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Note: Unsure if this is the correct place for this thread, but as Tactics uses math-hammer more than any other sub-forum I thought I'd put it here.

I was listening to the 11th Company podcast a few weeks ago and they had a very interesting segment revolving around dice rolls, statistical averages and the game of 40k. The Eternal Warriors also did a very similar segment and, whilst obviously those podcasts are widely available to people with access to iTunes, I thought I'd reiterate some of the major points that they made.

The first and most important point is that, contrary to popular belief, math-hammer and working out the 'odds of success' can actually be very misleading. The reasons behind this are quite straightforward: when you use maths to calculate the odds of something in 40k doing damage, you trying to find the mean percentage of something succeeding. However, the volume of dice thrown in a 40k game is vastly inferior to the amount of dice you needto throw in order to actually see an average spread of results. If you threw 10,000 dice you will find that, overall, your dice rolling will conform to the % that you calculated. In a standard game of 40k, however, you will never throw anywhere close to 10,000 dice and thus you'll find your results are skewed. Any fluctuations in the dice results will have a much, much larger impact when you only throw, say, 500 dice in any given game as opposed to 10,000. Luck, like it or not, has a much greater impact on a game of 40k than statistics and statistical averages.

And this is where math-hammer falls down. Math-hammer does not take into consideration an element as unreliable as luck, and so you find yourself calculating a %, coming up with a result, and then being surprised on the table when your dice don't conform to that result. When your dice are hot, you will invariably smash any opponent, regardless of any other variable such as list build or gameplay ability. Conversely, you could be the best gamer in the entire world, but if your dice go cold on you there is simply nothing you can do to prevent losing. The highs and lows of dice results, whilst generally ignored when rolling 10,000 dice (due to the huge number of rolls, any irregularities will invariably balance out), are felt much more keenly in a game of 40k when the sample of dice rolls is far smaller. You feel that luck factor much more keenly because of the reduced scale.

Let's use an example to illustrate my point. Let's say a Space Marine shoots a bolter at another Space Marine. He has a 66% chance to hit, a 50% chance to wound, and a 33% chance of his opponent failing his armour save and dying. So 0.666 x 0.50 x 0.333 = 0.11. So we say that Space Marine has, on average, an 11% chance to kill his enemy. Fine. But what if your dice suddenly go crazy hot? What if you roll a 5 to hit, a 6 to wound and your opponent rolls a 2 for his save. Now what if you do that 3, 4 or 5 times in a row? Your dice are defying the mean result by a vast margin, and your opponent's dice are doing likewise. If you had 10,000 Space Marines all shooting at the same time, there's a much more likely outcome that they will indeed kill ~1000 of their foes, but due to the much smaller scale of a 40k game, where its unlikely you'll have upwards of 10-20 marines shooting at any one time, any obscure dice results will have a much greater impact on the game.

You may be saying to yourself: 'We all know luck is a factor, so what?' Well, I think that in this sub-forum particularly, far too much emphasis is placed upon averages, and not enough emphasis on luck. I know luck is a completely unmeasurable variable, and thus we use math-hammer purely for the simplicity and so we are able to measure something and come up with a tangible result. I just think that occasionally the scale of the game needs to be taken into consideration, along with the likelihood of encountering particularly absurd results. Subsequently, I believe that math-hammer, whilst good as a 'quick-fix', should not become the defining characteristic that we base every single decision in 40k upon.

L. Wrex

Addendum: I used the sample size of 10,000 purely because the larger the sample, the more 'reliable' the result. I could have said 25,000, 50,000 or 100,000 but I didn't. If it bothers you that I used 10,000 as a benchmark, simply replace it with an equally large number of your own choosing.

In a single game, the number of dice thrown is comparatively small. Over a long series of games, things tend to average out.

For a tournament player, who is going to keep the same units/armies more-or-less the same possibly for years, the long-term averages are more important than temporary variations due to luck.

Also things where you throw a lot of dice at once--ten thunderwolves charging--tend to average out more reliably than things where you throw only a few dice--seizing the initiative. If there's one thing I see misunderstood a lot about mathammer, it's the distribution of the probabilities more than the mean values.


I know this is why I personally prefer, for example, multi-shot weapons over single-shot weapons in my Eldar armies. I'd rather get average results from a two-shot pulse laser than have to depend on a BS3 brightlance.

A unit performs statisticly more often then not. Mathhammer is a tool used to evaluate units. Luck is not.

So when considering a tactical decision and how it would impact your game, would you:

a) calculate the possibility of risk vs. reward via math and knowing the odds

or

b) hope you're lucky

Knowing the probability helps in making sound decisions. It helps minimize risks.

Feeling luck either makes you win big, lose big or, yannow, play average. Which gets you nowhere.

Therefore, should you base your tactics on statistical averages or should you just pra to the dice gods?

Flavius Infernus wrote:In a single game, the number of dice thrown is comparatively small. Over a long series of games, things tend to average out..

For a tournament player, who is going to keep the same units/armies more-or-less the same possibly for years, the long-term averages are more important than temporary variations due to luck.

Whilst this may be true, there are plenty of examples within this forum where a single statistic is touted for any given situation. 'S8 has an X% chance of stopping AV11', 'Plasma has an X% chance to wound models of T6 or higher'. The vast majority of people are the instant-gratification type, they don't look over the course of 10, 20 games to see if the averages balance, they want to know what that weapon/unit will do right here, right now and then are confused and/or upset when the dice go awry and their nice, neat %-based game play folds in front of them. Not to mention that there is an insane number of variables in the game itself that also sways the results one way or another.

I'm not saying 'never use math-hammer', I'm putting forward the POV that it shouldn't be relied upon for every single eventuality in a game which, unfortunately, us internet types have a habit of doing.

Flavius Infernus wrote:Also things where you throw a lot of dice at once--ten thunderwolves charging--tend to average out more reliably than things where you throw only a few dice--seizing the initiative.

Indeed, because the sample size is larger the results are more reliable. But even 10 thunderwolves charging is prone to the same limitations; the number of dice still isn't large enough to see truly average results. Were 100 or 1000 thunderwolves charging then yes, the dice would very likely lead to reliable results. As is, touting your chances as success as X% is, unfortunately, not always going to yield that result.

L. Wrex


Automatically Appended Next Post:

starsdawn wrote:So when considering a tactical decision and how it would impact your game, would you:

a) calculate the possibility of risk vs. reward via math and knowing the odds

or

b) hope you're lucky

Both.

L. Wrex

I do not agree with your argumentattion. It is unsound.

When that has been sead mathhammer is not very reliable because while 7 is the moast predictable resoult when you roll 2 dice it is mutch better ods of not rolling the predicted number.

The only way to relly on mathhammer is of you go in with an owerkill.

Mathhammer is a tool, not a panacea. Its application is strategic, not tactical; against a known array of opponents, how can I expect this unit or combination of units to consistently perform? Where is my list overweighted; I have two Vendettas and two Hydras and 125 points left to spend. What's the most efficient use of those points? Shave 5 to get another Vendetta? Shave 25 for another Hydra squadron? 1 Hydra and plasmaguns on my command squad?

I have 8 Razorbacks; Twin-linked ACs or las/plas? What is the range premium worth compared to twin-linked rending?

The players who understand the math ultimately tend to have balanced, flexible armies.

The players who don't tend to have 125 points worth of power fists on their tac squads.

The reason we talk quite a bit of mathhammer and averages is that were on a tactics forum.

There is a built in limit on the level of tactical discussions when your limited to saying "Dude, my grots totally wasted BA in assault!!"
In order to have a rational discussion, we use math to describe averages and probability.

I wanted to also say that was a well thought out and insightful post. I mean no disrespect when I say that it inspired me to go to a casino to try my luck.

Lycaeus Wrex wrote:

Both.

L. Wrex

Which means you did rely on probability. It's something you can objectively know. Can you know how lucky ou are? No.

So what's more productive or sound to do?

As alwas, probability is a tool to be used--nothing more, nothing less. It doesn't make you have an average score every single time. It just takes note of what you'll get if you had the average score, or what are your chances against something. It shouldn't be relied on because, yes, it doesn't happen 100% of the time (waddaaknow, it's called probability!). But so does luck.

But which one of them is quantifiable?

Yes, that's a rhetorical question.

I'd have to agree with everyone else here, especially Taoofss. As with anything there will always be a chance to fail. Tactical Choices in this game aims at reducing that chance. However small a difference, as you said, is a difference. Mathhammer tells us what decisions to make to make those differences in our favour. Also I really dont get your reasoning about the people of the forum being the instant gratification type. Most of the time I see someone bemoaning their losses, it's mostly done for comedic. As for the "X has a Y% chance of wounding Z" type of statements, it's used to compare various pieces of wargear to their cost, not really for mid-battle tactical needs.

Personally I've always made the average and so have my friends. Bar one unfortunate person (who the universe seems to be out to get him, not just in warhammer mind you) we've rarely ever gotten really good or really bad rolls and I find myself saying "You made the average!" so much that I just dont bother anymore.

Also, in regard to the "7 is the average of 2d6" thing. Yes 7 is the most predictable result and that it's actually harder to roll that specific number compared to all the other results you can get, but remember most of the time you're trying to roll Over that number. Hence anything (in this situation) that requires a minimum of 7 automatically has over 50 something chance of being rolled successfully already (As the odds of rolling a 7 is combined with half of the odds of rolling a non-7 number).

Wow ....You do realise that Maths hammer is purely the average and range (normally left off) that something will happen. It is a wonderful tool to workout what might happen when you use A on B. Luck plays no factor in it ... by that i mean that rough 70% of the time this will happen then out 1000 times roughly 700 will turn out the same.

When playing the game for real you use it to predict the future, so as to make tactically sound choices and justify taking risks.

You cannot win a game without taking chances. You can loose a game by taking the wrong ones. Maths-hammer just helps you choose which risks to take.

To say "mathammer can be wrong sometimes, therefore it's useless" is a logical fallacy (error of composition).

Also to say "It's misused sometimes, therefore nobody should ever use it" is the same fallacy.

Lycaeus Wrex wrote:...there are plenty of examples within this forum where a single statistic is touted for any given situation. 'S8 has an X% chance of stopping AV11', 'Plasma has an X% chance to wound models of T6 or higher'.

I think that ('single', as highlighted) is where mathammer gets misquoted or misunderstood - as mentioned in another thread, a 5% chance does not mean something will have happened after 20 attempts (it's something like 66% from memory - someone who knows more about this can direct folks to the workings).

Where it's used as a comparison I think it has more meaning - to answer a specific question, e.g.: "which has more chance of destroying an AV11 vehicle: a Str-7 two shot autocannon or a 3-shot Str-6 multilaser?" This allows a new player such as myself to make sensible target choices, allows comparison against points values (like the Flamer v. Heavy Flamer thread), etc.

I agree, percentages being quoted in isolation are not particularly meaningful.

I'm with Tri on this one.

Mathhammer shouldn't be considered as a constant, but rather as pointers in whichever direction seems to be of your choice, while building lists.

In other words; you use it for getting a hold of a model/units average statline against another.

I do, however, agree to some degree, that mathammer, in some cases, aren't reliable. When rolling several dice, such as when a large Genestealer unit assaults, mathhammer is much, much more reliable, than when rolling for smaller units, such as Hive Guards.
- And don't get me started on how awesome i am, at rolling 1's on my reserve rolls with +2 to reserves

Flavius has it in a nutshell.

Imagine you have a model with a rapid fire weapon within both shooting and charge range of an lone enemy who is contesting the winning objective.

Should you charge, or shoot? Mathammer won't tell you whether either option will be successful, but it will tell you which option requires the least luck.

Given a choice, will you go for the option that requires a little luck, or lots? How will you know which is which without mathammer?


Automatically Appended Next Post:
Also,

Subsequently, I believe that math-hammer, whilst good as a 'quick-fix', should not become the defining characteristic that we base every single decision in 40k upon.

Have you ever found anyone who does think that? I certainly haven't.

Information is never bad. It is only your usage of information that is bad

Take a lesson in statistics, either from a school or a tutor that knows what they're talking about. Play a few games of craps. Play a few games of poker. Try to understand how it all *actually* works.

It's your personal version of Mathhammer that should be avoided and not relied up, if you're expecting it to magically make up for bad luck, or make your units hit all the time.

I don't recall once in my original post saying math-hammer was 'useless' or 'nobody should ever use it'.

What I'm saying is that it shouldn't be the defining characteristic that drives decision-making. Use it as a way to gauge how a unit might perform, sure, but don't say 'The chances of X to happen are Y therefore do/do not take X' because 40k, by its very nature, isn't big enough to reliably churn out average statistics.

What I'm saying is that were a certain situation to re-occur in exactly the same way over and over and over again, then math-hammer would give you accurate results. What, however, is the likelihood of this happening? Extreme variances in dice rolls, whilst ignored in the vast scheme of things, are how 40k games are won and lost. Like I said earlier: you could make the soundest tactical decisions available to you and play in a way that the averages should always work for you, but if your dice go cold you will lose.

Were every 40k game the size and scale of Apocalypse or bigger I could see math-hammer being more viable as a way of saying 'will X beat Y'. When your playing at 1000-1750 pts, the limited number of dice you throw mean the extremes cannot be omitted, runs of good and bad luck win and lose games, regardless as to the percentages you attributed to your units.

L. Wrex


Automatically Appended Next Post:

Fifty wrote:Have you ever found anyone who does think that? I certainly haven't.

The Tactics forum is rife with people who claim a unit is good or bad based upon it's ability to do something as X%. In real life I don't know of anyone who doesn't take into account other factors, but on the internet I guess the easiest way to convey your point is through numbers, so that's what we see most of.

L. Wrex

Lycaeus Wrex wrote:What I'm saying is that it shouldn't be the defining characteristic that drives decision-making. Use it as a way to gauge how a unit might perform, sure, but don't say 'The chances of X to happen are Y therefore do/do not take X' because 40k, by its very nature, isn't big enough to reliably churn out average statistics.

With all due respect, isnt this statement contradictory? Gauging how a unit might perform is exactly what you wanna do to influence your decisions. Anything else and you'd be better flipping coins.

This reminds me of the fights I get into with my girlfriend: we're trying to agree on something, BUT FOR SOME REASON WE'RE YELLING

I think everybody here is trying to say the same thing:

Don't be an idiot when it comes to math. Mathhammer is good for general estimation, but don't forget we play games with dice, and sometimes they hate you.

We have the following means of judging what will happen in games ....

Experience ... we've played a several games and we know how this unit interacts with that unit. This is normally a good indication of what will happen as we are built to see patterns but it doesn't include all the facts because we are also good at see patterns where there are none.
Often people complain that they never make the moral test the true is on average every one will role more or less the same; however if we think we're always failing to make the test we'll look for ever failing and ignore those times we do make it.

Maths-hammer when done correctly, shows probability. Not what will happen but the chance that it will.
If you have a 50% chance of hitting and you fire twice do you hit once? On average yes however the probability is actually 50% that one shot will hit and 25% that both will. If you only need one to hit you can combine these; 75% chance that at least one shot will hit.

What's the argument here?

Is it:

- Be aware there is variation in dice rolls? Duh. Everyone knows this already, or should.

- Don't pay attention to the math, there's too much variation? This is of course of terrible argument.

- Math shouldn't be the defining characteristic that drives decision making. Uh, professor, how well units do on average is very important, in addition to general list composition. You've taken away math in most situations and replaced it with... nothing. Just because it isn't as useful as you argue some people think it is, you remove it all together from most situations / games? That's ridiculous.

Luck is irrelevant. In the end, tactics & strategy triumph over luck.

Mustela wrote:Luck is irrelevant. In the end, tactics & strategy triumph over luck.

Evil will always triumph because good is dumb.

Mustela wrote:Luck is irrelevant. In the end, tactics & strategy triumph over luck.

Oh god, now we have the opposite extreme.

In the long term yes, but even a full tournament is not long term enough for irregularities to even out. There will be people with sgnificantly better dice rolls than others by the end of a tournament.

Mustela wrote:Luck is irrelevant. In the end, tactics & strategy triumph over luck.

If by the end, you mean the long haul (many many games). In the short run or in a given game luck is often very relevant.

But since you can't measure luck, it makes sense to know how well your units can do on average.


EDIT - DOUBLE NINJA'D

Stavkat wrote:
- Don't pay attention to the math, there's too much variation? This is of course of terrible argument.

- Math shouldn't be the defining characteristic that drives decision making. Uh, professor, how well units do on average is very important, in addition to general list composition. You've taken away math in most situations and replaced it with... nothing. Just because it isn't as useful as you argue some people think it is, you remove it all together from most situations / games? That's ridiculous.

I don't know how many times I need to spell this out: MATH-HAMMER IS STILL USEFUL, I have in no way said 'never do the maths'. I am trying to convey that the 'luck' element in the game plays a much larger part in success throughout than simple percentages, and using those percentages PURELY as a mechanism for decision making CAN BE misleading because the scale of 40k does not allow players to roll enough dice to routinely see perfectly average results.

Look at my signature, that's a dice roll I made on Vassal about 2-3 months ago. What are the chances of that happening? Thankfully it wasn't a critical roll, but imagine that all those 1s are saving throws for Terminators. Suddenly a massive chunk of my army has disappeared; not through statistics, as the statistics say that such a roll should happen so rarely as to be obsolete, but through luck. This is rarely, if ever, conveyed to people and is an important aspect of the game, if a completely un-measurable and un-quantifiable one.

Is my original post unclear? Or are people intentionally misreading it for the sake of causing an arguement?

L. Wrex

Stavkat wrote:What's the argument here?

Is it:

- Be aware there is variation in dice rolls? Duh. Everyone knows this already, or should.

- Don't pay attention to the math, there's too much variation? This is of course of terrible argument.

- Math shouldn't be the defining characteristic that drives decision making. Uh, professor, how well units do on average is very important, in addition to general list composition. You've taken away math in most situations and replaced it with... nothing. Just because it isn't as useful as you argue some people think it is, you remove it all together from most situations / games? That's ridiculous.

I think the OP originally wanted to point out that Mathhammer has it's flaws, but quite frankly he only stated what people already knew. In trying to defend his position he really got off course. There was a similar argument wayback about how some people feel that dice really dont add up to the averages as they intended. Realistically though, they do. However certain psychological aspects make them so. a 5+ or 6+ save, universally, is almost synonomous with having no saves at all, and you really dont expect anything with that kind of a save to live longer than 2 turns (or, in the case of nids, survive without taking at least one or two wounds). a 4+ means that they have the chance to survive, while a 3+ somehow guarentees that they'll stick around for alot longer. 2+ reverses this, as you suddenly worry about every single save failure, as the units with those saves tend to be extremely high priced. Same goes for stuff like high toughness and FnP. When you really have those dice in your hand, suddenly 50% doesnt seem like much.

Mathhammer, however, is (again) used to ease all of that randomness. There will always be that moment where the Dice Gods shine upon you, and your lowly unit of 3 guardsman work up the courage to beat the gak out of a Daemon Prince. However, you cannot guarentee that will happen again. What you can, however, guarentee is that a majority of your BS4 shots will hit more times than if you had gone with BS3 scouts.

EDIT: MASSIVELY NINJA'D. Take the first half of my post with a grain of salt.

Right, ok then, Lyc, so you wrote a massive amount of text to tell everyone, hey, there's variation in math. The only thing that could POSSIBLY be misleading about the math is if people expect the average every time. Which could have been said in a sentence, not a massive wall of text.

Obviously, since you cannot measure luck, people are going to use math when coming up with lists. It will inform their list building, tactics, etc;

Thread's done now?

Fifty wrote:

Mustela wrote:Luck is irrelevant. In the end, tactics & strategy triumph over luck.

Oh god, now we have the opposite extreme.

In the long term yes, but even a full tournament is not long term enough for irregularities to even out. There will be people with sgnificantly better dice rolls than others by the end of a tournament.

If you blame things on luck, you will spend no time trying to improve, because you just had bad "luck" and there is nothing you could have done about it.

I am trying to convey that the 'luck' element in the game plays a much larger part in success throughout than simple percentages, and using those percentages PURELY as a mechanism for decision making CAN BE misleading because the scale of 40k does not allow players to roll enough dice to routinely see perfectly average results.

So your argument is that in any single given game, Luck trumps statistics more often then not as the deciding factor of said game? I disagree with this assessment wholeheartedly.