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 scuddman wrote:

Everything you've said is simply opinion. I'm from the WAAC and play to win crowd. If you want to win, you'll devise and learn better methods. To YOU it's losing sight of the goal because the average method is good enough for you. That's it. It's all straight opinion. Fact is, people use the average method and make incorrect conclusions. If you're so hot, why don't you come up with a better solution? You clearly haven't been in the 40k forum here very long, Peregrine is an extremely competent player, don't let the fact he plays DKoK fool you, go look at some of his posts in the tactics section and look how quickly people are to call him a WAAC TFG because of the soundness of his reasoning. Sure the average method is incorrect, but so is Simpson's method of calculating the area under the curve, but that does not make it wrong to use, the real problem is people's lack of understanding, which going to be helped by your 'improved' method, especially when its underlying assumption is incorrect.

I sincerely doubted you knew a ten man tactical squad killing 3 on the charge was worse than 10%. Closer to 5%. There is a big, significant difference between a 12% chance of success and 5%. I bet the majority on this forum didn't know that. I think the average method is an incomplete and incorrect model that people use often to get incorrect conclusions. That's an opinion. You think it's good enough. I don't. We'll just agree to disagree and move on. The thing is, its not about whether you, Peregrine, or myself think close enough is good enough, it is the player base as a whole that decides, and their decision has already been made..

First of all, if you think that MTG is all about money then you're hopelessly wrong.

Fluff bunnies think like this. And when you go to a casino and gamble, idiots like you are the ones I want to play against in poker.
Huh, Peregrine called a fluff bunny, THAT is a first

No, but I don't need to know the answer with that much detail. My average is 1.666, which means that I need to kill almost double my average to win. I know that is not very likely, so charging is a desperation move that I'm only going to do if I absolutely need to (and in that case it doesn't matter how bad my chances are, I have to do it anyway). Knowing that the chance is exactly 10% instead of 7% or 12% doesn't really add anything to my decision.

It's not unusual near the end of the game to be faced with a situation where you have two options and it's not necessarily clear which option is the better one to take because both are risky. Even in those desperate scenarios, the average method is more than sufficient

http://math.stackexchange.com/questions/397689/why-convolution-regularize-functions/398146#398146

With 3+ dice the distribution trends towards a standard distribution. With squads rolling 30+ dice, it's pretty darn accurate.

But, If people think the average method is more than sufficient, than it is what it is.

 Peregrine wrote:
The most important test for gaming math is whether it provides useful information in a reasonable amount of time.

IMO, this is the test that the proposed method fails for the majority of players.

I don't think it's a bad method if it doesn't slow down the game, but if you got carried away with this, you could be adding 5 minutes per turn, depending on how many units are in position and how many targets you have. In a game that takes 5-7 turns, that's 25-35 minutes added to a game that already takes over 2 hours to play. If both players do this...

I would encourage judicious use of this method.

 scuddman wrote:
http://math.stackexchange.com/questions/397689/why-convolution-regularize-functions/398146#398146

With 3+ dice the distribution trends towards a standard distribution. With squads rolling 30+ dice, it's pretty darn accurate.

But, If people think the average method is more than sufficient, than it is what it is.

if you seriously 3 dice approach a normal distribution then you are not as smart as you think you are.

Yea using St Dev for this is stupidity from the start, we have several DISCRETE pass fail tests, this is not a continous data set> you should be using a binomial probability distribution or test, as I stated earlier. If you;d like a Markov chain would also work, but thats a little tougher in your head. Please re read what requirements must be met before using each different statistical method. The funny part is you're bashing the bad math off averages, which while wrong is still useful data. Your method is both incorrect and more work than it needs to be. Also i dont buy this whole square roots in your head thing all the ways to find square roots (continuous fractions, Babylonian method, newtons method et cetera) all require a fair amount of arithmetic and based on your flawed grasp of math i doubt you are any real prodigy.

if you seriously 3 dice approach a normal distribution then you are not as smart as you think you are.

Good job on taking it out of context. Maybe you're not that smart if you can't read what trends towards a normal distribution means.

There is a standard deviation formula for discrete random variables...would you have preferred that instead?


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And yes, binomial probability is better, but standard deviation works with the average method people love to use so much. My bad for trying to make it more robust.

Sorry everybody is such lazy asses. "It's good enough even though it's wrong!" "Oh I like the other more wrong method better because it's EASIER."

 scuddman wrote:
Sorry everybody is such lazy asses. "It's good enough even though it's wrong!" "Oh I like the other more wrong method better because it's EASIER."

Except the point you keep failing to understand is that the average method isn't wrong. It doesn't give as much detail as other methods, but it almost always gives the same answer to the strategy question you're dealing with. What you're doing is the equivalent of estimating how long it will take you to drive from point A to point B at 65mph and doing a ton of extra math to account for relativity. Sure, you can obsess over how accurate your answer is, but in the end you didn't really give yourself any additional useful information.


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 scuddman wrote:
To YOU it's losing sight of the goal because the average method is good enough for you.

No, it's good enough for everyone. You still have yet to give an example of a real-world 40k situation where the average outcome approach gives you an incorrect answer, while considering standard deviations gives you the right answer.

Fact is, people use the average method and make incorrect conclusions.

Sigh. Why do you have so much trouble understanding that people make incorrect conclusions because they don't understand the method, not because the method is wrong? If someone gets upset that they didn't kill exactly their average worth of marines you blame the person who doesn't understand the difference between an average outcome and a guaranteed outcome, not the method that provided them with an average outcome.

If you're so hot, why don't you come up with a better solution?

Because there isn't any need for one. I know how to do the more complicated math, it just isn't relevant most of the time.

I sincerely doubted you knew a ten man tactical squad killing 3 on the charge was worse than 10%. Closer to 5%. There is a big, significant difference between a 12% chance of success and 5%.

And, once again, the point is that I don't need to know. Just by looking at the average outcome I can tell that the chances of killing three MEQs are pretty bad. Whether it's 12% or 5% it's still something I'm only going to do if I have no other option (for example, clearing an objective at the end of the game with my only unit in range to do anything), and in that desperate situation it doesn't matter what the odds are because I have to do it anyway.

Fluff bunnies think like this. And when you go to a casino and gamble, idiots like you are the ones I want to play against in poker.

Sigh. You do realize that people play MTG casually without any money at stake, right? And that if all you care about is winning and don't enjoy the game there are much better gambling opportunities to exploit?

Also, how much money have you won by playing MTG? Because I'm starting to get the impression that you're one of those "big fish in a small pond" types who congratulates themselves on how competitive they are because they crush everyone at their local friday night magic and win $10 in store credit.

 scuddman wrote:

if you seriously 3 dice approach a normal distribution then you are not as smart as you think you are.

Good job on taking it out of context. Maybe you're not that smart if you can't read what trends towards a normal distribution means.

Strictly speaking data sets don't tend towards one type of distribution, what you don't seem to grasp is that apart from one or two actions that I can think of the top of my head, the data sets in a game of 40k (or even a game of fantasy, although they will more often) are not large enough to approximate a normal distribution, which means your application of the three sigma (empirical) rule is misguided and inappropriate at best.

 scuddman wrote:
There is a standard deviation formula for discrete random variables...would you have preferred that instead?

No, because it is completley unnecessary baggage.

Strictly speaking data sets don't tend towards one type of distribution, what you don't seem to grasp is that apart from one or two actions that I can think of the top of my head, the data sets in a game of 40k (or even a game of fantasy, although they will more often) are not large enough to approximate a normal distribution, which means your application of the three sigma (empirical) rule is misguided and inappropriate at best.

This just proves you're an idiot. Take the sum of 2 dice. What's the probability distribution look like? There's a bell curve with 7 in the middle. On the ends with snake eyes and box cars, you have a 1/36 chance.

Now take the sum of 3 dice. It's a smoother bell curve with 10 and 11 in the middle. Now take ten dice. There are now 60,466,176 permutations. The number of discrete possibilities is exponential. It trends towards a normal distribution. And you typically roll a LOT more than ten dice to shoot/assault, etc.

See it isn't the average sum if several dice that's important, its a pass fail system, I can pass two 3+ with a sum of four but fail half with 7. Please stop being condescending when your stated method is inherently flawed.

It doesn't matter if it's a pass/fail system. It's still exponential permutations and the probabilities are still in a bell shaped curve.

Whatever, imnot going to tutor you in math anymore. What you are doing is wrong ( not just tangent like an avg). The sum is irrelevant and the sum is highly Dependant on the Pervious rolls (why you need Markov chains) if you want to use this fine, but stop acting like some pied Piper of mathhammer.

 scuddman wrote:

Strictly speaking data sets don't tend towards one type of distribution, what you don't seem to grasp is that apart from one or two actions that I can think of the top of my head, the data sets in a game of 40k (or even a game of fantasy, although they will more often) are not large enough to approximate a normal distribution, which means your application of the three sigma (empirical) rule is misguided and inappropriate at best.

This just proves you're an idiot. Take the sum of 2 dice. What's the probability distribution look like? There's a bell curve with 7 in the middle. On the ends with snake eyes and box cars, you have a 1/36 chance.

Now take the sum of 3 dice. It's a smoother bell curve with 10 and 11 in the middle. Now take ten dice. There are now 60,466,176 permutations. The number of discrete possibilities is exponential. It trends towards a normal distribution. And you typically roll a LOT more than ten dice to shoot/assault, etc.

Since you don't seem to understand still, I will spell it put for you. The normal distribution is a very specific type of distribution that, unless you know very specific things about your population (all dice ever rolled in this case), since we do not know these things we are only allowed to assume normality in the case of a large sample size (30 or more). As I have repeatedly stated, there are few actions in regular 40k that are large enough.

This means that even if you find the standard deviation, you cannot apply the three sigma (aka empirical) rule since it applies only to normal distributions, you would instead have to apply Chebyshev's inequality (no more than 1/k^2 of all results can lie k deviations from the mean).
I cannot state this any clearer than I already have, if you need to, spend some time to mull it over.

I want a mathhammer program that will give me the probability of getting a result instead of an average result.

So an average result of 7 on 2d6 is relatively useless when trying to determine a charge. I want to see the chance of getitng a 9 inch charge.

Or I want to see the probability of my guy with three attacks getting 2 wounds. Not the average results. It will allow me to make more informed decisions and risk/reward returns.

So something like what is the probability of making that charge, 20% not as likely to try it unless the rewards are greater. What is the probability of my chapter master failing 4 wounds out of 10 shots? So on and so forth, it wont help in game but while thinking about it would be nice to have an idea. Especially if you could make a input variables and get outputs.

Probability helps me make more informed decisions than averages since I am NEVER going to play enough games for the averages to average out.

 Leth wrote:
I want a mathhammer program that will give me the probability of getting a result instead of an average result.

So an average result of 7 on 2d6 is relatively useless when trying to determine a charge. I want to see the chance of getitng a 9 inch charge.

Or I want to see the probability of my guy with three attacks getting 2 wounds. Not the average results. It will allow me to make more informed decisions and risk/reward returns.

So something like what is the probability of making that charge, 20% not as likely to try it unless the rewards are greater. What is the probability of my chapter master failing 4 wounds out of 10 shots? So on and so forth, it wont help in game but while thinking about it would be nice to have an idea. Especially if you could make a input variables and get outputs.

Probability helps me make more informed decisions than averages since I am NEVER going to play enough games for the averages to average out.

The thing is though, you can already get a general gauge on these things when you know the average, for example, a wave serpent firing a twin linked scatter laser and its serpent shield will average 7.56 hits from memory, so you can tell that the likelyhood of getting 6 or 7 hits is pretty high, whereas getting 10 or 11 is quite difficult, but you don't need to know exactly how unlikely it is you will get those hits, just that it is, whether the chance is 12% or 5%, you still know that you will only go for it if you have no other course of action.

 Leth wrote:
I want a mathhammer program that will give me the probability of getting a result instead of an average result.

I think its interesting to look at this stuff too. All you need is binomial distributions to calculate it. It only takes three inputs: number of trials (i.e. number of dice, label n) and the probability of 'success' for one trial (label p) and the number of successes you want to calculate a probability for (label k). So if you have 1/2 to hit, 1/2 to wound, and 1/3 to not save with 10 different dice, your three inputs are n=10 and p=1/12 and k=whatever you want. Plug those into the equation and viola you have your probability of getting k successes. (see http://en.wikipedia.org/wiki/Binomial_distribution for formula, its the first equation). Sounds cumbersome but if you have access to a decent spreadsheet program it makes it a snap to put in the formula (Excel has it built in even) and you can simply change the variables as you please. More importantly sum them so you see probabilities for things like '3 kills or more' rather than just '3 kills'. This is how one does breakdowns such as in my post above.

 Leth wrote:
I want a mathhammer program that will give me the probability of getting a result instead of an average result.

So an average result of 7 on 2d6 is relatively useless when trying to determine a charge. I want to see the chance of getitng a 9 inch charge.

I made this for your question:

Yep, but now imagine that chart with varying numbers of dice.

So what is the probability of an assault squad scoring 3 wounds on a target instead of seeing the average number of wounds.

If I only need three wounds than I want the probability of getting that or better. I dont care about the average.

The issue seems to boil down to the margin of error which people are satisfied with.

I think it is somewhat rash to dismiss such a method out of hand due to some impracticalities in its use.

Perhaps rough estimates work for you and I, and perhaps Binomial distribution would produce mildly better results, but completely bashing Standard Deviation's use in mathhammer into the ground is a little metathesiophobic.

 scuddman wrote:

This just proves you're an idiot.

Please try to remain civil.

 ImotekhTheStormlord wrote:
The issue seems to boil down to the margin of error which people are satisfied with.

I think it is somewhat rash to dismiss such a method out of hand due to some impracticalities in its use.

Perhaps rough estimates work for you and I, and perhaps Binomial distribution would produce mildly better results, but completely bashing Standard Deviation's use in mathhammer into the ground is a little metathesiophobic.

 scuddman wrote:

This just proves you're an idiot.

Please try to remain civil.

That's the problem though. If you want a quick mothball number use averages. As a whole they're good enough. But the math for binomial distributions and ST Dev. Are roughly the same complexity with binomial probably being easier. So I think it's perfectly justified to say using the method that is both more complex and less accurate is nothing but stupidity.

 ImotekhTheStormlord wrote:
The issue seems to boil down to the margin of error which people are satisfied with.

I think it is somewhat rash to dismiss such a method out of hand due to some impracticalities in its use.

Perhaps rough estimates work for you and I, and perhaps Binomial distribution would produce mildly better results, but completely bashing Standard Deviation's use in mathhammer into the ground is a little metathesiophobic.

It's not the use of standard deviation we have a problem with, its the use of an incorrect formula and incorrect underlying assumptions we have a problem with.

 Krellnus wrote:

 ImotekhTheStormlord wrote:
The issue seems to boil down to the margin of error which people are satisfied with.

I think it is somewhat rash to dismiss such a method out of hand due to some impracticalities in its use.

Perhaps rough estimates work for you and I, and perhaps Binomial distribution would produce mildly better results, but completely bashing Standard Deviation's use in mathhammer into the ground is a little metathesiophobic.

It's not the use of standard deviation we have a problem with, its the use of an incorrect formula and incorrect underlying assumptions we have a problem with.

Respectfully, that is untrue. Almost every post made by Peregrine and one or two others stated that the average method functioned well enough.

Also in a lot of cases in 40k standard deviation is pretty pointless. For example using your method I can find a standard deviation for shooting a melts at a tank and killing it. That is absurd, it either dies takes damage or nothing. The problem is you mean to use a method of statistical evaluation that is wrong for the situation. Its like me trying to use an orange instead of nails when building. Sure you end up with a final result, but it doesn't accomplish or mean anything.


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 ImotekhTheStormlord wrote:

 Krellnus wrote:

 ImotekhTheStormlord wrote:
The issue seems to boil down to the margin of error which people are satisfied with.

I think it is somewhat rash to dismiss such a method out of hand due to some impracticalities in its use.

Perhaps rough estimates work for you and I, and perhaps Binomial distribution would produce mildly better results, but completely bashing Standard Deviation's use in mathhammer into the ground is a little metathesiophobic.

It's not the use of standard deviation we have a problem with, its the use of an incorrect formula and incorrect underlying assumptions we have a problem with.

Respectfully, that is untrue. Almost every post made by Peregrine and one or two others stated that the average method functioned well enough.

Respectfully the average method was never in question, it is mathematically valid even if it's a little misleading sometimes. The problem is this standard deviation calculation which is obviously invalid if you have ever taken statiscal analysis or upper level math.


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 Leth wrote:
I want a mathhammer program that will give me the probability of getting a result instead of an average result.

So an average result of 7 on 2d6 is relatively useless when trying to determine a charge. I want to see the chance of getitng a 9 inch charge.

Or I want to see the probability of my guy with three attacks getting 2 wounds. Not the average results. It will allow me to make more informed decisions and risk/reward returns.

So something like what is the probability of making that charge, 20% not as likely to try it unless the rewards are greater. What is the probability of my chapter master failing 4 wounds out of 10 shots? So on and so forth, it wont help in game but while thinking about it would be nice to have an idea. Especially if you could make a input variables and get outputs.

Probability helps me make more informed decisions than averages since I am NEVER going to play enough games for the averages to average out.

Also just FYI im actually working on a program for my C++ class that will output either a probability for a specific amount and a probability distribution graph (vehicles are taking a while) I'll try to port it to android and iPhone when I finish it (hopefully ~2mobths) expect a link on dakka.

Well if you don't want to do it yourself there's more than a couple websites out there that have these sorts of calculators that will do it for you. I still haven't found anything easier than a simple spreadsheet