Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

First of all, this model isn't completely accurate either compared to the average method everybody uses, but it's a lot more accurate. It's actually incredibly simple. You can find on any number of websites that the standard deviation of rolling N six sided dice is: (Sqrt(N x (35/12)))/N
As a simple recap, 1 standard deviation encompasses 68.2% of all possibilities, and 2 standard deviations encompasses ~95% of all possibilities.

It works really well with the average method. Say I have a basic tactical squad with 20 attacks on the charge attacking meq. The squad has 20 attacks * (1/2) chance to hit = 10 hits
Then 10 * .5 chance to wound = 5 wounds. Then of that 5 wounds, 1/3 will fail armor saves and on average you will do: 1.666 wounds To keep it simple, I'll assume that you will roll the average number of dice: 20 (roll 20 times to roll to hit) + 10 (roll 10ish times to roll to wound) + 5 (roll 5 times to see armor saves)
So N = 20+10+5=35

You do all the math and you'll get 0.28867 as your standard deviation. You'll have 0.5777 for 2 standard deviations

So instead of saying you'll do 1.66 wounds, you can now say:

I do 1.66 wounds +/- 0.58. ( or a range of 2.24 dead marines to 1.06 dead marines 95% of the time)

SO guess what? 10 marines charging will do 1 to 2 dead marines NINETY FIVE percent of the time. Pick up some dice and test it! You'll see it's pretty accurate. I think that's more useful than saying you'll do 1.66 wounds. For ease of use, I suggest programming it into a calculator or using excel or creating an app.

BTW, this is my way of showing that this game is not all that random, and that for the most part results can be predicted with a 95% accuracy.

EDIT: Of course, this method has some flaws. For instance, the dice rolled are NOT perfectly independent. After all, how many dice you roll is determined at each step. You roll more hits, you roll more dice. Simply put, rolling more hits should DECREASE your variance and rolling more hits should INCREASE your variance...but this model is simple enough to use and understand for most applications.

While it is a nice piece of maths you have done, it doesn't really tell us much more than we already know, the standard deviation is nice to know, but when comparing the firepower of various units, it is completely unnessecary.

It does though. This is why I don't like the average method. I'll see someone say before rolling, "I should kill 2 marines on average!" Then he's upset when he only kills one. He doesn't know that only killing 1 marine instead of 2 was pretty normal. I don't advocate it to compare units firepower...I mean using it to justify/not justify tactical decisions...like should I charge or not.

It also has another practical application in reverse. If I want to kill x number of marines, how many shots do I need to effectively do it 95% of the time? Now you can quickly solve for it.

 scuddman wrote:
I'll see someone say before rolling, "I should kill 2 marines on average!" Then he's upset when he only kills one.

That's not a problem with the math, it's a problem with stupid players that don't know the difference between an average outcome and a guarantee. The vast majority of the time you don't need standard deviations or other complex calculations, you just need an average outcome and the knowledge that dice are random and the real probability is a bell curve around that average.

I mean using it to justify/not justify tactical decisions...like should I charge or not.

But knowing the standard deviation doesn't really help you with that situation. Let's look at your example of killing 1.66 marines on the charge +/- 0.58 marines with a 95% probability. Just by calculating the average of 1.66 I can just round it to 1-2 and get almost the exact same conclusion as your 1.06-2.24. And, more importantly, I can do it without a calculator: 20 attacks = 10 hits = 5 wounds = a little under 2 failed saves. Now without a calculator I know that I'm pretty likely to kill at least one marine, have a reasonable chance of killing two, but shouldn't expect to kill three.

Or I guess you could benefit from the standard deviation calculation by having your opponent pack up and find someone else to play after they get tired of having to wait while you get out your calculator and do math before making any choices.

If I want to kill x number of marines, how many shots do I need to effectively do it 95% of the time?

Or, since you're already doing complex math, you could just look up a binomial probability calculator and find the shots required for any arbitrary chance to kill X marines, not just the ones that line up neatly with the standard deviation.

Just because the average is 1.66 doesn't mean the deviation is always so tiny. Sometimes the average is only 2 but the deviation is large. Besides, if you need to bring a calculator, you're doing it wrong. You just need to know the most common ones.

My point is the dice are predictable. To all the people that think it's a randomarse dice game..it's not really. The vast majority of the time shooting/assaulting I can predict accurately what will happen before the dice are rolled and with a minimum of effort.

Maybe you already know it, but somebody else might not. Heck, nobody on this site used binomial therorem for years on this site and most players incorrectly used the average method to calculate vehicle destruction.

EDIT: You know what's funny Peregrine? I think we had this exact same conversation in someone else's thread last year.

Could you give an example of a situation where you're comparing two units and just looking at the average outcomes tells you that A is better while doing a more detailed analysis tells you that B is better? And where the difference is significant, not just a case of a 0.1% difference either way where rounding error is more important than the type of analysis?

I think you asked this question in that thread. My research of this first came about back in the day when friends of mine were discussing the old psycannon vs. a lascannon (years ago). A psycannon has 3 shots strength 6 ap 4 in the old book, and a lascannon is a lascannon. They have the same average at killing marines. However, their deviations are not the same, and are actually pretty significantly different. Does it matter? It DOES. If the 2nd wound could kill a special weapon, I know which gun I would prefer. Especially since lascannons can't do 2 wounds. Also, if you only need to kill one model, the lascannon does it a LOT better (because it's deviation is small).

This is very nice but does seem somewhat pointless. As mentioned, the problem is stupid players, the system is fine.

 scuddman wrote:
The vast majority of the time shooting/assaulting I can predict accurately what will happen before the dice are rolled and with a minimum of effort.

Yes, and the point is that so can everyone else who calculates an average outcome and assumes some uncertainty in that average. The extra knowledge gained by calculating standard deviations is rarely, if ever, going go cause you to make a choice that you wouldn't have made based on a simple average.

Heck, nobody on this site used binomial therorem for years on this site and most players incorrectly used the average method to calculate vehicle destruction.

Yes, because the average method doesn't require getting out a calculator and doing math. You'd have a point if someone was using the average method and defending it as being absolutely correct, instead of using it as an approximation to save time. Likewise, you aren't correcting any bad math here, you're just trying to convince people to do extra work instead of settling for a faster approximation that accomplishes their goal most of the time.

What about for that example above? Let's say you knew the average charging in was about 2, and you needed to kill 3 meq's to win the game. Would you have known your chance was much worse than 10%? If you did, you are ahead of the curve, but the vast majority of players don't know this.

 scuddman wrote:
If the 2nd wound could kill a special weapon, I know which gun I would prefer.

But you don't need to calculate a standard deviation to know that. A lascannon has a 0% chance of killing two models because it only has one shot, therefore if you really want to kill a model that is second in line for wound allocation you only have one choice: the weapon that has more than one shot, and therefore a non-zero chance of killing two models. If you're calculating standard deviations to tell you this then you really have no clue what you're doing.

Also, if you only need to kill one model, the lascannon does it a LOT better (because it's deviation is small).

Nope. The thing you're missing here is that a lascannon doesn't have a standard deviation because you can't have fractional outcomes with one shot. A lascannon has a fixed 55.5% chance of killing one marine, a 44.5% chance of killing zero marines, and a 0% chance of killing any other number of marines. An old psycannon has about a 46% chance of killing at least one marine. So, all I need to do to answer this question is know that the multi-shot weapon generates the same average outcome based on killing multiple models sometimes, so its chances of killing a single model (where multiple wounds are wasted) are lower. No need to bother with standard deviations at all.


Automatically Appended Next Post:

 scuddman wrote:
Would you have known your chance was much worse than 10%?

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.

This is DexKivuii's response from the old thread:

This thread highlights two important issues associated with applied mathematical analysis: picking the right tool for the job.

Just reporting averages can misleading. Usually in warhammer, what we actually care about is the chance to do at least x wounds. For example, if we're shooting at a squad of 5 marines, what we want to know is the probability of getting 5 or more wounds (ie wiping out the unit). Knowing we'll kill 4 dudes on average is much less informative than knowing we'll wipe out the unit 40% of the time. Glances are another good example of this: 2 glances might be pointless, what we really want is 3 or more, and 7 glances would be no more useful than 3. And yet the fact that you can get 7 glances (potentially) could skew the average.

The main problem with mathhammering is that basic averages are pretty easy for anyone to calculate and so they are used a lot. But sometimes they aren't really informing you in the way you'd like.

For people who can do basic matrix algebra and know how to use excel, a 'markov chain' (see wiki) can do almost any calculation you like (since dice rolls aren't correlated with each other). In some situations you'd need to 'nest' it.

Overall, this can be great for comparisons. If you're equipping a unit of long fangs, depending on your meta, point for point you might sometimes want missiles, and sometimes lascannons.

However, this still hides a lot of stuff. Strategy, movement, cover, etc etc etc


Automatically Appended Next Post:

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.

Your average is 2 dead marines. You need to kill 3 marines to win with a 10 man tactical squad charging. Try randomly asking players what they think their probability is of killing 3 marines the next time you're in a game store. The vast majority of players will think that it's decently likely. I sincerely doubt most players would think 12% (and it's really closer to 5%).


Automatically Appended Next Post:

Nope. The thing you're missing here is that a lascannon doesn't have a standard deviation because you can't have fractional outcomes with one shot. A lascannon has a fixed 55.5% chance of killing one marine, a 44.5% chance of killing zero marines, and a 0% chance of killing any other number of marines. An old psycannon has about a 46% chance of killing at least one marine. So, all I need to do to answer this question is know that the multi-shot weapon generates the same average outcome based on killing multiple models sometimes, so its chances of killing a single model (where multiple wounds are wasted) are lower. No need to bother with standard deviations at all.

Concepts are awesome, but seriously...you might know that...but how many other people know that intuitively? We learn statistics in business school or in applied math, maybe in engineering, but most majors don't. And what about those that only get an associates or haven't graduated college? I think a couple years ago when I was still in business school, I could probably count on my fingers the number of business students I know that could properly answer this type of question correctly. Maybe you think it's pointless. <shrug> Maybe you're right.

EDIT: A lascannon may be only one shot, but you roll more than one die. You're right though, something that doesn't vary doesn't have a deviation.

 scuddman wrote:
This thread highlights two important issues associated with applied mathematical analysis: picking the right tool for the job.

Exactly. And anything more complicated than an average outcome is rarely, if ever, the right tool for the job. The most important test for gaming math is whether it provides useful information in a reasonable amount of time. Average outcomes provide a lot of information with very little effort, while more complicated math almost always ends up taking a lot more time to tell you the exact same thing about a decision.

Usually in warhammer, what we actually care about is the chance to do at least x wounds.

No we don't, because x is constantly changing as units take casualties. If I'm shooting lasguns at a 10-man tactical squad all I care about is the maximum average outcome because the chance of a full-unit kill is so small that it isn't even worth considering. Then, as the unit dies I'd need to consider the chance of doing at least 4 wounds, then 3 wounds, then 2 wounds, etc, all with a steadily decreasing number of lasgun shots. I'd end up having to create a whole table of math just to handle one basic situation, and that's just not practical.

With average outcomes, on the other hand, all I have to do is a bit of rough approximation and I get the information I need to make the decision.

2 glances might be pointless, what we really want is 3 or more

Except this is a bad assumption. Two glances leaves a vehicle with 1 HP left for the next unit or next turn, so getting those two glances is rarely pointless.

And yet the fact that you can get 7 glances (potentially) could skew the average.

But not in any meaningful situations. Very few units have a non-trivial chance of stripping 7 HP, and in the rare situation where it's likely (full pod of sternguard against a Rhino, for example) you already know that you're dealing with a case of massive overkill.

For people who can do basic matrix algebra and know how to use excel, a 'markov chain' (see wiki) can do almost any calculation you like (since dice rolls aren't correlated with each other).

And any time you start talking about matrix algebra and excel you're breaking the #1 rule of 40k math.

The vast majority of players will think that it's decently likely.

That's because the vast majority of players are stupid. If your average is 1.666 and you think that 3 is likely then you're either hopelessly optimistic or you don't know anything about how dice work. If you're a reasonably intelligent person all you need to know is that the outcome you need is almost twice your average outcome, so your chances are pretty bad and you should only do it as an act of desperation. The fact that many people aren't smart enough to figure this out doesn't mean that you should give them even more complicated math to tell them the exact same advice.


Automatically Appended Next Post:

 scuddman wrote:
but how many other people know that intuitively? We learn statistics in business school or in applied math, maybe in engineering, but most majors don't. And what about those that only get an associates or haven't graduated college? I think a couple years ago when I was still in business school, I could probably count on my fingers the number of business students I know that could properly answer this type of question correctly.

If so few people know enough to answer the question correctly based on average outcomes then why exactly do you think that trying to teach them about standard deviations is going to accomplish anything besides confusing them even more thoroughly?

Because 3+/-.5 is intuitive. Just like 3 is intuitive.

It's called abstraction. the calculations can be predone somewhere else. No one understands concepts unless they've been through it at least once. It's a formula you can autoplug into your calculator without a lot of effort.

I don't believe calculating standard deviation is a lot of effort, is it really that hard to use square root?

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

I was asserting that it was more robust but still pretty simple. If the assessment is that it's too complicated, then you have a point. But most people use the average method anyways. And with a calculator I might add. So why is it so hard to tack on a formula? Using binomial theorem and calculating doing "at least" types of calculations take just as much effort.

 scuddman wrote:
I don't believe calculating standard deviation is a lot of effort, is it really that hard to use square root?

Any method that involves getting out a calculator in the middle of the game is way too much effort.

That statement is opinion, not fact. Besides, like I said, you could learn the most common ones pretty easily. Or use the calculator at the end of a match to review your decisions. Math should be supporting conceptual thinking anyways.

EDIT: If I can, I routinely use a calculator to play magic, the gathering. And I always would in poker if I was allowed to.

 scuddman wrote:
That statement is opinion, not fact.

It's opinion, but it's an opinion shared by the vast majority of players. If you have to get out a calculator in the middle of a game then very, very few people are going to be interested. And even fewer will be interested when almost every time you do that extra work you get the exact same answer as when you use a much simpler method that doesn't require a calculator.

Besides, like I said, you could learn the most common ones pretty easily.

And which ones would those be? And why would all of the extra math be relevant in those cases?

Or use the calculator at the end of a match to review your decisions.

So now you're going to make a list of all your decisions, complete with exact dice that would be rolled and every relevant fact about the target? And your opponents aren't going to have a problem with all of this slow play? I really fail to see how this is supposed to get better results than approximating some average outcomes and spending all the time you save on improving your strategy.

If I can, I routinely use a calculator to play magic, the gathering.

I'm surprised that you find anyone willing to play against you.

I`m with Peregrine 100% here, you pretty much say that most people that use mathhammer are so dumb that they can`t take advantage of the info they get. Then you want the same dumb people to learn much more complex math, sit down with their lists, calculator and excel sheets and find the odds of their units doing stuff to possible units they can encounter.

This is very smart-stupid (Sheldonesche?) topic. Clearly, you are good at math, but you just don`t seem to be able to see why the "old mathhammer" method is simply better.

Because I see people use the average method all the time and tell me dumb things. Because until last year, people used the "average method" to calculate vehicle damage. Besides, this is a tactics and strategy thread. When I use mathhammer, I do so because I care about getting better and I care about the knowledge. Because I"m an accountant and crunching numbers is something I like to do and I just naturally do it, and sometimes I can't understand why everybody doesn't do things the same way.

Oh, and about magic the gathering. In 40k I might be a fluff player, but magic is all about tournaments, all about winning, and all about money. Playing 40k doesn't make you money. Think like poker, but more broken. Poker requires way more luck.

Since Peregrine has basically said everything I was gonna say, I'll simply say, that you are thinking way to hard about this dude.

Might just be a different environment. In street fighter, top players often spend hours just working on getting out of a setup. It doesn't seem all that intense to me. Besides, I see games where people are taking pictures every turn. That's gotta be at least as slow. Plus, you only really need to check the decisions you weren't sure of. You can write those down...there shouldn't be too many of those. But yeah, your mileage will vary.

Standard deviations are pretty lame for calculating thing ms with non normal distributions. Like small amounts of dice being rolled. The far better thing to do is just find a binomial probability of a certain outcome. As it gives more realistic data and is something you Cando in your head assuming you can handle basic arithmetic.

Finally the most pertinent statement of the bunch - thanks Jakobokaj. Although Peregrine is generally right on the money, the real issue is that you're working with a uniform distribution scuddman. Uniform distributions do not have 95% of all observed values within two standard deviations - so your entire premise is wrong. This is besides the fact that it's pointless - most people tend to understand what units work in what situations just from experience, so why do all this math? I teach math and I think it's silly.

Also, you might have gained more traction if you went with the statement that if there are two potential attacks with the same average wounds, the one with more shots will have less variability. Which almost everyone knows - check out any discussion on single shot weapons and how unreliable they are.

One thing that i read to keep things simple was "for every 5 dice you roll, add +/- 1 to the average, then add another +/- 1 for every full multiple of 10 dice you reach". That way you can follow the steps through and get a most pessimistic or most optimistic result as well as the average.

I have no idea if that actually works, statistics was always a branch of mathematics I've never been any good at. I am curious if there's any basis for it though.

Most things in this game require buckets of dice. Even for 1 shot you have to roll to hit, roll to wound, then roll armor saves. That's already 3 potential rolls for 1 shot. It's so rare you don't roll at least 5 dice. It trends towards a normal distribution. I DID say it was just a model.

I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

I tend to agree with some of the others in that busting out calculations at the table is a bit extreme. That being said, as a scientist, I love mathhammer. Its a great way to build your intuition about probabilities so that you don't need a calculator at the table. I agree with scudd in that the average is only half the story so to say; the variance can be just as useful. The problem I have with the (sqrt(N * 35/12)/N) method described above is that its... well... wrong. Not even a good approximation. The portion (35/12) represents the variance of one die, assuming an average value of 3.5. However, the method scubb describes in the OP deviates from this significantly. Where it really breaks down is where N is assumed to be 35. This is very different than rolling 20 dice with multiple conditions for 'success'. Even if it were a normal distribution, this would not work like this. The good news is, as Jakobokaj points out, exactly calculating probabilities with a binomial distribution is not any harder than whats being suggested here. In fact, if you put it down in a spread sheet it becomes a snap to calculate any relevant quantity!

and they sad math wasn't fun!


Automatically Appended Next Post:
blah, forgot to put numbers to back it up.
20 attacks at 1/2 hitting, 1/2 wounding, 1/3 unsaved has the following breakdown:
0 kills: 17.5%
1 to 2 kills: 59.5%
3 or more kills: 23.0%
So it can be seen that the 95% 2 sigma band (1 to 2 kills) given from the other method is quite misleading

 scuddman wrote:
I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

Well, that puts you in the top what, 0.0001% of people in the world that can do that in their head. You could get more from just memorization with those results (i.e. 5 = 0.8; 10 = 0.5; 20 = 0.4; 30 = 0.3; 50 = 0.2) but that really doesn't tell you that much more than using the average.

 scuddman wrote:
Most things in this game require buckets of dice. Even for 1 shot you have to roll to hit, roll to wound, then roll armor saves. That's already 3 potential rolls for 1 shot. It's so rare you don't roll at least 5 dice. It trends towards a normal distribution. I DID say it was just a model. Unless your are attacking with a horde unit, nothing in the game out of apocalypse that I can currently think of, uses enough dice to approximate a normal distribution, some get close, but not many.

I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

It may not be much math, but most 'mathhammerers' don't even understand what the average does, now we throw standard deviations at them?

 Krellnus wrote:

 scuddman wrote:
Most things in this game require buckets of dice. Even for 1 shot you have to roll to hit, roll to wound, then roll armor saves. That's already 3 potential rolls for 1 shot. It's so rare you don't roll at least 5 dice. It trends towards a normal distribution. I DID say it was just a model. Unless your are attacking with a horde unit, nothing in the game out of apocalypse that I can currently think of, uses enough dice to approximate a normal distribution, some get close, but not many.

I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

It may not be much math, but most 'mathhammerers' don't even understand what the average does, now we throw standard deviations at them?

What, they never took a class with statistic in high school? I find that very unlikely.

 Co'tor Shas wrote:

 Krellnus wrote:

 scuddman wrote:
Most things in this game require buckets of dice. Even for 1 shot you have to roll to hit, roll to wound, then roll armor saves. That's already 3 potential rolls for 1 shot. It's so rare you don't roll at least 5 dice. It trends towards a normal distribution. I DID say it was just a model. Unless your are attacking with a horde unit, nothing in the game out of apocalypse that I can currently think of, uses enough dice to approximate a normal distribution, some get close, but not many.

I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

It may not be much math, but most 'mathhammerers' don't even understand what the average does, now we throw standard deviations at them?

What, they never took a class with statistic in high school? I find that very unlikely.

while I cannot speak to the US school system, it is my experience that stats classes, unlike maths or science classes don't emphasise as much on want the various things mean.

 scuddman wrote:
Because I see people use the average method all the time and tell me dumb things.

So what? People say stupid things based on average outcomes because they don't understand what they're talking about, not because the method is flawed. Giving someone more math isn't going to fix that lack of understanding, it's just going to make them say different stupid things based on standard deviations.

Because until last year, people used the "average method" to calculate vehicle damage.

So what? It's a useful approximation that requires less work than a more accurate model, especially now that in 6th you have to consider both the chance of destroying a vehicle through the damage table and by HP removal. Once again you're nitpicking the fact that a model isn't perfect without actually demonstrating how the model leads to incorrect conclusions that are avoided by your preferred method.

and sometimes I can't understand why everybody doesn't do things the same way.

Because your method adds extra work, but rarely, if ever, gives you a different answer.

Oh, and about magic the gathering. In 40k I might be a fluff player, but magic is all about tournaments, all about winning, and all about money.

First of all, if you think that MTG is all about money then you're hopelessly wrong. MTG can be played for a lot of money, but there's a lot more to the game. Second, when did WOTC start letting you use a calculator/phone/whatever in the middle of a high-level tournament game? Or are you just bragging about how you "compete" at the friday night magic "tournaments" at your local store?

 scuddman wrote:
I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.

It's not complicated for a calculator, but it means that you have to use a calculator unless you're one of the few people who can accurately calculate square roots in their head. And if your method requires a calculator but doesn't actually provide any greater insight into the decision you're trying to make then you're just getting obsessed with the math and losing sight of the original goal.

So what? People say stupid things based on average outcomes because they don't understand what they're talking about, not because the method is flawed. Giving someone more math isn't going to fix that lack of understanding, it's just going to make them say different stupid things based on standard deviations.



Because until last year, people used the "average method" to calculate vehicle damage.


So what? It's a useful approximation that requires less work than a more accurate model, especially now that in 6th you have to consider both the chance of destroying a vehicle through the damage table and by HP removal. Once again you're nitpicking the fact that a model isn't perfect without actually demonstrating how the model leads to incorrect conclusions that are avoided by your preferred method.



and sometimes I can't understand why everybody doesn't do things the same way.


Because your method adds extra work, but rarely, if ever, gives you a different answer.



Oh, and about magic the gathering. In 40k I might be a fluff player, but magic is all about tournaments, all about winning, and all about money.


First of all, if you think that MTG is all about money then you're hopelessly wrong. MTG can be played for a lot of money, but there's a lot more to the game. Second, when did WOTC start letting you use a calculator/phone/whatever in the middle of a high-level tournament game? Or are you just bragging about how you "compete" at the friday night magic "tournaments" at your local store?



scuddman wrote:
I don't think (sqrt(N * 35/12)/N) is very complicated. It's not that much math.


It's not complicated for a calculator, but it means that you have to use a calculator unless you're one of the few people who can accurately calculate square roots in their head. And if your method requires a calculator but doesn't actually provide any greater insight into the decision you're trying to make then you're just getting obsessed with the math and losing sight of the original goal

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?

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.

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.

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.


Automatically Appended Next Post:
If there's anything you take from this: BTW, regardless of which side of the fence you're on, and whether you choose my method or not, the concept of deviation still stands: You will find that 40k does not vary a lot, and that for the most part 40k is a game with predictable outcomes. It is a dice game, but it is NOT random. Not usually anyways.