Anyone using mathhammer should be beaten with a funmallet in my opinion

 

...But, I ENJOY calculating chances T_T

Frankly, people who assume the average will work is kidding themselves.
Plan for the worst, hope for the best, that's the way to play.
If something NEEDS to die, make damn sure it will; if it dies before you're done, good for you, shoot other things.

 

Hmm well Deflier is WS 3 so each attack has 66% chance of hitting, Glances can't destroy it so we only care about pens, 33% chance of a pen. Of those pens only 5's or 6's can destroy it so again 33% chance. So roughly a 7% chance with each hit. With his 3 attacks on the Charge about 22% I would guess.

Aramoro

 

I also factored in the chance that the Defiler would kill him before he got to attack.
And I am absolutely certain that it was 1/~7 now.

 

I had made the assumption that the Sarg would have ablative wounds. If not things don't look good for our hero, Deflier has 3 attacks, hitting on 4's killing on 2's. So what a 72% chance to murder him before he gets to strike.

Aramoro

 

Oh yeah, it being a 1-1 fight was a part of the question (a friend asked me to calculate it, for no particular reason).

 

I'm afraid I don't understand your math. I'm not saying it's wrong, as it may very well be just over my head.

Why are you using ^? Shouldn't you just be using multiplication?

I mean, in the original example, if each bolter shot has a 17/18 chance of not killing the terminator, which translates into each shot having roughly (by my math) a 5.55% chance of killing the terminator. 5.55% * 18 shots = 100%, which is basically just saying that 1/18 * 18 = 1. I don't see what bringing it to the power of 18 proves.

 

No, you don't use multiplication.
To get the chance of, for example, two shots killing a Terminator, using the example chance of 10% per shot, you do:

10% chance for the first shot.
You get the remainder of the 100%, which is 90%, and then get 10% of that (the chance of the next shot doing it), which is 9% of the original 100%.
So you have a 19% chance of killing one Terminator with those two shots.

If you want the chance of killing two Terminators with two shots, you do the opposite.
You get the chance of killing one, 10%, and get 10% of that, which is 1% of 100%.
So a 1% chance of killing 2 Terminators with 2 shots.


If you have different chances, of for example 3 shots but you want the chance of killing 2 Terminators, it doesn't really matter how you order them.

It gets pretty complicated sometimes, but that's how I do it, the manual way

 

Odds and averages both have their place, it depends on the question. How likely a given weapon is to destroy a target (to know what kind of things you want to take), or a given model to take a wound (to know what kind of heat they can take) or similar things are odds. When you start rolling entire units against entire units with questions like 'how effective are dire avengers at shooting space marines v orks?' or more broadly 'what kind of offensive output can I reasonably expect from this unit?', then you're talking about averages which work out like a bell curve or normal curve (google it if you're unfamiliar with the term) as far as odds of getting numbers near those averages go.

You just need to realize that when using averages, you aren't guaranteed to get the average result. You will get within 1 standard deviation (again, if you're unfamiliar with statistics, look it up) of the average result ~68% of the time, within 2 standard deviations ~95% of the time, and within 3 standard deviations of the average result ~99.7% of the time.

Looking at the King of Cheese's numbers, they fall in pretty well with this idea.

Therefore, there is a 64.3% chance to kill the Terminator with the 18 shots, and a 35.7% chance that you wont.

Those seem to be about the numbers that the result will fall within 1 standard deviation of average. Not a coincidence. :wink:

Here's a normal curve so you get an idea of what I mean. Basically the fatter the section of the graph (with the average in the middle denoted by the greek letter sigma), the more likely an individual random result will fall there.

 

looking at these responses im gonna need a bigger mallet!

 

I don't know what this standard deviation thing is

 

Standard Deviation is pretty much what it sounds like, it tells you how much things vary from the mean.

The Wiki article is actually pretty good on http://en.wikipedia.org/wiki/Standard_deviation

I knew my maths during my during my degree would come in handy one day.

Aramoro

 

Ah, I see what the OP means now. I've actually heard this elsewhere, and the basic conclusion I've found is that while this method is indeed far more accurate, it's not very practical to figure out during the game. On the other hand, it is useful when deciding between units, such as in the 3 BS 4 shots VS 4 BS 3 shots example.

A good rule of thumb I use is that if you MUST destroy a target, you should throw twice as many shots/attacks at it that you would normally need to kill it, on average. It's not exactly accurate, but it's a lot easier to figure out.

 

Holy shit. My brain hurts after reading all of the numbers. I took statistics in college and I was never sure which hurt my head more... the statistics or the hangovers!

I generally use averages over probability. I do, however, recognize the difference between the two.

 

The only thing I would say on this topic is just know what your units strengths are and find targets that they will benefit off of those strengths. Using probability to dictate your games is never a good choice.

 

Haha it would be kind of funny to see someone with a laptop while wargaming, plugging into probability numbers!

I think the value here is in understanding what your units are capable of. If you know who your opponent is or what they will field, you can take that information and use probability to predict viable strategies. So rather than saying, on average my marines will do this, you can say, the odds of my marines accomplishing this task is this. And use that information to plot out a strategy.

 

Damn, I get on here to get away math class and now you guys are reminding me of that fucking calculus homework I should be doing right now.

As for averages or odds, I try to stick to my third meathod of mathhammer:
Put the situation into one of these two catagories "hes got a pretty good chance" or "hes totally screwed"

 

While i agree that most people go by pure instinct, some peoples opinions of what unit X can do to unit Y could be completely different to what the actual odds are.

For example, you might charge a mob of 30 Boyz into a Trygon thinking that with 120 attacks and only a 3+ save you are bound to kill it.... only to be disappointed when all you manage to do is piss it off lol.

 

...Wow.
Just did the numbers, assuming a squad of Shoota Boys, and that the Trygon kill 3 of them before they attack.
They deal 2.3 wounds, roughly :S

 

Alright math crunchers. Here's one for you. A squadron of 3 vendettas going for an av14 target. So you have 9 twin linked lascannons vs a monlith/land raider. What are the odds?

 

Oh dear, well, I'm gonna have a shower, I'll work on it after that

 

If we assume you want to destroy it, rather than just immobilise it (and considering weapon destroyed means very little to Mono's or LRs), we get the formula:

(1/2+1/2*1/2)*1/6*1/3= 0.042

(1/2 chance to hit + the chance you'll reroll a hit, which is the chance you'll miss (1/2) times the chance you'll hit on the reroll (1/2)) * the chance to penetrate (1/6) * the chance to destroy (1/3).

So approximately a 4.2% chance per twin-linked las to destroy it, 96% chance it does nothing. Now then:

(0.958)^9 = 0.68

(96% chance you don't destroy it, to the power of the number of chances you have (9 shots = 9 chances). It doesn't work the other way round, so you have to flip it to the chance that you won't penetrate, rather than the chance that you will.

So a 67% chance that you do not get a Destroyed result, or a 33% chance you manage to destroy it. Now, you'll probably get a few stunned/shaken results, and have a good chance to immobilise them, and possibly strip a few weapons, but there's a good chance it will still be alive and able to do something next turn.

The chance to immobilise, Stun or get a Weapon destroyed also have the same 33% chance of happening each. You'll end up shaking the target about 55% of the time.

For these numbers, I worked them out in a similar way to the "destroyed" chance. To work out the chance to immobilise, It works like this:

You have a (1/2+1/2*1/2) chance to hit. Now, it's a little more difficult with Immobilised/stunned results, as they're on two different charts (the pen and the glancing chart), but just remember that with either a Pen or a Glance, you have the same 1/6 chance to roll an immobilised result. That means you end up with

(1/2+1/2*1/2)*1/3*1/6 = 4.2% to immobilise - the same as for the destroyed result.

Shaken, meanwhile, has 4 different results on glancing/penetrating hits. Because each result on the chart has a 2.1% chance of happening, 4 possible results would be mean a 8.4% chance of getting a shaken result altogether, or a 91.6% chance of not shaking. So, using this (0.916^9) = 45% chance that you wouldn't stun, or a 55% chance that you would.

[Edit: After a request, I added stuff in quotes for information on how I calculated everything, and fixed a small mistake I made calculating other damage results

 

If we assume you want to destroy it, rather than just immobilise it (and considering weapon destroyed means very little to Mono's or LRs), we get the formula:

(2/3+1/3*2/3)*1/6*1/3= 0.049

So approximately a 5% chance per twin-linked las to destroy it, 95% chance it does nothing. Now then:

(19/20)^9 = 0.63

So a 63% chance that you do not get a Destroyed result, or a 37% chance you manage to destroy it. Now, you'll probably get a few stunned/shaken results, and have a good chance to immobilise them, and possibly strip a few weapons, but there's a good chance it will still be alive and able to do something next turn.

Thanks.

Interesting though, I thought they would have a better chance of destroying it.

 

You are now officially called mathhammermax.

 

Maddermax, first of all you got their BS wrong
It's 3, not 4, so a 3/4 chance to hit per shot, not an 8/9.

And I officially ragequit, I need more maths to be able to do that sort of thing.
I was, being a bit of a perfectionist, going to try and calculate the chance for every possible outcome, which in hindsight is fucking stupid.
I mean really, just figuring out the chances of different number of hits got up to 4^9, WHICH IS 292,144!

 

Maddermax, first of all you got their BS wrong
It's 3, not 4, so a 3/4 chance to hit per shot, not an 8/9.

Damn guard, giving their vehicles to the newbies while their vets walk around with small arms *grumble grumble*

At any rate, fixed. Made a surprisingly small difference, except to the chance to stun.

And I officially ragequit, I need more maths to be able to do that sort of thing.
I was, being a bit of a perfectionist, going to try and calculate the chance for every possible outcome, which in hindsight is fucking stupid.
I mean really, just figuring out the chances of different number of hits got up to 4^9, WHICH IS 292,144!

Bwahahahaha!

Be honest now, you're just rage quitting because you're going to make trouble in the rules forum while Klokk is away

 

This thread needs to be a sticky!

 

Calculating odds and averages seems a bit self-defeating to my thinking.

First it fails to take account of those times when the law of averages seems to go out the window. The number of times I've seen myself or an opponent rolling fives and sixes, to the point where someone jokes that the dice are loaded, makes a complete mockery of the idea that mathshammer can be a consistently useful tool.

Second, it takes the fun out of the game. As an Ork player I'm used to people scoffing at my shooting, then getting a shock when they realise that with Orks quantity is a quality all of it's own.

Finally as a great man once said sometimes you've just gotta to roll a hard six

 

That's a pretty naive point of view really.
It's not self-defeating to know approximately how your unit will perform against X other unit, it's a judgemental aid.
If you can say "If I charge that, I will, on average, kill it." then you're a damn sight more informed than just guessing.

 

Im glad other people are enjoying the thread as much as i did writing the OP.

And regarding the comments about luck playing a larger part than the statistics, thats all well and good when your rolling a single die, but over several games things will start to average out.

Rolling a 1 on a single die is a 1/6 chance, so luck can play a big part.
Rolling a 1 on 2 dice is a 1/36 chance, which statistics start to come into effect making the possibility a lot less likely.
Rolling a 1 on 3 dice is a 1/216 chance, and will rarely ever happen.
You might say "But it happens to me all the time".
Reason being (as someone else mentioned) is because the human brain only remembers extreme outcomes. In things like Wardollies you remember the big losses and that "luck" caused you to lose the game, where as you say that skill made your wins.
This is the reason why pokies are so addictive. They are designed so that you only remember your big wins and not your losses.


If you were to roll a single die, the possibility of the average total being 1 is just as likely as it is to be a 3 or 4.
If you were to roll an unlimited number of dice, the possibility of the average still being a 1 is 1/infinite, while the possibility of the average being between 3-4 is extremely likely.
To find the possibilities of the average of X dice to be within a certain range, simply refer to standard deviation.



At the end of the day, there is no such thing as luck, and i STRONGLY believe this.
I will be happy to smash a mirror over a black cats head whilst standing under a ladder to prove it wrong.

 

I will be happy to smash a mirror over a black cats head whilst standing under a ladder to prove it wrong.

You should take into consideration the outcomes:

Mirror with cat and lader event (if luck does exist): you are screwed mate
Mirror with cat and lader event (if luck doesn't exist): point proved

Probability luck exists: damn thats an interesting debate we ought not have

Still, lets assume PLE = PLNE = Cheese as we cannot prove either way:

MCLE(-) x Cheese = some number
MCLE(+) x Cheese = some number

So you got to weigh being screwed against being right, caution would be decision here :laugh:

Edit: and yes this is a good thread, it's enjoyable to work with, now the hard part - is it possible to make up a combat calculator (like those reference cards with moving bits in) and give weighting to the outcomes of common events?

 

meh, mathhammer always been a waste of time in my opinion, whats the point spending entire days figuring out the odds how unit X will perform against target Y?, seems pointless, when due to the random nature of the game unit Y could wipe X off the board every single game without any negative effect.

seems like your just wasting time when you could just get on with it and have fun instead of dragging the game down into a pile of meaningless numbers.

 

seems pointless, when due to the random nature of the game unit Y could wipe X off the board every single game without any negative effect.

If you like to play like that fine, but "due to the random nature of the game" I like to have at least an idea of what my chances are, otherwise I am just moving units around an hoping they do well.

seems like your just wasting time when you could just get on with it and have fun instead of dragging the game down into a pile of meaningless numbers.

Believe it or not some people find numbers fun, meaningless? definitly not, all games and strategy are comprised from essentially two things the maths + theory of the game and the psychology of the game. A good general uses both of these in the correct measures, sometimes you need to psych people but by 40k/WFB's very nature ultimately it comes down to numbers.

The difference is whether you want to min max your chances and understand how the units in the game interact or whether you are happy to go with gut every time - both are just as valid, one is actively working things out the other your brain is doing it all passively, if you are lucky then your brain is good enough at these things that it will calculate for you, but for me I prefer to do some rough estimates of chance to reduce its influence on my game.

As I improve my game I find myself doing more and more subconsciously, however on the really hard decisions I still go back to numbers.

 

meh, mathhammer always been a waste of time in my opinion, whats the point spending entire days figuring out the odds how unit X will perform against target Y?, seems pointless, when due to the random nature of the game unit Y could wipe X off the board every single game without any negative effect.

To be fair, it doesnt really take days. And probability tells you what the odds of something happening are, its not a method of predicting the future.

seems like your just wasting time when you could just get on with it and have fun instead of dragging the game down into a pile of meaningless numbers.

Its one of those personal choices isnt it? Some people dont care about the painting side of the hobby. Some dont care about modelling. There are many players who think fluff is irrelevent. And then there are people who think the mathhammer is a waste of time. And for those people it surely is. But some people will invariable find it interesting. Sure, someone could take it too far and program a whole battle via computing and just watch a script run and have it finally spit out a victor. Thats obviously too far. But to some mathhammer isnt a drag on the game, its a method of strategizing.


And the whole point is the numbers arent meaningless


tl:dr Mathhammer isnt for everyone, but it is for some