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MechaEmperor7000 wrote:This may be borderlining flaming

I hardly would consider that post a flame, it's the truth.

This type of thread pops up everyone once in a while because people get tired of reading the over-the-top posts of "don't take that squad, unit X is 3% more officent" and they react by saying "tone it down."

I think most everyone would agree that while considering Mathhammer, you have to take into effect the potential effect on the game. Obviously, a squad stuck in dangerous/difficult terrain with bad LOS in a far corner isn't worth attention in the fifth turn of an objectives Mission compared to a squad that is about to claim a game-tying piece of scenery no matter what the odds are. But that is the balance of a game. If you have a great opportunity, but with a slightly less chance, of taking out an important piece of an opponent's army as opposed to knocking a few models off a less influential squad, you weigh that out and act on it, but tha is using the two halves of the game, tactics and "luck" (which is really just probability).

I think the counter-balance for the cut-throat threads in a tactics section of a gaming board comes in the general discussion section where everyone, hardcore mathhammers and just-for-funners alike, discuss the time they had a single scout hold up a Wraithlord for the entire game or a unit of 20 Night Goblins broke a 500-pt High Elf block.

So Wrex basically has 100% no point with this thread because he can't make up his mind.

Math hammer is bad because it doesn't always work, but still use it because it works in broad stroes, but when deciding what to shoot at don't use it because of small dice pools and luck, but use it so you have some idea of what could happen...

The best way to sum up how to use math is use it as something to hope for. If you know that on average a certain unit will only put two wounds on a three wound model, you might want to use a second unit to finish the three wound unit off if the chances are good that the unit you'd be pulling off of another duty to shoot at it could actually land that wound. You also need to assess if what you pulled aside and shot with would actually be worth it, for example do you badly need to crack a few more transports or try to throw the kitchen sink at a death star unit.

One thing I've learned about dice games is to take into account something that someone once told me was called "Cascading Dice Failure Risk" or some such thing. Basically it's the idea that all highs or all lows are just as likely as an 'average' roll. So for each dice roll you have to consider the consequences of massive failure, due to the fact that, as the OP points out, the number of dice rolled in a game will not be large enough to support statistics.

Therefore you have to decide how much risk you're willing to take each and every turn, with each and every unit, depending on the tactical situation. This goes beyond what mathhammer can tell us about the value of units and weapons, and I think that's what Wrex is trying to get at. Not that mathhammer is useless, or that a firm understanding of it doesn't help one build a list or choose a target; just that mathhammer has its limitations for tactical analysis, and that Dakka discussions often don't go very far beyond it's bounds. I have to agree.

Jesus Xavier Christ, why is this thread still going on?

Norade wrote:So Wrex basically has 100% no point with this thread because he can't make up his mind.

Math hammer is bad because it doesn't always work, but still use it because it works in broad stroes, but when deciding what to shoot at don't use it because of small dice pools and luck, but use it so you have some idea of what could happen...

Hey, that's a pretty good summary of what we've got here. The End?

Nah, murdog got it just after that quote.

Seriously 3 pages to find someone that understood the premise. I can't believe I read all of that!

Okay now we are done.

Obviously I'm a bit late to this party, but I think the OP has a subtle point: There are times when it makes sense to ignore the mathhammer results given how people usually do mathhammer.

My point is that proper mathhammer uses probability theory to choose between options, such as which squad to shoot at. As has been pointed out, mathhammer (as typically used) calculates the average result for a given action. While this makes sense in a lot of contexts, basing your decisions on the average result can sometimes be silly. The Trygon assaulting a Wraithlord example is really useful here. Suppose it's the last turn, the objective is kill points, the score is tied, and the Trygon has some wounds on it. A better thing to do here would be to calculate the probability of the Trygon killing the Wraithlord on the charge and compare to the probability of the Wraitlord killing the Trygon. A lazy application of mathhammer here could lead to disaster, but a proper one could lead to victory, and I would guess that the result of the math would not be intuitively obvious to most players. Of course, given luck, the outcome could go the other way, but the beauty of probability is that if you undertake this kind of analysis, you will be making the correct decision more often that not.

Finally, a more general observation: The usefulness of normal (based on averages) mathhammer results should diminish as the game swings towards one player or another. I play bridge, and one thing that bridge books will teach you is that if things are looking really bad for your team, you should be as optimistic as possible, and if things look really good, you should be a paranoid as possible. I think this applies to 40k in the sense that if you're winning, you should focus any calculations on the worst case scenarios, and if you're losing, you should focus on the upside. This is another case where standard mathhammer will lead one astray.

All this said, one benefit of standard mathhammer is that it is reasonably easy to do at the table. Doing the stuff I've mentioned will often be much more difficult and slow.

MrEconomics wrote:Finally, a more general observation: The usefulness of normal (based on averages) mathhammer results should diminish as the game swings towards one player or another. I play bridge, and one thing that bridge books will teach you is that if things are looking really bad for your team, you should be as optimistic as possible, and if things look really good, you should be a paranoid as possible. I think this applies to 40k in the sense that if you're winning, you should focus any calculations on the worst case scenarios, and if you're losing, you should focus on the upside. This is another case where standard mathhammer will lead one astray.

This is absolutely incorrect, and the wrong way to interperet averages and probability as a whole. Luck is not a zero-sum game. When you're rolling crappy, your luck does not have to "come around" as a habitual gambler might wish. It's just as likely to stay crappy as it is to get better.

If you want to be superstitious yourself, go ahead (I do thigs like this, too), but don't associate it with math.

Less math-oriented: If you're a good general, and you've been rolling well, you should actually press your advantage. The odds of rolling a bunch of 1's are the same as before, but you should have capitalized on your success to be in a good position to absorb some bad rolls without losing momentum. If you're "rolling hot" and suddenly play a defensive game, you probably won't be able to capitalize on the opportunity your success has granted you.

a1elbow wrote:

MechaEmperor7000 wrote:This may be borderlining flaming

I hardly would consider that post a flame, it's the truth.

For the record I was refering to my own post, not the OP's (I am unsure which post you are refering to, so I would just like to make mine clear). ^^;

Mathhammer in the context of army building is built purely on theory, as you do not know how your opponent is going to react nor (most of the time) which mission you're going to play. It really helps you narrow down what should be eliminated from your army and what should stay. Quick Mathhammer can also yield desirable results in-battle, but you need one quick mind to do it without your opponent flipping out at having to sit there for 30 or so minutes every turn. The scope of the mathhammer involved, though, will determine how much accuracy it has. Take for example a unit of Space marines VS an equal points amount of termagants. It's pretty easy to figure out which one is the better one in that instance. However, there are other variables, such as the possibility of the SMs having cover fire (due to the opponent choosing to focus fire on this particular squad of Termagants), the Termagants being buffed by a Tervigon, lowering number of attacks each turn due to both units loosing models from shooting, potential Difficult Terrain and Dangerous terrain, etc... These can all change the factors within Mathhammer, and really we have no control over it as it changes with every game. If you know exactly (or at the very least, some idea of) what the battle field is and your opponent's general strategy, you can migate these variables with mathhammer. For example, I know my friend ho runs Space Marines ALWAYS turtles in a corner, all mech'd up and waiting for me to get close while he takes potshots at me. If I get close, he always springs his CC termies on me. In this instance, Lascannons and Rail Guns would be mroe effective than Termicide squad with Combi-meltas or DSing Obliterators, as I'm not exposing myself to their charge range and can potentially pick them off before they do any damage at all. However, this is because I know his strategy. If I was to go up against someone I just met and I saw that they're running Mech Marines, I'd probably take a squad of Chosen with Melta Guns or Sternguard with Combi-Meltas. Mathhammer is thus simplified to compensate for even more uncontrollable variables, giving us a more level ground comparison between two units.

Grey Templar wrote:Lady Average may not be as good looking as Lady Luck, but she comes around more often.

MFing SIGGED.

Great points made by many in this thread. Flavius, Sourclams, Mechaemperor in general, though I think Schadenfreude may have won the thread.

The only thing I'd add to his excellent post which might be useful to the OP is that other elements of the game like Positioning and Planning are much harder and more complex to describe, and much more dependent on visual information like the precise terrain setup of the table.

Lyceus, I think the phenomenon you're reacting to is much more a product of difficulty and laziness than of people genuinely thinking math is the be-all, end-all of warhammer. It's relatively easy to describe math, and it's broadly-applicable. It's tough to describe tactical maneuvering and planning on a particular tabletop (at least without multiple good diagrams and/or labeled photos), and even if you do it, the lessons taught are most easily-applicable to that unique table setup. I do suspect that you're right that some players get the wrong idea from the constant discussions of math and overestimate its importance a bit. Failure to take terrain into account sometimes results in people getting the idea that a given shooty SW or BA build will reliably beat my comparatively-weaker Chaos army; when in fact terrain and the mission are critical and more important elements than how badly their army outshoots mine based on the math. But we can't know in advance what the terrain or mission are going to be, so we wind up talking a lot more about unit selections and math.

Hesperus wrote:Maybe this is a summary, or maybe it's something original. I'm not sure.

Math allows you to pick the most efficient weapon or action for a purpose, both in building a list and in playing a game.

Math cannot tell you the outcome of a particular action in a game, so it doesn't let you act with absolute certainty.

A small number of rolls make crucial differences in a game of 40k, so luck plays a crucial role in a game of 40k.

However, there's no way to predict one's luck on a given roll, so we can't factor luck into ex ante (before the fact) calculations.

The best we can do is make decisions in accordance with the math, and have contingency plans if we get better-than-average or worse-than-average results.

Agreed?

Yes. It gets a big thumbs up from me.

@ ElCheezus:

I think you're misinterpreting MrEconomics's post. He's obviously not suggesting that, when you roll well, you HAVE to roll poorly immediately after. I think he's making a point about strategy, not about probability.

Basically, he's saying that it's better to play conservatively when you're ahead, because it protects your lead, and it's better to play riskily (I think? It's not an exact synonym of 'optimistically') when you're behind, because if both players' luck is dead on average, you'll lose.

Agreed that the lower the sampling (a game) the less dependable the statistics but here is a simple mathhammer use as a tool.

You are building a marine army with tactical squads and you want to determine if you are better off outfitting the sgt with a PF, a PW and melta-bomb or just count on the squads default krak grenades. It is not a be-all-end-all but it has ramifications to his army list as a whole because of the cost expenditure for some options will end up with less points available for other options. It also helps determining whether it is smart to unload a plasma rifle at say a dreadnought or perhaps to determine if there is a likelyhood of success when charging the dreadnought.

That is how you use mathhammer but - in the background - you have to understand you are talking probabilities not certainties.

Hesperus wrote:@ ElCheezus:

I think you're misinterpreting MrEconomics's post. He's obviously not suggesting that, when you roll well, you HAVE to roll poorly immediately after. I think he's making a point about strategy, not about probability.

Basically, he's saying that it's better to play conservatively when you're ahead, because it protects your lead, and it's better to play riskily (I think? It's not an exact synonym of 'optimistically') when you're behind, because if both players' luck is dead on average, you'll lose.

If you're ahead, I still think it's worth pressing your advantage. Not to the point where you're counting on luck or overextended, mind you, but you may as well use what momentum you've gained throughout the game.

If you're behind, it comes down to the mission, I think. If you're playing annihilation or some sort of equivalent, then you kind of have to take some risks. Playing too conservatively at that point just guarantees the loss. If you're playing something more objective based, it might be possible to change your strategy to play for the draw.

Thank you Hesperus, that is exactly what I'm arguing. Another example comes from (American) Football: When a team is behind late in the game, they will usually start making risky throws down the field, even though the probabilities of bad results like sacks and interceptions are much higher than good ones. They simply need to try risky stuff to give themselves a chance to win.

And to clarify, past dice rolls have no bearing on the probability of future dice rolls. To say that bad luck is just as likely to continue as average luck is completely false, since by definition an event that can be described as bad luck must have been improbable as well as bad.

if you have a 30% chance of coming out victorious in melee and 60% chance of coming out victorious in range, according to the math hammer, then your going to want to stay in ranged.

This is what math hammer is for. Determining what has a better chance, not what will happen.

These threads always crack me up.

Probability and luck are two ways of describing the same thing.

There.

Is.

No.

Difference.

You can't escape probability by rubbing a rabbit's foot or some other such idea.

Luck can't make you roll a 7 on a 6 sided die.

Math-hammer is just a tool that good players use to their advantage. That's it. A lot of people think it is something it is not. It does not predict what will happen, it predicts what is most likely to happen.

"Luck" is our perception of the results. Good luck is favorable outcomes while bad luck is unfavorable. When you roll a set of numbers that is highly unlikely to occur (snake eyes or box cars, for example) at a good or bad moment relative to your situation, it is seen as "really" good or bad luck. But again, that is merely perception. Good luck for one player is bad for the other. So who's luck was that?

Also, as others have said, you can't plan "luck" but you can plan for averages.

Anyway, we have talked to death about this topic.

Just remember, whether you "trust" in luck or math-hammer, you are doing the exact same thing, with the only difference being that one is backed by math and more accurate than the other.

Lycaeus Wrex wrote: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.

Wouldn't the first natural really large number that comes to mind be 40,000?

We do enjoy on the spot math-hammering during games because we're nerds and like calculating fantastic odds. Plus it helps us remember really great/odd games.

This one time my KFF negated 12 penetrating hits in a row. We still talk about that game and all remember it due to the statistical abberation. It's fun, you know, like the game should be.

P.S. Where I play, the person who makes the least amount of mistakes usually wins.

... we know orks on the charge are horrible but which is better ... Rapid fire or pistols and charging?

10 man tac. vs 20 boys and a nob (2xBS +BP+PK&shoota)
Tac. rapid fire 9 bolsters and a flamer 2/3 hit (12+8f) 1/2 wound (10) no saves ...10 boys die. 11 models left still fearless
Orks 9 sluggers and 2 big shootas 1/3 hit (3s + 2B) wound (2.83) 1/3 fail their save... 0.94 die ...9 models no moral test.
Orks charge.
SM go first ...10 attacks 1/2 hit (5) 1/2 wound(2.5) 5/6 fail their save ...2.083 die (rounding down 2) ...
Orks 7 boys ... 28 attacks 1/2 hit (14) 1/2 wound (7) 1/3 fail their save ... 2.3 die (rounding down 2)
Nob strikes ...4 attacks 1/2 hit (2) 5/6 wound (1.6) ... no armour save 1.6 die (rounding up 2)
SM have lost combat by 2. SM 5/10 Orks 8/20

Tac. 9 pistols and a flamer 2/3 hit (6+8f) 1/2 wound (7) no saves ...7 boys die. 14 models left fearless
Tac charge.
SM go first... 21 attacks 1/2 hit (10.5) 1/2 wound (5.25) 5/6 fail their save 4.375 die (rounding down 4)
Orks 9 boys ... 27 attacks 1/2 hit (13.5)1/3 wound(4.5)1/3 fail there save 1.5 die ( rounding up 2)
Nob strikes ....3 attacks 1/2 hit (1.5)5/6 wound (1.25) no save 1.25 die (rounding down 1)
... thanks to LD10 + a reroll chances are the orks wont run ... round 2
SM go first ...8 attacks 1/2 hit (4) 1/2 wound (2) 5/6 fail there save 1.6 die (2 rounding up)
boys .... 21 attacks 1/2 hit (10.5)1/3 wound(3.5)1/3 fail there save 1.16 die ( rounding down 1)
Nob ....3 attacks 1/2 hit (1.5)5/6 wound (1.25) no save 1.25 die (rounding down 1)
combat is a Draw. SM 5/10 Orks 8/20

So what is the point? We know ether way we'll be down to 5 men by our next turn; this is where skill and strategy come in. If we charge we're stuck in combat for another turn but if we rapid fire we can fail our moral test and fall back. That way we can regroup at the start of our turn and fire both our missile launcher, flamer and 3 bolters at the 8 orks (hopefully they didn't sped out too much with there consolidation move)

Will this pan out this way every time? No. There is a possiblity that the SMs will kill all , some or none of the orks. There is the possiblity that orks will wipe away the SM in combat ... on average they won't.

Now before you complain the maths above is highly simplified ... if i was doing this correctly i would not round and we'd have 0.5 of ork and 0.7 of a sm but that's confusing and over complicating for a thread about maths-hammer. If i was doing this to the n'th degree i would need to do it for all permutations (DT, different weapons, more or less .......................)

Reecius wrote:These threads always crack me up.

Probability and luck are two ways of describing the same thing.

There.

Is.

No.

Difference.

Actually there is, but oooonly via definition. Luck is unquantified probability. So it's the difference between buying a juice bottle, not knowing how much is there and buying a 35ml juice bottle. Although technically it's the same substance: the only difference is that you have an idea of how much is it when it comes to probability and you have no idea when it comes to luck.

MechaEmperor7000 wrote:

a1elbow wrote:

MechaEmperor7000 wrote:This may be borderlining flaming

I hardly would consider that post a flame, it's the truth.

For the record I was refering to my own post, not the OP's (I am unsure which post you are refering to, so I would just like to make mine clear). ^^;

I was referring to yours.

I don't think most of these late game analogies are applicable here. Football teams have to score, but they are still playing the odds. A deep pass is less reliable, but also could result in a pass interference. Football aside, the point is that late in the game you have to take desperate attempts sometimes, but your not just firing S4 weapons at a Land Raider. You are still factoring in odds, it's just that you are having to modify them because your opponent is ahead and your ability to follow through with the best math-plays has been limited.

People are still arguing the same thing anyway, never ignore the math, never only base decisions on the math.

OK that is an interesting topic imo.

I have to say, that I share Lycs opinion about people being quite simple in mathhammer.
The way I see most argumentations are like this:

We have a 75% chance, so most of the game they will make it. (which is true)
So I rely on them making it (which is not true)

So in basically 3 of four games the job is done. But what happens in the fourth game? (statistical average of course, it also can happen 4x in a row...)

In the course of a tournament we will always have games, where the average results are just not happening. Sometimes 2 games, sometimes 3 and so on.
What do we do about this?
Just ignore the fact and continue acting straight out of average assumptions?

No.

Thats how we deal with luck:

1. Minimise decisive dice rolls. They can be ehm decisive against you.
2. If you still have to roll something important make sure to have a plan B in case the expected does not happen.

Now my theory:

40k dice roll results are very unreliable. But what else do we have at our disposal? Movement, physical sizes, distances, time and objectives. These things dont betray us.
So we can to rely on these.
Of course we have to kill something, and in order to do that, we have to roll dice or provoke the opponent to roll dice, which is actually the same story.
But the main focus of the gameplay should not be on dice (it really doesnt matter if the chance is 56,7% or 65,8% for a tournament, but it does matter being in 3" to an objective or being in 3,0001" of an objective), it should be on the movement phase, on good terrain and model use concerning cover, LOS, crossfire and so on and on a clear strategy.
This is the sort of gameplay where you dont need rolling averages. If a model is hidden, it is unkillable (in most cases...^^). If an objective is claimed, it is yours. If you are in 25" to your enemy he certainly will not fire a single boltgun and you certainly will suffer no casualty.

This is the way to go especially in the following situations:

The opponent has the superior army
Your dice went crazy and you must fight for survival.

Of course this leads to a very defensive gameplay only exchanging pot shots or binding charges (or nothing at all if exaggerated).
But it is quite reliable if you do this carefully and disciplined.

If the situation is not so important you can go after bonus kills, but thats all.