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wuestenfux wrote:The probability to destroy a Falcon with holofield (never go out without it) not moving more than 12'' (no vector engines required) is
2/3 to hit * 1/3 to penetrate * 1/9 to roll 5,5 or 5,6 or 6,5 or 6,6, that is, 2/81.

Then add in the possiblity of cover saves, AP- or AP1 weapons, and you suddenly have very different numbers.

Oh and Tau Railguns markerlighted...make Falcons cry shizzle.

Nurglitch wrote:Excellent material so far nrs02004. I don't want to hijack the thread, but I was wondering if you could show us an example using Striking Scorpions.

I have this hunch that, if a Striking Scorpion Exarch does not get bonus attacks from its Mandiblasters and charging, that the Scorpion's Claw is one of three live options for assaulting Guard, Orks, and Space Marines (WS3, T3, I3, Sv5+|W4, T4, I2, 6+|WS4, T4, I4, Sv3+), rather than being the 'no-brainer' option per cost. The other options are the Biting Blade, and the Chainsabres.

If the Exarch assaults, and doesn't get the bonuses for the Scorpion's Claw, the numbers would be something like:

Scorpion's Claw

A2 S6 AP2 Pts15

Biting Blade

A3/4 S4-(7 v 8) AP- Pts5

Chainsabres

A4/5 S3 AP- Pts5 Re-roll to-hit and to-wound

Scorpion Chainsword & Shuriken Pistol

A5 S4 AP- Pts0

Scorpion's Claw

A2 S6 AP2 Pts15

Biting Blade

A4 S4-(7 v 8) AP- Pts5

Chainsabres

A5 S3 AP- Pts5 (Re-roll to-hit and to-wound)

Can you show how to check the veracity of this hunch?

So first we figure out the probability of wounding with each attack type verse each opponent (ignoring the biting blade for now b/c it's a bit trickier):

SCh&SP
guardsmen: 2/3*2/3*2/3 = 0.296
Ork: 2/3*1/2*5/6 = 0.277
MEQ: 2/3*1/2*1/3 = 0.111

SCl
guardsmen: 2/3*5/6 = 0.555
Ork: 2/3*5/6 = 0.555
MEQ: 2/3*5/6 = 0.555

Cs
guardsmen: (1-1/3^2)*(1-1/2^2)*2/3 = 0.4444
Ork: (1-1/3^2)*(1-(2/3)^2)*5/6 = 0.4115
Marines: (1-1/3^2)*(1-(2/3)^2)*1/3 = 0.16461

from here we have a few different approaches we can take:

1) we can multiply this number by the number of attacks to get our expected number of kills, which in this case works OK because we assume that we are fighting large squads and that we won't kill everyone.

2) we can calculate the median of a binomial (with n= number of attacks and p = probability to kill per attack) to give us the number which we will do better than 50% of the time and worse than 50% of the time.

3) we can actually calculate the distribution of kills ie. the probability of getting each number of kills, using a binomial distribution again.

So, now lets do each method:

1)
SCh&SP
guardsmen: 0.296 * 5 = 1.48
Ork: 0.277 * 5 = 1.385
MEQ: 0.111 * 5 = 0.555

SCl
guardsmen: 0.555 * 2 = 1.11
Ork: 0.555 * 2 = 1.11
MEQ: 0.555 * 2 = 1.11

Cs
guardsmen: 0.4444 * 5 = 2.22
Ork: 0.4115 * 5 = 2.0575
Marines: 0.16461 * 5 = 0.82305

2) As it turns out for a binomial, the median is either the integer directly above the expectation or directly below and takes a bunch of checking so we're gonna skip that (my girlfriend is pushing me to go out with her... so i'm short on time)

3) For the distribution (which is quite useful) we use our handy dandy R program (free!).

SCh&SP n=5
guardsmen: p = 0.296
0.172927194 0.363540125 0.305704196 0.128534719 0.027021503 0.002272263
Ork: p = 0.277
0.197556574 0.378445166 0.289984263 0.111100471 0.021282732 0.001630793
MEQ: p = 0.111
5.552759e-01 3.466570e-01 8.656678e-02 1.080867e-02 6.747823e-04 1.685058e-05

SCl n=2
guardsmen: p = 0.555
0.198025 0.493950 0.308025
Ork: p = 0.555
0.198025 0.493950 0.308025
MEQ: p = 0.555
0.198025 0.493950 0.308025

Cs n=5
guardsmen: p= 0.4444
0.05313418 0.21215445 0.33883660 0.27058175 0.10803803 0.01725500
Ork: p=0.4115
0.07058824 0.24678895 0.34512711 0.24132508 0.08437151 0.01179911
Marines: p= 0.16461
0.4068612802 0.4008513110 0.1579720473 0.0311277113 0.0030667907 0.0001208596


The numbers below each unit type are the probabilities of killing each number of guys (from 0 on the left, to the total number of attacks on the right)

Say you want to figure out the probability of killing 3 or more orks with chainsabres? You add up the 3,4,5 entries for chainsabres and orks.
0.241+0.0843+0.0117 = 0.337
so we have a 33.7% chance of killing 3 or more orks with chainsabres.

Anyhow, biting blade will be done later (my GF is attacking me with her vagSabres (always wound on 2+) so i hafta run)

but that's the gist of it. You can use those numbers to calculate what you like (I think having a little chart of these numbers would be damn useful to bring to a game, so I might write one up...)

winterman wrote:Brings back memories of P. Chem and the brain exploding math I had to learn back then.

P. Chem was the worst class ever. Nothing like doing mind numbing amounts of crazy ass math that, in the end, has absolutely no practical application. *sigh* I. Chem wasn't much better but at least it had less math and slightly more basis in reality as it was possible to perceive.

P. Chem.? No, that involves no real math. Representation theory of Hecke algebras is my favorite.

wuestenfux wrote:P. Chem.? No, that involves no real math. Representation theory of Hecke algebras is my favorite.

congratulations...? Sounds like you have been waiting all thread to write that.

congratulations...? Sounds like you have been waiting all thread to write that.

Thanks. But good job done here in this thread.

Zeta functions on lattice problems in additive combinatorics! can I have a cookie? :0) We should turn it into a game, you hafta start with something that ends with the last letter of mine, or we can make it the reverse alphabet game.

No real math in P Chem? I guess that explains why no one in the math department could help our class with the homework. "Eigen what?"

That any mathematician would not know of eigenvalues/vectors/functions is really implausible.

winterman wrote:No real math in P Chem? I guess that explains why no one in the math department could help our class with the homework. "Eigen what?"

ummm, your math department = fail. Also, 1 word: mathematica. It can find your Eigenvalues or just solve the DEs by brute force (assuming you were using eigenvalues for DEs in chem, as it doesn't seem like a very operator theoretic subject...)

nrs02004 wrote:assuming you were using eigenvalues for DEs in chem, as it doesn't seem like a very operator theoretic subject...

I think quantum mechanics is taught in p chem, and q.m. is all about operators. Any measurable quantity from classical physics, like position or energy, is an operator in q.m.

Hmm.. this thread has lost its focus.

YOU'VE LOST YOUR FOCUS! Good point on the quantum mechanics.

I say we consider the game of Warhammer 40k as a markov chain and go from there :0).

kick-ass thread...

here are a couple...

When people take 10 saves at 3+ and get mad when they only pass 6 of them. "that is below odds"

When your necron opponent picks up his 6 hits with gauss weapons and says "i SHOULD get a glance here"

The idea of truncation is a great one to introduce to the theory and math guys.

I don't have a mathematics background, so maybe someone can tell me if there is a name for this concept, but when I'm given a choice between a bucket of mildly effective shots versus a small handful of high strength low ap shots, I ALWAYS prefer the former. If they are roughly equivalent in projected wound output, I always prefer the set that has more potential wounds caused rather than less.

A good example would be a lascannon and an autocannon both shooting at armor 12. Mathematically speaking, they both have the same statistical chance of affecting a damaging hit (glancing or penatrating). The lascannon has a higher likelihood of penetrating. I always prefer the autocannon shot to this though. Because when you strip away the statistical average, the lascannon can only hit once, or miss, whereas the autocannon COULD get two hits, followed by two damage results. It's not likely, but in a game like 40k, occasionally creating situations that can go wildly well for you when your opponent rolls well below odds for saves, or when you get a sequence of good rolls...

The sequence of good rolls thing reminds me of the phenomenon known as "statistical clumping" That is another idea that I think more math hammer guys should know. Packs of results with a high density of '6's exist just as commonly as a more 'expected' result. But if you have rending weapons, or gauss... then seeing large clumps of results with no '6's, or seeing a small result set with a large amount of '6's in it, makes most players say "you're so lucky"

Great thread!.... more fallacies and misconceptions! I'll post again if i think of more.

I reject you, Mathhammer and all your vile works! The power of friendly gaming compels you! The power of friendly gaming compels you! The power of friendly gaming compels you! Leave this servant of the spirit of Warhammer 40,000 and retreat to the pit of nerd-dom whence you came! Praise Jervis! Praise Paul Sawyer! Praise Andy Chambers above all! (And bring back Epic Space Marine while yer at it!)

Yeah it was introductory quantum mechanics and yes the tutors were full of epic fail in my experience. I exagerrated a bit, as I am sure there was someone that could have helped, just not apparently when we went for help. In the end we ended up finding stuff on the internet and bugging our own professor. Also Mathmatica would have been useful but you couldn't take a computer with you for the test I did use it on some of the labs though IIRC.

Sorry for the OT.

So for common mathhammer mistakes, I think the one that is prevailent at the moment is the effect of the changes to blast weapons. Seems like alof of people are looking at the max possible scatter and freaking and not taking into account the 0" scatters or the large chance of low scatters for BS4+. Run the numbers and things aren't so bad.

I say we consider the game of Warhammer 40k as a markov chain and go from there :0).

I always thought that 40k is a hidden Markov model. The observer sees the output while the states are hidden.
The output is what is observed at the battlefield and the states correspond to tactics (how far am I away from achieving the mission objectives or winning the game).
In this model, the task is to calculate the most probable states from observing the output.

What happens when your dice roll into a bit of Terrain and they are an "edge"??? Huh? what then?

Quantum Theory-Big Bang Evolutionary egoists.....

Back OT.

Why is it, when I need to roll 5, 2+ saves, I only make 1? Thats Balls.

I have always taken Shep's 'take' on things too.

Hit twice, MAYBE, rather thon ONCE_MAYBE!(with punch)