Why do I see all of these guys pull out their calculators to do mathhammer? Dont you get the same thing from experience? The only problem with mathhammer is that it is like a science experiment under perfect conditions the results do not reflect in game results. I mean you may figure out the chances of certain results but it doesnt take into considerations of certain results at certain times. Such as a glancing hit destroying a battlecannon or immobilized transports.

I know I am about to be bombarded by mathhammer evaluation responses but you should evaluate units when they are on the field, not with a piece of paper and calculator.

If you know the chances, it helps you decide what to do during the game. I hope people aren't bringing calculators to a game, some quick math in your head should be just fine. It allows you to direct the correct amount of firepower/cc power to a situation and have better odds at coming out on top. You don't have to rely as much on luck, and it may save you from doing mistakes.

CKO wrote:
I know I am about to be bombarded by mathhammer evaluation responses but you should evaluate units when they are on the field, not with a piece of paper and calculator.

Why not do both?

In my experience, math-hammering is good for picking the types of units you might want to try on the tabletop or in determining how best to use a unit.
Its an initial guess often. A good player will evaluate the statisticals against their experiences with that unit and others, compare them to their playstyle and determine what works best for them.

Often, I find that doing math-hammering for the sake of math-hammering does yield interesting results that go against your common sense.
Examples are how 1 Flamer shot = 1 Plasma shot if you can hit 3 Marines or how Autocannons usually superior against light armor then the more expensive Lascannon.

"No thanks, no gaming today, I'm staying home doing mathhammer". Not likely :-)

I calculate when I can't play the game due to lack of time or opponents. I also do it because I really like math, and because it gives me interesting insights into mechanics of the game. And I honestly believes it gives me a good foundation for the practical testing of units. In a play situation my subjective view of things and my enthusiasm for the game often gets in the way of analysing. Also, it's hard to get a reliable statistic for an effect unless you do many iterations of it, something that takes a lot more time if you do all the attempts "live" on the table top.

Not this again.

Look, statistics (a.k.a Mathhammer) informs your decision making during the game.

Do I shoot my Lascannons at the Monolith or the Heavy Destroyers? Do I shoot my Autocannons at the Rhino or the Drednaught? Which attack will have the best chance at being successful and not just a wasted shot.

Do you shoot an autocannon at a Land Raider? No, why, because basic addition says str 7 + D6 has no chance against Armor 14. Statistics are a simple extension of this concept. Do I shoot my Missile Launcher at the Land Raider? Basic addition says str 8 + D6 can glance Armor 14, should I take a shot or are my chances so slim that the shot is wasted?

This helps prevent you blaming the "Dice Gods" when you don't get that miracle 6 needed to pen the Land Raider with a Lascannon. Or when your single shot gets cover saved and that was the one thing you needed to win the game and didn't get.

As a simple example. Your opponent moves Nasty Unit A towards you. Logically, on the field, you know you have two possible counters for this that are in range. However, you also know you can only commit one of these, as you need to other for a counter-tactic you have planned. Which do you use? Mathhammer tells you that one of these units has a 60% chance of success; the other 70%. In a situation like this, you would use the 70% unit. Either could potentially win or lose, but you would play the odds to give yourself the best possible chance of success.

cko not only is math hammer boring... the math people are using when they throw out these percentages is wrong. you can't model warhammer with arithematic. you need probability and statistics.


Automatically Appended Next Post:
and yes you can do much better with simple experience. somebody on another thread mashed numbers together to find, amazingly, it takes 20 shots to kill a predator at long range. and we all know from experience that is not true...

And the good thing about being a nice math geek is that I do not make sweeping assumptions on how a loosely defined group such as "math people" do calculations. *looks pointedly at GTT16th* An average number is just an average number, and it is easy to find with arithmetics. The trick is to know what use you can make out of this number, the difference between data and information. One use is that you can apply it into probabilities.

If you want to look at the spread of probabilites you need another set of tools. Questions like: "How many SPM HBs do I need to shoot to have at least a 75% chance of taking out a rhino?". "How many more do I need to have a 90% chance?". "How many more for a 99% chance?" And you need probability, statistics and good knowledge of the rules to realise that you can never up this probability into a theoretical 100%.

And on the subject of statistics: A single result, (not even consider the reliability of the source "somebody on another thread") does not merit any evaluation of the method. This is applicable for how a particular unit/weapon/special rule performs if tried in just a few battles. And it is definitely applicable when evaluating the effectiveness of mathhammer on these forums.

Mathhammer is just a tool. It helps me do clever things.

since you're a nice person i know you won't mind sitting through some remedial grammar with me. watch.

the math... people... are using. subject, object of the subject. verb. as in the math *that* people use.

constantly amazed.... constantly....

no s in arithematic.

anyway yes you can find the average chance of, say, a bolter shot wounding a marine, with arithematic. what you cannot find with arithematic is how many bolters you need to shoot at that marine to be reasonably certain (say 95 times out of 100) of killing him. which is why... math hammer... without the aid of probability and statistics... is nonsense.

GloryToThe16th wrote:anyway yes you can find the average chance of, say, a bolter shot wounding a marine, with arithematic. what you cannot find with arithematic is how many bolters you need to shoot at that marine to be reasonably certain (say 95 times out of 100) of killing him. which is why... math hammer... without the aid of probability and statistics... is nonsense.

Depending, of course, upon what information the user is attempting to glean. Both pieces of information are useful and applicable to the game.

Aha, then I follow you. I blame me being raised speaking swedish, together with a relatively low expectations of people ability to write proper and polite sentences on internet forums. Sorry for my snarky remark on that subject, it was entirely undeserved.

However, my point remains this: I do believe that mathhammer can include the use of statistics and probability, and will benefit from doing so, but it doesn't have to. And, it can still be a useful tool just looking at the simple P(hit)*P(wound)*P(fail save)=P(kill) calculations. For example: "Is it worth the +1p to upgrade my termagants flehsborers to a pair of spinefists?" Simple multiplicative mathhammer says that 100 shots with a fleshborer will on average kill more targets in several important categories such as MEQ, TEQ and ORKs. So the upgrade is definitely not worth the points. For this, I don't need statistics and I don't need to consider the spread of the results. Simple multiplication is "good enough". This is especially true since fleshborers and spinefists are usually fired in huge numbers, so tends to conform better to the average.

However, In situations where a few dice are rolled, statistical spread (that is the proper word in english, right?) becomes more important. It is a lot more timeconsuming to calculate though, so I usually settle for the "good enough". The trick is to know just how good that is, so I don't expect a predator to go down after exactly 20 shots of a HB.

I do agree with you that a lot of people tends to take the multiplicative mathhammer a bit too literal. But that doesn't make the method nonsense.

Is it just me, or is GloryToThe16th presuming to give Mellon lessons on English grammar like a fish trying to teach Lance Armstrong how to ride a bicycle?

x

GloryToThe16th wrote:its you

GloryToThe16th wrote:which is why... math hammer... without the aid of probability and statistics... is nonsense.

I always thought use of the word "Math Hammer" included (or is primarily comprised of) probability and statistics.

Mellon then i apologize too. Please excuse my rudeness.

You can get a basic idea of what's going on with arithematic i agree. I don't know how to model 40k with statistics and probability myself. Wish I did. I'm just starting to study math in college. It's my major.

I'm not sure if statistical spread is the right word. I understand what you're saying. The fewer dice you roll the more likely it is that your actual results will vary from what the math suggests will happen. Conversely the more dice you roll the more closely it will conform.

I agree with the way you're approaching it. I was quick on the trigger. What I mean to say is that when you see tables of percentages showing how likely one unit is to kill another, it's often based on flawed assumptions. For example if I want to kill a terminator 100% of the time I have to make it take 6 armor saves because 1/6 x6 = 1. I would guess that you would have to make it take like 10 or 12 saves to kill it even 95% of the time. Anyway it's bad math, but people talk about their percentages like they're dead certain.

Mathhammer leads to a comfort zone that frustrates people and is unrealistic on the battlefield.

Maybe if you do it badly. You're better off determining the probability of each potentiality rather than determining which potentiality or fraction thereof is most likely, for example.

CKO wrote:Mathhammer leads to a comfort zone that frustrates people and is unrealistic on the battlefield.

Every player know that the game depends on the dice roll , and math hammer just helps tips
over the chances to achieve what they hope to achieve.

As to the average vs probability issue, for most people averages are enough to give you an idea of what to expect. Anything more and it would get too complicated for your typical game and frankly, few people have the energy to be doing calculations (or looking up results of those that they already did) to go for the probability.

A prime example of this is "how many Bolter shots does it take to kill a Marine?"
For me, knowing that it takes roughly 9 shots to kill a Marine is enough. This gives me the information I need to make the assessment on the battlefield that if I rapid fire two 10 man squads into a 5 man combat squad, I stand a reasonable chance of killing off the heavy weapon guy buried inside.

minigun762:

Actually the example that you give is the sort of thing where people get mislead by averages. If it takes 9 shots on average, at minimum it takes 1.

Let's set the problem like this:

You have four Tactical combat squads within 12" of two Tactical Squads. Two of your combat squads have Heavy Bolters, two of your combat squads have Plasma Guns.

Supposing everything else being equal, in what order do you commence shooting to maximize the efficiency of your shooting? Remember to show your work...

Nurglitch wrote:
You have four Tactical combat squads within 12" of two Tactical Squads. Two of your combat squads have Heavy Bolters, two of your combat squads have Plasma Guns.

Supposing everything else being equal, in what order do you commence shooting to maximize the efficiency of your shooting? Remember to show your work...

1) rapid fire the 2x PG squads into 1 Tac squad.
Average result should be:
4 S7 = 2.67 hits = 2.2 dead Marines
16 S4 = 10.67 hits = 5.33 wounds = 1.78 dead Marines
Total = 4 dead Marines

2) rapid fire 2x HB squads into 1 Tac Squad.
Average result should be:
6 S5 = 4 hits = 3.33 wounds = 1.11 dead Marines
16 S4 = 10.67 hits = 5.33 wounds = 1.78 dead Marines
Total = 2.89 dead Marines

End result = 10 Tac squad + 3-4 Tac Marine squad leftover. Considering the amount of wounds placed on the target squad, there is a fair chance you've killed off one of the SW, HW or VS models. This is the reason I fired the PG before the HB. The PG shots will help to reduce the squad to a smaller maximum number meaning that when you start stacking wounds with the Heavy Bolter, you have a better chance of torrenting the important stuff.

EDIT:

Nurglitch wrote:minigun762:
Actually the example that you give is the sort of thing where people get mislead by averages. If it takes 9 shots on average, at minimum it takes 1.

I should have been more clear on my previous example. To be useful, you must understand that the averages are just a best guess. Nothing is stopping you from killing 1 guy or 8 guys even though the average would be 4. For me, the best thing to do is put a +/- on it. If the average says 18 Bolters = 2 guys, I should understand that my expected results will probably be 1-3 guys dead.

Experience is a really unreliable tool for calculating the probability of something happening because experience is clouded by psychological distortions like preconceptions, loss aversion and confirmation bias. Check out the Monty Hall problem or the Gambler's Fallacy for good examples of how people's assessments of odds can't deal with mathematical probabilities that are counter-intuitive.

...or just check out one of the billions of Dakka threads on how assault cannons are more likely to hurt a landraider than a lascannon, or one of the half-billion threads about how lascannons are extremely unlikely to kill a landraider, and you can see for yourself how many people cling to what they remember as their "experience" against what the numbers say.

In general, experience is pretty reliable. But in places where the probabilities aren't intuitive, mathhammer actually gives you the more accurate expectations.

Glory to the 16th, your apology is gladly accepted!

Actually, I'd like to offer you a gift of friendship. I had to dig a bit in my old math knowledge and on the internet to get some tools, and it took a bit of work, but I managed to create a small table that lets you look up what probability you want of hurting your target, and what saves your target has, then it tells you how many saves you must force to get this probability. It's not very useful in a gaming situation, since it doesn't care how many wounds are failed. But it was a fun excercise none the less, and I might be able to rework the formula to work better for hurting bigger units. Anyhow, I named the table after you.

No hard feelings here, I hope that I can gain a lot of 40k related insights out of your math-studies in the future, and a lot of interesting discussions until then.

Here it is, the Gtt16th table:

minigun762:

Sorry, it was a trick question: I left out something of extraordinary relevance: the make-up of the Tactical Squads. That definitely affects the utility of stuff like Plasma Guns when mixed in with weapons with a higher AP value because even if the Plasma Gun hits twice, both hits may be allocated to a single model.

Assume further, then, that the Tactical Squads have a Sergeant, a weapon specialist, and a heavy weapon specialist.

thanks melon. glad to meet you

My statistics professors would probably end themselves if they ever have the misfortune of stumbling upon this thread.

Nurglitch wrote:
Assume further, then, that the Tactical Squads have a Sergeant, a weapon specialist, and a heavy weapon specialist.

I just went ahead and assumed that the Tac squad had the standard loadout of SW, HW and PW/PF Sarge.

flavius everyone agrees math is better than going by experience. but experience is better than going by bad math... and thats what math hammer generally is. you cant model the game with arithematic. you need probability and statistics.

I mean if you take a marine in close combat with another marine then it has a 1/12 chance of killing that marine with each attack. that's true because 1/2 x 1/2 x 1/3 = 1/12. so math hammer-ers go on to say well I need 12 attacks to be reasonably sure of killing that marine because 1/2 x 1/2 x 13 = 1/12 and 1/12 x 12 = 12/12 or 100%. this is bad math. if it were good math the marine would always always always die whenever you roll 12 attacks against it, since 100% means all the time and 12/12 = 100% we all know that isnt how it plays out. when you roll 6 dice you're not going to get 1 2 3 4 5 6 very often... and thats basically what the arithematical approach assumes. you're going to get 1 1 2 3 4 6, 2 2 4 5 5 etc. that's what you need stat and prob to model.

if you just want to take an educated guess with numbers, math hammer without prob and stat is fine. if you want to have mathematical certainty then it is not.

GloryToThe16th wrote:mini each bolter shot has a 1 in 12 chance of killing the marine... but that does *not* mean you're going to kill 1 marine for every 12 bolters you fire. remember?

No, it doesn't mean that it will happen, Thats what I'm saying.
9 Bolter shots = 6 hits (on average) = 3 wounds (on average) = 1 failed save (on average) so (on average) it takes 9 Bolter shots to kill a Marine.
You could shoot 9 shots and kill 0, 2, 3 or 9 Marines but chances are that it will be 1.

My point was that for most people, this is enough "math-hammering" to make an informed decision on the tabletop.

ok as long as we all agree its guess work.

GloryToThe16th wrote:ok as long as we all agree its guess work.

Well hell thats all probability is right? An educated guess.

To the OP's point, I would assume that a player who used experience and math-hammering would probably end up winning more games then a player who relied only on one of those (all other things being equal).

For me, thats enough to make it worthwhile.

It's kind of reductionist to call it guesswork. It rather distracts us from the fact that we are working from facts, such as the number of attacks, the relative strenth and toughness values, and so on.

Take the problem of four combat squads on two full Tactical Squads. I would have gone with the two combat squads with Heavy Bolters first. They have the potential to wipe out the first Tactical squad, allowing the subsequent squads to either mop up the survivors, and being more likely to apply AP2 wounds to specialists, or to direct their firepower to other units.

ok nurglitch I'll concede this: math hammer is good for telling you things you should already know. that the plasmaguns will kill more marines than the heavy bolters, for instance.

GloryToThe16th:

Actually no, the statistics, if we take mathhammer to be purely about statistics, will only tell us what is more likely to happen if we assume perfect dice and average results.

Would someone like to calculate the odds of a combat squad with a Plasma Gun (Bolters otherwise) killing two Space Marines out of ten with AP2 wounds?

you have no idea what you're talking about. admit it.

minigun762 wrote:My point was that for most people, this is enough "math-hammering" to make an informed decision on the tabletop.

QFT

Of course people know that you CAN kill 0-9 marines with 9 bolter shots, but as minigun says, with some light math, you know that you are most likely will kill 1 marine

GloryToThe16th wrote:mini each bolter shot has a 1 in 12 chance of killing the marine... but that does *not* mean you're going to kill 1 marine for every 12 bolters you fire. remember?

Stop being condescending, he is not a moron, and neither are most other people on these boards.

GloryToThe16th wrote:flavius everyone agrees math is better than going by experience. but experience is better than going by bad math... and thats what math hammer generally is. you cant model the game with arithematic. you need probability and statistics.

Yes, I agree that mathhammer can have a couple of problems in application. For example, players who are too fixated on it can sometimes lose their heads when the dice drift too far from the averages. And players with less experience (or less math knowledge) often don't account for, not sure what it's called in math, the distribution? The way the amount of variation in the possible outcomes of particular die rolls reflects the reliability of certain risks in the short-term? I'm not really a math person; this phenomenon is something I picked up from experience.

But I think the way mathhammer is used on message boards is both legitimate and useful as long as players understand the application.

I'm new to the game and I don't know much about the probabilities and what-not, but for player like me who enjoy a little bit of imagination and realism in their games, Mathhammer tends to strip that fantasy away. In real combat, generals don't pull out calculators and determine the probability of their snipers taking out an infantry unit. I know that real-life combat is different from miniature combat, but I stand by my point. If you can do it in your head, all the power to you. However, using calculators, in my mind, is the same as pre-measuring your shots.

I use it before games, to round out my army list (if I know what I am fighting). It's a tool to get an idea of what would happen. However, you can't factor in random chance, such as rolling 5 1's at once. It's a useful tool, but its significance should not be overestimated.

It isnt exact but say you have a squad of 6 Dire Avengers plus exarch with powerblade and bladestorm.

so three shots for six dire avengers agains a tac squad will on average do

18x2/3=12x1/2=6x1/3=2 kills on average

this is not exact and there are chances that it will stray but what if you have multiple squads of Dire Avengers, mathammer helps you to determine how many squads to focus on the tacs.

because you could focus five squads on the marines and on average kill the whole squad or you could focus two which would have a 7/36 chance of them routing.

The whole "mathhammer" idea is most useful outside of any particular game. Its most helpful when trying to determine which type of unit is better at a particular job; Ive seen it used very often in the debate over which is the better cc squad, eldar scorpions or banshees. If one wants to spend several years playing with both banshees and scorpions one can get a general idea which is better in each sort of cc situation. Or one can simply sit down and do calculations for a bit to save several years of work.

As with any tool, it just needs to be applied properly, and to proper problems. Digging out a calculator during the middle of battle to try and figure out which squad to shoot at that termagant squad first isnt a good idea. Between games taking a few moments to figure out what type of heavy weapon to take when you expect to face swarms of termagants IS a good idea.

And where did the notion that probability/ statisticics isnt involved in mathhammer? Simple math gives you simple mathhammer, more complicated math gives you better quality mathhammer. Experience is great, mathhammer is great, using both will tend to beat either alone. And yes, tend is the core of mathhammer, its ALL about probability. Its just a good idea to know enough about a situation to be able to tell that an event has a 97.5 likelyhood rather than a 60% likelyhood.


Sliggoth

Using math for pre-battle calculations is fine. I don't object to it. It's the in-game math that I have a problem with.

jimbob123432:

If you have a problem with people pulling a calculator out of their pocket, keep an abacus handy.

I don't have problem with the calculator itself per se, it's just that a) it gives a slight advantage to those people who can do Mathhammer, and 2) It can eat up a lot of time that can be used for, I don't know, gaming!

I can't think of any situation I've had in a 40k game where pulling a calculator would really help. In most cases, any necessary calculations can be performed mentally.

Slow playing, whatever its purpose, shouldn't be encouraged regardless of the form it takes. However mathhammer really shouldn't take long enough to slow a game down significantly. I often do the numbers in the midst of many of my matches just to figure out the optimal choice between a few possible selections.

Having an understanding of probability and statistics within the very predictably random structure of 40k has definitely helped me to become a better player overall. It's also helped me to coach a newer player or two on where their list can improve.

I kinda think that if you need to pull a calculator during a game you're either
A) Doing to much maths for what the game entails
or B) A moron who can't do fractions
Bit harsh I know but all the game needs is a slight pre-knowledge of what is likely to happen and if you get too wrapped up in the maths you leak most of the fun out of the game and cause breaks in play.

Basically try to keep it in your head and speedily.

Advanced mathhammer and actual gaming is like icecream and mustard, it's great one at a time, but horrible together.

Mellon wrote:Advanced mathhammer and actual gaming is like icecream and mustard, it's great one at a time, but horrible together.

Haha awesome. I think I might just sig that.

I think most people already done their math hammer when they are deciding what to place in their army list.

Mathhammering on the spot doesnt usually end well (when you need calculator that is )

I never take my math hammer as law. It is nice to have a frame of reference though. Semi-informed choices are better then shooting in the dark. Even the potential has enormous power.

I just have to ask, since it's the way the conversation has drifted a few times, some of you have actually played games where an opponent literally pulls out a calculator and punches in some computations in order to make a decision?

I've never seen that happen.

Nope never seen that happen. But tbh I wouldn't trust such complex calculations in the battle. I would much rather play it as I see it. =]

Oshova

I've seen opponents count on their fingers... that's sort of a bilogical abacus/calculator. But no, no calculators seen around here. My experience is that the serious mathgeeks are the only ones that would find it enjoyable to do math in the middle of a game, and they can handle these calculations in their head.

I would however consider bringing a table like the Gtt16th table above to a game, but mostly to test it out and see how reliable it is. Sort of like a math lab :-)

I have watched games where one opponent pulls out a calculator during a match. He took 5 minutes to decide his turn whilst his opponent only took about 2. Calc-man eventually loses the match.

That's because you can never rely on the law of averages. Also you've got to have sound tactical planning not just doing what the maths tells you to.

Oshova

I don't get all the hostility toward math hammer during a game (unless it's causing slow play, which I've never seen personally).

I often run the numbers in my head while my opponent is counting up his to-hit dice on a big roll and call out my prediction for the number of wounds. It gives me something to do while my brain is idle and it's fun for everybody to see how close the average comes to the actual result. (Also if my opponent is making a bad tactical decision, it helps to control his expectations for how many of my guys that huge handful of dice is actually going to take out.)

It's a tool like any other. I don't see any sense in making value judgments about it or taking a moral position on the idea that mathhammerers deserve to lose because of their focus on math.

I think the problem is when you solely rely on mathhammer, and forget about all other tactical decisions . . . admittedly you could do mathhammer with all of that built in, but to factor in all variables etc it would take a very long time to make a decision. Even longer than those slow horde players . . . lol

Oshova

To quote Mark Twain "There's three kinds of lies: lies, damned lies, and then there's statistics."

Yeah, but studies show that only 49% of Mark Twain quotes are true...

at least there's that

IIRC Twain was quoting some British Lord or PM...

Again, I have no problem if you run the numbers in your head, but pulling out a calculator during games does two things. First, it ruins any modicum of fantasy either player may have and second, it does tend to pull away from the tactical way to play. Besides, there are WAY too many variables to put into a calculator, so what's the point?

To the poster who said that real generals don't do math on the battlefield, I say, you're right.

They have teams of ballistics experts running numbers in an HQ somewhere, who pipe that information to the general to inform his decisions. We 40K players just have to do it for ourselves (and it is FAR less complicated than real-world calculations).

I refer you to this article:
http://query.nytimes.com/mem/archive-free/pdf?_r=1&res=9C04E2D8113AE63BBC4851DFB3668383669FDE

This is just the first result I found of MANY that shows the kind of abstract statistics and probability that are applied every single day of warfare, and have been since the days of the Persian Janissaries (calculating quantities of gunpowder to length of fuse, etc.). I've seen wall-size posters with pictures of ordnance size to plating thickness that can be *reasonably expected* to be penetrated given a direct hit after accounting for armor slope.

If you don't respect or understand the use of probability and statistics in warfare (or wargaming, where it applies even more directly), then you obviously have no idea what it takes to wage modern war. Modern generals do not guess. They do not fling ammunition at targets to "see if it works". They calculate what should do the job, then up it a little bit to be absolutely sure. Even then, things go wrong, but more often than not, doing the homework pays off bigtime.

In 40K, Mathhammer is just a fancy term for the statistical analysis of the result of average rolls. Everyone who uses it should know that dice are random, so there is a huge range of possiblity, but knowing the *probability* is how you determine your application of force density.

If you overkill a unit by positioning too many of your units to kill it, but it only takes half, you've wasted the shooting AND positioning of the other half of your units. Knowing roughly what a unit will do in a given situation allows you to prevent wasting force, or from relying on a long-shot by under-committing. Really, like everyone says, it *informs* your decision, it does not make it for you.

I begin every game with a simple prayer to the Dice Gods.

"Please, oh please, please oh Gods, just let me roll average."

*applaud*

Thank you! Also, I was the one who posted about general and math in the field. I'm well aware that people do do pre-war calculations, and that what I was arguing for. I'm against in-battle calcs.
All praise to the Dice Gods!

I stand by my previous statement, mathhammer will only frustrate you let me re-phrase that it will frustrate me! If I play another game and some one says the dice screwed them because on average I am going to scream.

I just like mathhammer to know how much I can complain about dice rolls. When I get 30 attacks from charging CSM and kill zero enemies, I know I did pretty darn badly. Or when those same charging marines lose combat to fire dragons in hth.

It's not unreasonable to say "27 bolter shots should kill about 3 marines". It really isn't. So when I'm moving in the movement phase and I want a squad dead, I'll position myself to put the right amount of firepower on them. What I'll also do is have a couple backup units that can shoot them if I roll badly, but also have other targets if things go as planned. Rarely does it work out perfectly. There'll be that last marine with a meltagun that you KNOW is going to blow up your landraider if you don't kill him. But having fired all your firepower you've allocated, he's still alive. Now you use your reserve and....still alive. Now you turn your long-range lascannon devastator squad you were going to use to take out that dakka predator on him because you KNOW he's got your landraider in his sights and he still won't die!

These things happen.

My goal in the Movement phase is always to set up a multi-layered shooting plan. Priority targets will be surrounded so they are in the kill-zone of multiple units in case the "normal" amount of force doesn't finish the job. If it does, they have been placed so that they can direct their fire elsewhere. This tends to lead me into a staggered advance, keeping units inside one another's threat radius, and thereby protection. Balancing these offensive maneuvers with positioning designed to protect me from the upcoming enemy phases is the greatest tactical challenge in this game, IMHO.

If we consider that probability means a single grot can take on a fully kitted terminator unit, it makes it apparent how silly the "probability negates your mathammer" argument is. Sure, the grots /can/ kill the terminators. However I'm not going to let the game hinge on that. I might, however, let the game hinge on three Vindicator pieplates dropping on the Terminators' heads.

jimbob123432 wrote:Thank you! Also, I was the one who posted about general and math in the field. I'm well aware that people do do pre-war calculations, and that what I was arguing for. I'm against in-battle calcs.
All praise to the Dice Gods!

You keep bringing up this wierd point. I'm wondering, how many games have you played against people who pull out calculators during the game? I haven't played, met or ever seen any... and I doubt many (if any) people here have.

I have never PLAYED against someone using a calculator but I have watched games where it happens.

The only problem with mathhammer is that it is like a science experiment under perfect conditions the results do not reflect in game results.

Translation. "I don't really understand X, so it must be stupid."

It's already been beaten to death what Mathhammer does for you. If you don't get it, you don't get it, but that doesn't make it any less useful to people who do. So let's try to get a more actionable take away from this thread.

Here's what I'd suggest: Don't negatively judge something you don't understand.

Or: Don't negatively judge something that is entirely optional, and nobody is forcing you to do.

That, right there, is two very good reasons for your post to never have existed.

The best reason, though, is probably that it doesn't just make you look confused, it makes it apparent that you're frustrated enough with your confusion that you needed to post about it.

but experience is better than going by bad math... and thats what math hammer generally is.

It's not "bad math." There are so many false assumptions here...

First off, you seem to think that "Mathhammer" means basic multiplication of odds and trials to provide an average outcome. It doesn't have to mean just that. It can mean any form of mathematical examination of probabilities and statistics in 40K.

Regardless, even if we're talking about the simple approximations generated by muliplication of odds and trials, these approximations are still fairly accurate. They're not as comprehensive as a full binomial distribution, but they nicely capture the expectation of the situation. They're far more accurate than the "feeling" one might amass over any number of games.

If nothing else, they're a common language. If you tell somebody that a weapon kills "about 3 MEqs" they know a lot more clearly what you mean than if you said "a good number of MEqs."

In real combat, generals don't pull out calculators and determine the probability of their snipers taking out an infantry unit.

Actually, they do.

Well, not exactly, but being able to reduce things to expected outcomes is very much a part of military leadership. They run simulations, determine what their expectations are, etc. While they don't, say, calculate the average bench press of a given infantry squad, and divide that by the number of machine guns, they do try to determine the expected outcomes of given situations.

But, whatever. Even if they didn't, this isn't real combat, it's a game based on... Ohhh, that's right. Probabilities and statistics.

Let's instead compare it to something that's far more analogous: Casinos.

40K is a whole lot more like a casino game than it is like real warfare. I hope it's obvious just how much effort casino operators and game players put into examining those probabilities and statistics.

I fully agree with Phryix

LunaHound wrote:I fully agree with Phryix

+1

imweasel wrote:

LunaHound wrote:I fully agree with Phryix

+1

More like 1/3*1/3+1

jimbob123432 wrote:Again, I have no problem if you run the numbers in your head, but pulling out a calculator during games does two things. First, it ruins any modicum of fantasy either player may have and second, it does tend to pull away from the tactical way to play. Besides, there are WAY too many variables to put into a calculator, so what's the point?

I agree, if your gonna pull out a calculator in the middle of the game, and start evaluating your chances, rather than just do it in your head. then id be a bit put out.
I always fallow the good rule of 50/50. you do or you dont, of course playing and knowing what your army is capable of will win for you a hell of alot more than some pencil necked geek whipping out the calc in the middle of the game.

you have no idea what you're talking about. admit it.

Obvious troll is obvious.

Phryxis +1, 'atta boy!

+1 Phryxis.

I'll be honest. I make my lists in excel, usually have my laptop with me to make changes at the store (copying to paper for the actual list.)

One tab of excel has a basic template for a binomial distribution built in. Have I ever used it in a game? Well, actually once, but only because my opponent asked me to. It was more of a "what are the chances" thing, and he knew I had the program and wanted to know.

I set up my lists based on probabilities because I don't give two turds what the average is, I want to know what is "likely." I base my probabilities on importance. If I NEED something to work, I'l pull it out to 90% If I would really like something to work, I'll just pull it out to one standard deviation.

For instance, I NEED to stop a Rhino with my (Tau) Missile Pods. So I plug the numbers into my spreadsheet, and I find out that three battlesuits with TLMP and TA have a little over 67% of rolling an immobilized result on the vehicle damage chart. To me, that is not good enough. If I bring in two Broadsides as back-up, they have roughly the same chance as the three deathrains, giving me a combined probability that is much more closer to my acceptable limit, plus they have a chance of taking out that land-raider after the Rhino is popped, allowing my Deathrains to rain... death on the Marines that popped out of their Rhino 12" off my opponents board edge.

Obviously that is just the tip of the iceberg, but even though I don't make true probability calculations in my head (with the exception of ones I have memorized) it really helps me allocate my forces effectively pre-game.

One thing that I absolutely despise (and other people have mentioned) is the passing of statistical means as probabilities. People, they are NOT probabilities and should not be used as such unless you are either rolling a crap-ton of dice or understand that statistical averages are almost always over-estimates of the probable outcomes. My most recent example is the Tervigon. I started a nid army, so I wanted to see what this monster was made of. Statistically is should poop out 23 Termagants before it goes kaput, which is nice, but that is so horribly skewed by the large results from unlikely rolls further along the distribution that it can be misleading. The P(max) is more like 14 and you can not reliably count on more than 16-18 per game. The reason the average is so high is because on the off-chance that you do get 3,4 or 5 rolls in a game the numbers are HUGE, pulling the mean far far far to the right.

Also, +1 Phryxis

I'm probably using the wrong terms here, because it's been several years since I've tried to do any statistics, but:

Something I've always wanted to see but haven't is a discussion of the standard deviation of various weapons or units. For example, according to arithmetic mathhammer, it should take about 30 bolter hits (45 shots at BS4) to kill 5 marines. It should take 6 plasma hits (9 shots at BS4, 12 at BS3) or 18 autocannon hits (36 at BS3) to kill the same 5.

My question is, which weapon has the lowest standard deviation? In other words, which is most likely to kill exactly or very close to the 5 marines?

This would be very helpful, I think, because it would let you a) choose weapons that fit your style of play (risky or dependable), b) better allocate shooting during the game (i.e. put 'dependable' weapons on the really important targets, shoot the 'risky' ones at targets of opportunity).

Also, Fizyx, that program sounds very helpful. would you mind posting or PMing the details?

+1 Phryxis

Also, I find Mathhammer to be extremely helpful in deciding what I want to field. Several of us have gone so far as to make Binomial Distribution programs which graph the most likely outcomes of a given situation.

Frankly we all think its kinda fun.

Statistically is should poop out 23 Termagants before it goes kaput, which is nice, but that is so horribly skewed by the large results from unlikely rolls further along the distribution that it can be misleading. The P(max) is more like 14 and you can not reliably count on more than 16-18 per game.

I'd like a little more detail on this... I don't see how anything is getting skewed. Not that you're wrong, just that I don't understand what you mean. To me, the 23-24 figure seems perfectly reasonable.

My question is, which weapon has the lowest standard deviation? In other words, which is most likely to kill exactly or very close to the 5 marines?

Looking at the binomial distribution helps a lot with this. Typically there are a cluster of results that are likely, and then nothing outside of that. You're almost always dealing with a bell curve, and then your question is basically asking how flat the curve is.

I think it's important to be able to handle all the possible results: it may not be likely to wipe out a Terminator squad with a single round of Lasgun fire, but you have to be able to handle it all the same.

For example:

Which would you prefer? A Sx APy weapon that is Heavy 2, or a Sx APy weapon that is Heavy 1 Twin-Linked?

You should prefer the former, because while the latter has the same likelihood of causing a single hit, it has a greater potential for damage.

Fizyx wrote:Statistically is should poop out 23 Termagants before it goes kaput, which is nice, but that is so horribly skewed by the large results from unlikely rolls further along the distribution that it can be misleading. The P(max) is more like 14 and you can not reliably count on more than 16-18 per game. The reason the average is so high is because on the off-chance that you do get 3,4 or 5 rolls in a game the numbers are HUGE, pulling the mean far far far to the right.

I disagree with you. Probability would say that you should get more than one successful spawn. Two spawns (the smallest number that is more than one) should yield more than 16-18 total Gants simply because of the 7+x distribution on 3d6 is going to be more common. 19-21 isn't much more than 16-18, but it certainly is more.

Now, I do agree with you that the incredibly small number of rolls you can expect to make with a Tervigon before it burns out (more than one but less than three) means you really can't bank on the bell curve being normalized. This doesn't push the mean in any direction, though (maybe to the left since you can burn out and therefore your results will be skewed lower by no longer having opportunity to normalize the curve).

So... to be good at warhammer, you have to be good at math? What about people who do absolutely no math during the game, and are terrible at math in general?

BobTheChainsaw wrote:So... to be good at warhammer, you have to be good at math? What about people who do absolutely no math during the game, and are terrible at math in general?

Some players instinctively realize what they have to do and what to do it with.

If you don't have that, and are terrible at math, there is a common term for those players.

Food.

sourclams wrote:

Fizyx wrote:Statistically is should poop out 23 Termagants before it goes kaput, which is nice, but that is so horribly skewed by the large results from unlikely rolls further along the distribution that it can be misleading. The P(max) is more like 14 and you can not reliably count on more than 16-18 per game. The reason the average is so high is because on the off-chance that you do get 3,4 or 5 rolls in a game the numbers are HUGE, pulling the mean far far far to the right.

I disagree with you. Probability would say that you should get more than one successful spawn. Two spawns (the smallest number that is more than one) should yield more than 16-18 total Gants simply because of the 7+x distribution on 3d6 is going to be more common. 19-21 isn't much more than 16-18, but it certainly is more.

Now, I do agree with you that the incredibly small number of rolls you can expect to make with a Tervigon before it burns out (more than one but less than three) means you really can't bank on the bell curve being normalized. This doesn't push the mean in any direction, though (maybe to the left since you can burn out and therefore your results will be skewed lower by no longer having opportunity to normalize the curve).

I ran a numerical analysis and plotted a histogram. There is a sharp drop-off right at the 16-18 mark. The graph is on BOLS forums.

Fizyx:

Links please.

http://www.lounge.belloflostsouls.net/showthread.php?t=5295

My goodness, what had become of Dakka?!?! People saying NOT to use Mathhammer? What the hell is going on around here?

I think the overall message has been "Use Mathhammer, but do it before the game so you don't look like a jackalope."

Fizyx wrote:I ran a numerical analysis and plotted a histogram. There is a sharp drop-off right at the 16-18 mark. The graph is on BOLS forums.

Can't see the link (work comp) but without knowing the minutiae of the calculation all I can say is that it doesn't pass the smell test. The only way you could consistently achieve such a low average is if you're burning out after one spawn in the majority of cases.

Think about it, if your histogram is accurate, then Eldar Runes of Warding would be a marginal psychic defense and LD10 casters would pass their test in the majority of cases, which simply is not true. Same with melta versus AV14.

I think I figured out why the histogram was looking so funky.

The histogram is, by the way, very much correct. I'm just not thinking it through all the way. It explains why there are so many sharp peaks in the histogram.

Here it is: You run the probabilities and on average you should get 2.3 rolls with an average of 10.5 per roll, netting 23.65 gants on average. Obviously, this can't happen, it will be 23 or 24, but we are talking averages.

Now, that is a statistical average, and the numerical average for 100k iterations supports that conclusion. However, what the statistical calculation doesn't take into consideration that the numerical analysis shows is what number you roll changes the odds of if you can roll again. For instance, if you roll a 3, 4, or 5 you will have rolled doubles, so you can not roll again. This creates a deficit in the 13-16 region just because the highest probability 3d6 roll (10.5) can not be added to a initial roll of 3,4,5. Now, a roll of 6 has 10 possible outcomes, but only 4 of them doubles. So even though the chance for an outcome of 5 is 6/216 (or 1/36, same as rolling double 1's or 6's) the probability of rolling a TOTAL of 6 is lower at 4/216. The chance of rolling a 6 and getting to roll again is 1/36. This means that a chance of getting a TOTAL of 6 is lower than a total of 5. Now, this also means that a total of 16-17 should be a little higher than others around it, based solely on the roll of a 6. Now, a roll of a 7 has 15 possible outcomes, but 9 of them are doubles. So if you happen to roll a 7, you are MORE likely to roll a double than not. Which, again, threatens the totals further to the right from subsequent average rolls that will never happen. This is also true on the other end of the range. 16,17,18 will also kill your roll. While they themselves are not very likely, they make rolls of 26-28 even less likely since it caps the amount of number combinations you can roll to get those numbers.

What this ends up doing is creating a large region from 10-17 where the probability of rolling that TOTAL amount is actual very very similar. Then there is a SHARP drop at 18 to a lower plateau from 19-23 which are each about half as likely as 10-17. The median, by the way, is 18 even though the average is 23. The peak of the "probability" curve (which can't be drawn as a simple Gaussian or even double Gaussian) is 14, but a 15 is 2/3 as likely. 16, however, is almost as likely as 14. This is all a artifact of you are more likely to roll doubles with certain numbers. Since there are twice as many numbers in the area twice as likely, you are 4x as likely to roll one of those numbers than you would the larger ones. The curve is a very nice decaying exponential after that point.

Basically, the answer is this. All these probabilities for individual numbers is rather low, but the probability of 10-17 is much more likely than 19-23. What skews the average so far away from the median is the fact that if you do get 3+ rolls, the numbers that are more likely to give you those rolls are in the 8-13 region (24-39 total.) In other words, the more average you roll, the more times you will roll. Honestly, though, looking at the numbers a little more critical, even though the 19-23 is 4 times less likely than the 10-17, the 10-23 region is still well within what you would call one standard deviation from the peak of a Gaussian, if you really could fit one. 10-23 only encompass about about 50% of the area under the "curve" with about 17% below it and 30% above it. It looks really weird to someone who is not used to these kinds of distributions (me).

I hope that makes sense. This is WAY outside of my area of expertise.

GeneralRetreat wrote:I think the overall message has been "Use Mathhammer, but do it before the game so you don't look like a jackalope."

Ah yes, that is right. I got past the first few replies and had a heart attack.

I really liked your post, GernealRetreat on the real worl use of probability in actual warfare.

Also, Phryxis +1 from me as well, thanks for delivering the goods as usual.

GeneralRetreat wrote:I think the overall message has been "Use Mathhammer, but do it before the game so you don't look like a jackalope."

Yup. well put.

Fizyx wrote:
I hope that makes sense. This is WAY outside of my area of expertise.

You are making loads and loads of sense. Thank you for taking the time to not only figure these things out, but also sharing them with us. Your brain makes me horny...

I'd really like to see a repost of the graph, here on dakka for example, or anywhere that doesn't require me to register with BoLS.

Here it is. Honestly, I think the numbers higher than 18 are more likely than I was preaching earlier, but you can see why I was freaking out, lol.

Thanks, Fizyx, this format makes a LOT more sense to me. What this really shows is that probability of spawning less than ~15 models is a little less than 40%. Since spawn burnout will occur after one spawn ~44% of the time or you could roll a low number for two spawns, that seems perfectly reasonable.

The "meat" of the distribution, however, occurs to the right of that threshold. So if you do manage to get past that first critical spawn roll without screwing the pooch, you have greater than a 40% chance of totaling 16 or more total models spawned.

Thank you Fizyx. I really like the seemingly random peaks and lows. Goes to show just how organised a random function can be :-)

And I'll risk stating the obvious: When making educated guesses during the game, always remember that your dice does not have a memory. No matter what you rolled the last time, you always have a ~44% chance to roll a double. As an anecdote: The high-rollers wheel at the monte carlo casino once came up "black" 27 times in a row. A lot of people lost huge amounts of money by thinking "OMG, 25 black in a row, the chance of the wheel coming up black again is less than 1 in 67 millions, let's bet for red." Unfortunately the wheel always has ~49% chance to come up black.

CKO wrote:Why do I see all of these guys pull out their calculators to do mathhammer?

Because it is useful as everyone - including yourself - knows.

Dont you get the same thing from experience?

Sometimes, sometimes not. Everyone can spend some time with a calculator but not everyone can pull out experience from his pocket. Knowing chances on top of experience is even better.

The only problem with mathhammer is that it is like a science experiment under perfect conditions

Rubbish. You're just making up stuff again.

Generally speaking, I'm a rather indecisive player, and being an Imperial Guard player I'm rather often faced with the decision of what to shoot. For example, I've got an autocannon and there's a damaged killa kan squad (lets say 2 guys out of 3, assorted missing weapons and things) coming at me from one angle and a dread on the other. While I don't bring out a calculator I do something much, much worse.

I ask the clubs resident accountants and/or bankers what is the ones I have a higher chance of killing, even if its my opponent!

Shameful, yes, I know :(

I do think experience does count a lot though, if you're either instinctively know, or by experience know that this should do better at killing that, you become that more efficient in your game, with far less uhmming and aaahing like I do!

I do know I've improved in the last 6 months though now that I've gotten more into the swing of the game.

+1 Fizyx. That last analysis lines up a lot better with my memory what I've observed tervigons doing in actual gameplay--often crapping out on the first roll, and I have yet to see a pair of tervies spawn more than about 30-35 gants total.

All the more reason, as Shep pointed out, why nid players should run their tervigons like transports: haul forward at full speed and not spawn until they're in the opponent's grill instead of trying to drop one spawn after another while slogging across the board.

I think another thing that was screwing me up is that I normally run this analysis for a given number of shots. That is, I run 100k iterations of 24 pulse rifle shots that hit on 4, wound on 3 and save on a 3+. That means the maximum number of wounds will be 24 (it is also why the x-axis says "wounds," lol.)

In this case, though, there is no theoretical maximum except for the kill I put in at turn 7. When I ran the simulation for a maximum of three iterations, the real possibility of the 23+ range really shone since basically everything that would normally be after 30 was now added into the final third roll.

In other words, Flavius and others are right. There is really no good reason to spawn anything on turn 1 or 2. Too bad you can't pod it in.

This is a fantastic thread. I've always used probabilities in my games and it has helped tremendously over the years. I apologize before hand if my point has already been covered in this thread, but here goes.

I see one of the major problems with the application of probabilities with players is the misinterpretation of data.

For example, on average you need to cause 3 wounds to expect 1 failed power armor save. So most players expect to kill 1 marine for every 3 wounds they cause. But what this leads to is that people start to believe that this the rule and not the expected average.

Truth of the matter is that when you have caused 3 wounds, there is actually only a 70% chance of actually killing that marine. In other words, there is a 30% chance you can successfully consecutively pass 3, 3+ armor saves. (Odds of pass a single 3+ save is 2/3, odds of passing all 3 3+ save is 2/3x2/3x2/3 = 8/27 or 0.2963).

My point is this, the expected average is just that. An expected AVERAGE. It is not a guarantee that you will get the result you are expecting, and in a lot of cases, the actual chance is a lot lower than you think. What this leads to is a lot of times players either don't apply enough resources to solve a problem, because they have a false sense of security, or they don't take a shot because they think the odds are much lower then in reality.

Expected averages are quick and simple arithmetic problems that everyone can do in the middle of a game. It has its uses, but we all need to think a little deeper to get to the truth.

So if anybody is willing to revisit the infamous lascannon vs. assault cannon against a land raider numbers, I'd be really curious to see that (maybe on a different thread, though?).

It always seemed to me that even though the assault cannon gets higher average penetration, the fact that you only roll that additional die when the rend rule is "triggered" by a 6 on the penetration roll meant that a bunch of relatively infrequent outcomes with big numbers were pulling the mean artificially high, away from the actual probabilities.

Chance of Penetrating hit (any result)

BS 4 Lascannon vs AV 14

Hit on 3, Pen on 6 x1 shot
(66.6% x 16.6%)

11.0556 Chance per round of shooting

BS 4 Assault Cannon vs AV 14

Hit on 3+, Pen on 6, then 5+ x4 shots
(66% x 16.6 x 33.3%)

3.615 Chance per shot
(x4) 14.462X chance per round of shooting


As you can see, the difference is marginal (3%) but distinct, and only results from the higher rate of fire of the Assault Cannon.

Some other factors to consider:
Lascannons have 48" range, so technically, an Assault Cannon has a 0% chance from 25"-48", and 11% is better than 0%.

Twin-linking will raise the statistics of both equally, except for the fact that it allows more chances at a Rending result for the Assault Cannon. Since Rending results are all that matter in this example, this swings the probability even more towards the Assault Cannon (inside 24" of course).

Case in point, I have had my Land Raider popped once by a T-L AC. Never by a Lascannon. But that's just experiential evidence and has no real bearing on the stats above.

Here is the quick and dirty version. I can go into more depth if you think is necessary, but I think the following analysis is sufficient.

Note: The odds reported are the odds of a hit bouncing off (i.e. not causing either a glance or pen), to calculate the odd of getting a glance or pen is the 1 - the odds. Lower is better.

Odds of a single lascannon hit bouncing off against AV10 is 0 (0%), AV11 is 1/6 (17%), AV12 is 2/6 (33%), AV13 is 3/6 (50%), AV14 is 4/6 (67%).

Odds of a single assault cannon hit bouncing off against AV10 is 3/6 (50%), AV11 is 2/3 (67%), AV12 is 5/6 (83%), AV13 is 5/6 (83%), AV14 is 8/9 (89%).

The inverse of these odds are the the odds of either a glance or pen, each additional hit you put on will lower the percentage of a bounce by the percentage of a not bounce.

For example, a single assault cannon hit on AV 14 has 8/9 (88.89%) chance of bouncing, meaning it has a 1/9 (11.11%) chance for a glance or pen. 2 hits will lower the odds of bouncing to 64/81 (79.01%). The difference in the odds of bouncing (8/9 - 64/81 or 88.89%-79.01%) between 1 hit and 2 hit is 8/81 (9.88%), which is a 11.11% improvement (8/81x9/8 or 9.88%/88.89%).

So what does this all mean? Well if you hit with 1 lascannon and all 4 assault cannon shots AV14, your have a 4.24% better chance of getting either a glance or pen. Assuming you have BS4, you have a 66% chance to hit with 1 lascannon, but only 19.75% chance of hitting with all 4 assault cannon shots. 3 hits from the assault cannon hits give you a 70.23% chance of bouncing vs a 66.67% chance of bouncing a lascannon hit.

Bottom line, the expected average of an assault cannon vs AV14 is better than a lascannon. However assuming BS4 shooting, you will only ever see that about 20% of of the time, and during that time it is only better by 4.24%.

*Edited for clarification.

Will wrote:

Odds of a single lascannon hit bouncing off against AV10 is 0 (0%), AV11 is 1/6 (17%), AV12 is 2/6 (33%), AV13 is 3/6 (50%), AV14 is 4/6 (67%).

Wait doesn't a roll of 1 always miss?

Sorry if this was covered in your description but I didn't notice it if it is.

CrazyThang wrote:

Will wrote:

Odds of a single lascannon hit bouncing off against AV10 is 0 (0%), AV11 is 1/6 (17%), AV12 is 2/6 (33%), AV13 is 3/6 (50%), AV14 is 4/6 (67%).

Wait doesn't a roll of 1 always miss?

Sorry if this was covered in your description but I didn't notice it if it is.

I assumed that you have already hit, as the roll to penetrate a tank is independent of how well you hit.

You can also look at it this way. With BS4, 33% of the time you will miss, thus giving you 33% chance of not doing anything to a vehicle right off the bat with a lascannon. An assault cannon firing with BS4 has only a 1.23% chance of missing all four shots, so right off the bat the odds of you not doing anything with an assault cannon is much better than the lascannon. I should have clarified this better.

Ok thanks for the clarification

Will wrote: I apologize before hand if my point has already been covered in this thread, but here goes.

If you truly feel this way you could try READING the thread before posting. It's actually a great way of getting to know what is already covered in it. Much like how real life works actually... Allright, sorry for that sarcasm, you just happened to be the latest one to post that actual sentiment, and it always annoy me. So I took it out on you. Nothing personal.

Apart from that sentence your post is very sound. Data is worthless wihtout interpretation. And yes, that has been stated earlier in this thread, but not nearly enough times. Data != Information. Average != Effect.

Speaking of evaluating the value of various combat/shooting configurations, there's something I'm calling "weighted expected value".

It's basically the expected value of a set of attacks (the product of the total number of attacks multiplied by the likelihood of any particular attack having some effect), multiplied by expected utility if those attacks hit at a 100% rate, or the maximum potential value.

Weighted Expected Value:
EV = (Number of Attacks x Likelihood of Effect)
PV = (Number of Attacks x Likelihood of Effect or 100%)

WEV = EV x PV

The easiest way to explain it is to consider two Bolters and a Twin-Linked Bolter. While they may be equally reliable, having the two Bolters is better because they have a greater potential for damage.

The basic notion is that while thinking only of the expected value is nice, seeing as that's what's most likely to happen, we also need to consider what's less likely to happen: getting lucky and getting unlucky. Getting unlucky, thanks to the Warhammer system of potential for failure, is a wash. But getting lucky maximizes the potential of any number of attacks. If we think of the totality as divided into thirds (not really, but close enough), we can consider bad luck as happening 1/3 of the time, the expected value 1/3 of the time, and good luck as happening 1/3 of the time.

So because the weighted expected value accounts for 2/3 of the time rather than 1/3 like the expected value, we have a more accurate gauge of the value of various configurations, and a reason to account for the number of attacks twice (once when they increase the likelihood of something happening, and once again when they are what has happened).

To me the use of mathhammer is in deciding which units belong in my list. What am I playing against? Is it an all-comers list? How do I intend to use the unit? What is it delivering versus what does it cost to field?

When you get to a game, I follow the role I have for that unit in my army - If my primary AT unit is a devastator squad with 3 ML and 1 LC I am firing it at the enemy's biggest threat armor - albiet I may ignore the landraider and go at the predator but I am using mathhammer to develop an effective force mix not to figure out turn by turn what to shoot at or should I charge. That is by instict and experience. As an example, based on situations I may do something that mathhammer says I will lose but it may serve a vital purpose for the rest of my army... 10 tacticals with no PF sgt may just charge that wraithlord or ork boyz unit because I need to tie them up for a turn/turns to hold that objective even if mathhammer says I will lose.

WEV = EV x PV

The idea here is sound, but this specific implementation strikes me as being a bit skewed.

At various points in 40K, there are situations where you'd have a huge number of trials that have a very poor chance of success. Say, lots of S4 models trying to hit a Skimmer on a 6+. This result would end up looking far better than it should. It also places a lot of emphasis on hitting, rather than "getting a result."

What I'd suggest instead is going with the standard deviation, and then giving the values that describe either edge of the standard deviation.

If you don't like the standard deviation, you could use some arbitrary percentage, and then use the edge values such that you have that percentage for results between your two values.

To put it more clearly, you might say "when X shoots at MEqs, 90% of all results will be greater than 2.5 dead MEqs, and less than 3.75 dead MEqs." This will give you a range of results that you can be pretty certain will cover whatever result you get.

Actually, i have a question regarding mathammer.


Has anyone figure out how to apply rending rules as far as fractions/percentages go?



Automatically Appended Next Post:

Nurglitch wrote:

The easiest way to explain it is to consider two Bolters and a Twin-Linked Bolter. While they may be equally reliable, having the two Bolters is better because they have a greater potential for damage.

Sorry nurglitch, I mean no flaming, but that actually is wrong, or maybe I am misreading your post... this seems more likely, because you said a whole bunch of intelligement sounding stuff and I confused me.


When accounting for re-rolls, you take the original percent chance of something missing, and square it, and subtract this total from 100% or 1 if you prefer to use fractions. I prefer fractions myself, but I'll use your example of the two bolters and one twinlinked bolter against say... another space marine.

the original miss chance of an SM firing a bolter is 2/3, so the miss chance is 1/3. 1/3*1/3 = 1/9 so the miss chance of a TL bolter is 1/9.

therefore the equation for a TL bolter firing and wounding a space marine is 8/9*1/2*1/3= 4/27

The equation for one bolter is of course 2/3*1/2*1/3= 1/9 because there are two bolters, the value doubles to 6/27.

So two bolters aren't less reliable than a twin linked bolter.

Again, apologies if this is what you were trying to say


Btw, what you're saying about the luck factor is spot on

There is absolutely no reason to dislike off-table mathammer. Sorry OP, but that's the truth, and if you don't like it, ignore it. It's perfectly fine to calculate your chances of getting a certain number of kills or termegant spawns or whatever in a given situation.

However, when you whip out a calculator mid-game, that's just lame. Let's face it: you're not a general, you're playing with little plastic men on a table. When someone takes out a calculator mid-game because "real" generals do it, that just ruins the whole atmosphere and completely takes any fun out of it. It's a fun game. So keep the fun in it, and don't be that guy that has to calculate his chances of killing the whole squad of terminators with a single Firewarrior assault when any n00b can see that the skinny anime guys are gonna get destroyed.

Shrike78 wrote:Has anyone figure out how to apply rending rules as far as fractions/percentages go?

I can do it, but I don't have the formulas for rending in my program, so I have to do it all by hand.

Basically, I calculate the normal wounds like normal, but wounding on one higher (to remove the 6 for wounding), then add in the rending results after-the-fact. It takes a few moments, but it is doable.

I have two programs. One actually takes seed numbers and calculates the binomial distribution. The other just does 100,000 iterations of the dice rolls and plots a histogram of the results. The second I am modifying to allow for rending and other effects. I just haven't had the time, but next week looks clear.


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Overall I have two rules of thumb when it comes to Mathammer.

The first is this: happens. I account for this by rating probabilities. Average is "average." One standard deviation above average (84%) is "likely." Two standard deviations (98%) is a "sure thing." One standard deviation below is "unlikely."

For instance, when Tau was my main army there were certain rolls I NEEDED. I need to pop transports. Well, one squad of Deathrains has a "likely" chance to pop the Rhino, but I needed a "sure thing." Well, two Broadsides also has a "likely" chance to immobilize a Rhino, and when you put them together you have almost a "sure thing." So, at 1500 points that is what I had vs. a Mech army. It had the added benefit of being able to go after a second target if the first "likely" result succeeded.

Similarly, if I knew a certain load-out had an "unlikely" chance vs. MEQ, I just wouldn't bring it unless it had a secondary purpose (like a Pathfinder squad.)

The second is this: Dice Gods favor the odds. It sounds like a "duh" thing, but if you look at a probability distribution for a moderate number of shots with a low likely-hood of success for each individual shot, you will see the opportunity to roll poorly is more devastating than the equivalent rolling higher. That is, there is a larger number of wounds separating the standard deviation above the distribution curve than below. The exact opposite is true of low count shots with higher probability. Yes, the deviation is technically higher, but the chance for rolling exceptionally well is better than rolling like . That is why you should never let you terminators out of cover in range of my Helios suits with Markerlight support, lol.

That is how I plan my lists pre-game.

Of course, there is some stuff that just *doesn't* make sense on paper, but is phenomenal on the table. That is one thing a good player can recognize and why experience is still necessary in army list construction.

Fizyx wrote:

Shrike78 wrote:Has anyone figure out how to apply rending rules as far as fractions/percentages go?

I can do it, but I don't have the formulas for rending in my program, so I have to do it all by hand.

Basically, I calculate the normal wounds like normal, but wounding on one higher (to remove the 6 for wounding), then add in the rending results after-the-fact. It takes a few moments, but it is doable.

so the formula for say sniper scouts vs MEQs would be

Normally 1/2*1/2*1/3

with rending X*(1/2*1/3(?)*1/3) + X/6(?)

My friends and I actually figured out the equation a few months ago, but none of us for the life of us can remember what it was... I blame super glue fumes

IF you wanna play the game the way its supposed to be played, you dont use a calculator. Doing it in ur head is different in most cases...

Shrike78 wrote:
so the formula for say sniper scouts vs MEQs would be

Normally 1/2*1/2*1/3

with rending X*(1/2*1/3(?)*1/3) + X/6(?)

Something like that. It'll be 1/2*((1/3*1/3)+(1/6))

So the non-rending is 1/12 (or 3/36) and rending is 5/56, or 66% better. Daaaaang.

Shrike78:

You are correct. It is not flaming to point out when someone gets something wrong, particularly if you explain how they are wrong. Thank you for crunching the numbers so I didn't have to!

Nurglich and Shrike:

I love where your discussion is going. Nurglich, I never thought of it in those terms, or, I should say, extrapolated the figures far enough to see the difference in expected returns vs maximum potential returns. That's a great way to see the "upper limit" and work backwards, too.

Shrike, I like fractions for mathhammer, too. It's cleaner, but as my final step, I just divide them in to numerals for clarity to my American mind. Most if not all of my longhand work is done in fractions.

To whoever asked about converting back and forth, just do the math ( "/" means divide!). Each side of the dice that can succeed is 1/6 chance of success, or roughly 16.667%.

Nurglitch wrote:Speaking of evaluating the value of various combat/shooting configurations, there's something I'm calling "weighted expected value".

It's basically the expected value of a set of attacks (the product of the total number of attacks multiplied by the likelihood of any particular attack having some effect), multiplied by expected utility if those attacks hit at a 100% rate, or the maximum potential value.

Weighted Expected Value:
EV = (Number of Attacks x Likelihood of Effect)
PV = (Number of Attacks x Likelihood of Effect or 100%)

WEV = EV x PV

I am ashamed of my mental faculties. I understood the rest of this post, but I am completely lost as to this part's meaning or even application. Being something of a mathhammer geek (hey, i'm not too great at tactics, so I might as well know how much of what kills what right? ) I thought I could handle the majority of statistical figures in relation to dice roles...

This has proven me wrong

Mathhammer is an advantage, why shun it when it is so readily availibale. To know how a unit should preforme is really useful, also since warhammer is a game of averages it really becomes useful. (wow my spelling sucks)

Stepping back to the rending issue...wouldn't it be:

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

To explain, it is your 50% chance to hit plus the probability to get either a normal wound with a failed armor save or a rending shot with no armor save allowed. Which is about 13.89% (5/36, not 5/56)

Then, if you want to find the chance to get a single wound for X amount of shots:

1-(31/36)^X

Axyl wrote:Stepping back to the rending issue...wouldn't it be:

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


To explain, it is your 50% chance to hit plus the probability to get either a normal wound with a failed armor save or a rending shot with no armor save allowed. Which is about 13.89% (5/36, not 5/56)

holy crap man! that equation is absolutely right! High five! you win a cookie.

Then, if you want to find the chance to get a single wound for X amount of shots:

1-(31/36)^X

This model is incorrect i believe. If for no other reason than because according to your equation you will never have a 100% statistical likelyhood of wounding a model. While practically there are never 100% guarantees, statistically speaking there are.

Yes, Axyl, that is the correct rending formula.

And, Shrike, you can never, ever have a 100% probability. Yes, it gets very very likely the more dice you throw, but you can never be sure. 100% - (the chance not to wound)^(number of rolls) is correct. Yes, the (1-p)^N gets very small, but it will never actually reach zero.

Shrike78:

The notion is to compare the combat potential of weapons and models. This potential is not merely by the expected value of their attacks, or averages, as despoiler52 puts it, but by the maximum potential values of attacks in relation to the reliability of those attacks.

In theory, there's the average, and then the margins of error, or deviations from the average. Given the small sample of dice rolled in a game of Warhammer 40k then predictions based solely on expecting the average are prone to error when the results of the dice deviate from the expected average. You'll miss something like 2/3 of the bell curve.

But that's okay, because there's hard and fast limits on what might happen. Potentially, thanks to the Warhammer system, the floor is always 0, and the ceiling is limited by the number of attacks or shots.

So we weight the expected value only by the maximum potential ceiling, because the floor is the same in all calculations and can be safely ignored. This gives you a value, the greater the better.

There's a number of objections to doing this:

(1) If the expected value happens most of the time, why worry about an unlikely potential?

A: The answer to this is that you should worry about an unlikely potential because Warhammer is about capitalizing on good luck as much as it is about relying on average luck.

(2) This over-values effectiveness over reliability!

A: No, this values potential only so much as increases in potential outweigh losses in reliability, rather than over-valuing reliability as the expected value does by ignoring the unlikely in favour of the likely when both are a part of the game.

(3) This doesn't tell you how the weapon should be expected to perform!

A: No, that's what the expected value does. The weighted expected value lets you compare the value of a weapon to its comparative price when determining a model/unit/army configuration. After all, this is how spam works: you throw out enough shots or attacks and something will stick, and sometimes it all sticks. If you're looking for more familiar numbers, divide by 2, but be careful not to confuse the ensuing number with the expected value as it will over-state the reliability of the weapon.

(4) You count the number of attacks/shots twice!

A: Sure, but we also count the likelihood of both the average and the maximum potential occurring. It's just that the maximum potential always occurs when it occurs, by definition.

The ratio of expected value to weighted expected value is probably indicative of something, though what I haven't figured out yet. I find the weighted expected value reflects the notion that "Quantity has a quality all its own".