do this, then I do this, then I win. It isnt a game...

Corvus Corone
16-01-2012, 17:09
All diceless games are unbalanced, as you can then calculate the UNFAILING conclusion of a fight.

If the game starts and I can go, right, so my 10 guys do this, then you do this, then I do this, then I win. It isnt a game...

Yea I hear is chess is totally unbalanced. =)

Scaryscarymushroom
16-01-2012, 17:59
Yea I hear is chess is totally unbalanced. =)


Where is the like button on warseer?

Indeed! XD

I love chess! :p

Actually, black is invariably at a small disadvantage to white. White always takes the first turn.



Calculating the game based on averages would be the only way I could think of creating an ultimate mathhammer army.
Another issue: the distribution of armor saves. Power weapons are a waste of points against light armor, but against 2+ armor 10 power weapon wounds are statistically just as good as 60 ordinary wounds occurring in the same initiative step. Unless there is an invulnerable save on the model, as is the case with terminators. So, in determining the overall value of AP and close combat attacks that ignore armor, one would need to consider how likely it is that certain kinds of armor saves and invulnerable saves show up on the table. I think you would use only the rules that competitive players use in their games as a control for determining the statistical chance of running into 2+, 3+, 4+, 5+, and 6+ armor. For example, people don't like Kroot, so you don't factor them in to the % of models that could make up 6+ armor saves in a game. People DO like Wyches, however, so you would factor their 6+ armor in; but only in the shooting phase, as they have a 4+ invulnerable save in close combat.

There might even be a complex algorithm or a non-linear function that someone could use to determine point-value effectiveness of a unit based on the size of your game.


Warhammer is complicated! :o

micf2302
18-01-2012, 06:23
[This is the answer of a Ph.D. in Economics doing Game theory. Stop here if you are not interested]

I believe the question the OP ask is: What is the mathematically best way to maximize your chances of winning?

The question definitely has an answer. However, it is unlikely anyone will ever be able to answer this question (other then proving the existence of a solution) before I die.

The proof of the existence is quite simple, this is a Bayesian Nash Equilibrium (or a Sequential Equilibrium) after-all... However, the Sequential Equilibrium would most likely include randomization on which army to use by both players (This randomization could potentially be on the space spawned by all possible armies).

Game theory has been used to try to find the best strategy in chest, even that game is to overly computationally complex to solve given the current state of our technology. So I believe you will have to wait for an answer to your question.

So in conclusion:
Your question as an answer, and I have no freaking idea what it is!



[/edit]

Everyone else saying there is no way to solve this, or that the only way to solve this is threw average or whatnot are just completely wrong...

[/end edit]

The Death of Reason
18-01-2012, 07:40
The obvious solution is to go check out the most whined about army on warseer - IG/GK atm - then go check the army list forum to see whats the most common copy/paste variation on that list.

Since marines are the most numerous (despite their ingame rarity), people will gear their armies primarily to deal with them, so you should have some perfect examples there :)

The Marshel
18-01-2012, 07:41
Snip

[/edit]

Everyone else saying there is no way to solve this, or that the only way to solve this is threw average or whatnot are just completely wrong...

[/end edit]

sorry, but your answer is like saying "we can technically cure cancer, we just haven't figured out how to do it yet". If we don't have the technology to do it now, then we cannot do it now, ergo, saying we cannot do it is no less wrong then saying we may be able to do it in the future

micf2302
18-01-2012, 07:59
sorry, but your answer is like saying "we can technically cure cancer, we just haven't figured out how to do it yet". If we don't have the technology to do it now, then we cannot do it now, ergo, saying we cannot do it is no less wrong then saying we may be able to do it in the future


I beg to differ. This is math, the existence of a solution is often pretty easy to prove. It's proof will usually rest with ether concavity or a fixed point type of argument. Where your cancer analogy fail is that there is no way to prove that a cure to cancer does in fact exist. However, it is usually pretty simple (and most often trivial) to prove the existence of such an equilibrium. That we can't compute it, or that it's to computationally intensive change nothing to it's existence.

Beppo1234
18-01-2012, 10:38
[This is the answer of a Ph.D. in Economics doing Game theory. Stop here if you are not interested]

I believe the question the OP ask is: What is the mathematically best way to maximize your chances of winning?

The question definitely has an answer. However, it is unlikely anyone will ever be able to answer this question (other then proving the existence of a solution) before I die.

The proof of the existence is quite simple, this is a Bayesian Nash Equilibrium (or a Sequential Equilibrium) after-all... However, the Sequential Equilibrium would most likely include randomization on which army to use by both players (This randomization could potentially be on the space spawned by all possible armies).

Game theory has been used to try to find the best strategy in chest, even that game is to overly computationally complex to solve given the current state of our technology. So I believe you will have to wait for an answer to your question.

So in conclusion:
Your question as an answer, and I have no freaking idea what it is!



[/edit]

Everyone else saying there is no way to solve this, or that the only way to solve this is threw average or whatnot are just completely wrong...

[/end edit]

ma in econ here, trying to calculate the relative skill as well as the behavior of players is impossible in the case of 40k. But you could easily build probability trees for different ranges and weapon configurations. Ie. probability tree for a vanilla marine squad with a certain weapon build, and their rate of success and failure against another given unit, at the various ranges.

you'd end up with a huge spread sheet with chances of killing, and chances of dying at different ranges against the given unit. Enter the rest of the data, and fill down, and have these probs for every single unit of one flavour (success and failure) against single units of every other flavour.

then you'd have to account for speed and ability to jump from the one range to another. This would obviously be a flawed study, given that it would have to based on a flat playing surface where the minis move at each other without cover or tactics, but it would allow for a baseline picture, from which to start.

then you can complicate things by messing with unit sizes, multiple units, vehicles, special rules. One could look at point cost vs. theoretical effectiveness, or money cost vs. theoreticl effectiveness

I thought about doing this for a project in my game theory class actually, as the simple data is already there in nice chart forms. I would be interesting, because you could compare the theoretical data, to actual, and pump out some interesting statistical data about how a game went, and then figure out where the difference between the theoretical data, and the actual results comes from... be it the environment, the tactics, etc. But I just got lazy, and decided to study natural disaster damage vs. preparation with orbital data.

Rhana Dandra
18-01-2012, 11:10
It's a very difficult question to answer given the amount of variables.

There definitely IS an answer though and given time it will surface but not until we have the computational power to process the amount of variables (terrain, restrictions, the small 'chance' element etc.).

However, I have seen an IG list from someone's blog (can't remember where sorry!) that really looked like it couldn't lose whilst being matched-up to any tier 1 list.

That was at like 2500 pts though so unless you play that high, fear not.