Terminators vs. Obliterators - Part 2 - Obliterator Anaylsis

First, let's take a moment and be grateful that Obliterators got a resculpt.  I took a look at Terminators earlier, and decided this was going to be two posts because of the amount of math.

Obliterators, the short version - your gun is random (but not as bad as you think) - but a 24" gun is hard to hide from when it comes out of deep strike, and hard to retaliate against.

The Assumptions

I'm keeping my assumptions from last time.  They are -

1) Take the Mark of Slaanesh so we can shoot twice via Endless Cacophany

2) Assume Prescience (or some other to-hit buff; Obliterators don't blow themselves up with plasma so avoiding a '1' isn't as big a deal - but you'd be silly not to bring a buff)

3) Assume we have the CP for Veterans of the Long War because +1 to wound is great

4) Legion Trait - I'm going with Alpha Legion because I run that, but I'll discuss other legion traits as well.

Obliterators Part 1 - The Gun, at a glance

In a way, this is simpler than Terminators because there's only one gun.  

Fleshmetal Guns - Assault 6, S6+d3, AP -d3, Damage D3 at 24 inches.

The special rule that's going to make us all hate math in a minute is Fleshmetal guns - you drop a D3 when firing to figure out your final strength your AP, and your damage.

This means you could have S7, AP-1 shots that do one damage, OR you could get S9, AP-3, 3 damage shots, or anywhere in between.

It also means you're going to hold onto a CP to potentially re-roll one of these D3, depending on the target you're after.

On the bright side, a 24 inch range means it's much harder to screen targets - a 9" buffer zone is fine.  If you want to screen out a 24" range shot, you may be looking at specialists with a "no deployment within 12 inches rule" or multiple screens and/or breaking line of sight.  You also have the luxury of dropping in outside of easy charge range.  If someone does charge you, each Obliterator has three S6, AP-1, 1d3 damage swings - so you CAN punch something to death, but it's a mop-up operation instead of something to rely on.

A full unit of 3 Obliterators is 385 points - which is pretty close to terminators in the previous example.

Obliterators Part 2 - On Randomness

So here's where it gets interesting - the guns are random as all get-out.  Strength is 7-9, AP is -1 to -3, and damage is 1-3; you have no idea what you're getting until it happens.  I absolutely advocate shooting your Obliterators first so you can keep a command point available to re-roll any of the D3 - but note that you roll the dice one after the other, so you pick strength, AP, and then damage.  

Remember that on average, you'll get a '2' - so only re-roll for the max value if it really matters, because you can always drop to a '1' instead.

The D3 you're going to re-roll is going to depend on your target.  I would worry about strength and damage most of all; the AP can be frustrating but you need to wound your targets, and the multi-wound fellows (IE - Primaris Marines, for example) really really want you to roll a '2' on damage - when you need multi-wound infantry dead, doing 1 damage a wound just won't cut it unless the unit has already taken a beating.

Re-rolling strength depends on your target's toughness - so it matters on T4 (S8 is your break point), T7 and T8.  You'll always wound T3 on a 2+, and you'll always wound T6 on a 3+ before Veterans of the Long War (VoTLW).  In a pinch, VotLW can overcome this if you're firing against multi-wound infantry.

Re-rolling AP matters if you already got the strength you want, and you don't care about damage.

Re-rolling damage really depends on the target.  It doesn't matter if you're chewing up high-value single-wound targets, but once you get to heavy infantry and vehicles you REALLY want to make sure you're doing at least two damage.

My gut says that if anyone skips over Obliterators at this point, it's because doing the math hurts.

Obliterators Part 3 - The Math

The math is where things get real fun, and we break out the spreadsheets.  Assuming prescience goes off, we get 15 hits.  That's the last of the easy assumptions.

In order to actually provide something consumable and usable, I'm going to do math for the final outcomes - IE, what value do you need to wound a target, and what's the target's final save.  We can do to-wound math easily, and once we know the final save (be it an invulnerable save, or the save after AP, cover, etc.) we know the number of wounds that went through.  And if it's a single big target, we can then figure out the damage depending on our damage roll.

Obliterators when wounding on 2+

This category includes T3 infantry, OR T4 infantry with S8+, or Veterans of the Long War when you'd normally wound on a 3+

I'd say your biggest pie-in-the-sky number here is the 5+ save vs. wounding on a 2+ - that's your golden scenario vs. T8 superheavy that can pick up an invulnerable save.  

A more reasonable benchmark is the 2-damage output vs. a 4+ save - on average you should still clean out two-wound primaris marines, and VotLW means you should be able to delete dreadnoughts, etc.

Obliterators when wounding on a 3+

This bin includes T4 infantry when you roll S7, T5-6 targets all the time, T7 targets when you're S8 and T8 targets when you're S9.

Assuming you can swing average AP and damage rolls with this, you can still put some solid damage (average 13.3) on something like a Knight, and still probably take out a tank.

Assuming you get two damage and so-so AP, even S7 means you can still probably nuke most or all of a two-wound T4 infantry squad unless they're in hard cover.

Obliterators wounding a on 4+

This category is slimmer - it's T7, 8, and 9 targets when you roll strength equal to their toughness.

Frankly, this table is a little disappointing - you need good AP to do decent damage to heavy targets.  

age

Obliterators wounding on 5+

You should have used VotLW, or re-rolled strength if you have to hit a target that you wound on a 5+.  You get 3 wounds off that, which isn't going to do a blessed thing.

What Do These Numbers Mean?

Ok, let's be real - that's a large wall of math and text to get through.  

Obliterator Perks

-24" range on the gun means you can stay out of counter-charge range, if applicable, to do your damage.

-24" gun range means that the only safe place is out of line of sight

-Obliterators are durable - T5, four wounds, and a 2+/5++ mean that they can soak a LOT of bullets.

-Unlike terminators, you don't run the risk of blowing yourself up.

-From a tabletop perspective, you can actually batch roll faster because a '1' doesn't kill your model.

-Randomness of the gun means you might kick out a half-dozen S9 AP-3 three-damage shots per guy, which is HILARIOUSLY nasty

-You don't need a huge footprint to drop in on with three models, even if you do have heftier bases.

Obliterator Drawbacks

-Randomness on the gun is the major flaw here, and you have to think about whether or not it matters.  Against line infantry, it's not a big deal - but you're kind of wasting yourself if you do that. 

-The AP of the gun is (to me) the biggest drawback - low AP vs. hard targets (most vehicles have a 3+ save) can hamper you, and it's the roll you're least likely to end up wanting to influence.

-The strength of the gun may matter, depending on the target.

-The damage is where it can get you - rolling a '1' for damage against heavy duty targets is just wildly disappointing.

A Note on Legion Traits

Alpha Legion - your 24" range lets you drop in far enough away to benefit from the -1 to hit.  If someone does charge you, you can drop 1CP for Feigned Retreat, walk away, and shoot again.  You probably have the range to use Conceal as well, which means no one is shooting these guys unless they're the closest target.

Black Legion - the trait is irrelevant.  You have a couple of stratagems to get re-rolls without nearby support, such as Let the Galaxy Burn - or Tip of the Spear if you ARE somehow the closest to the enemy.

World Eaters - you lose out on Prescience and Endless Cacophony.  Skip unless you're die hard pure World Eaters.

Word Bearers - you don't really care about the trait.  Malevolent Covenant can let you auto-pass the psychic test  for Prescience and won't let someone use Deny the Witch on it.

Night Lords - you definitely aren't close enough to use the trait yourself.  You can get -1 to hit vs. enemy shooting for 1CP via In Midnight Clad.  Leadership 8 may make you a candidate for Prey on the Weak - getting +1 to hit is never bad.

Iron Warriors - you're (potentially) light on AP, so ignoring cover is helpful if you're going after infantry or the odd vehicle that can get cover.  The Tank Hunter stratagem is good for rerolls vs vehicles.

Emperor's Children - Your legion trait doesn't really do anything.  I suppose you could use Combat Elixirs to go up to T6, but that seems excessive.

Renegades - There really isn't a huge perk for the initial volley here.

In Closing

The Obliterator gun is hilariously (and obnoxiously) random - however, it's still capable of dishing out some solid pain.  The benefit is that the 24" range means that it's difficult to hide from unless you're out of line of sight, and it's on a pretty durable platform.

Terminators vs. Obliterators - Part 1 - Terminator Analysis

Few things are more fun than dropping onto the table out of reserves and shooting - especially because a gun's range is a lot more predictable than a charge roll.  Chaos Space Marines have a couple of nasty shooting options with built-in deep-strike capability - Terminators and Obliterators.  The problem is that you're probably only going to have room for one of these.  So, of course, the follow-on question is 'which one?'  Given the versatility of terminator weapon loadouts, and the random nature of fleshmetal weapons, it's not the easiest question to answer.

UPDATE - had a buddy remind me of the stratagem 'honor the prince' - Emperor's Children terminators become a sub-species of "probably get stuck in after shooting" which is more fun.

Given the amount of math and space involved, I'm going to break this into two posts - the Obliterators are here.

Terminators, The Short Version - Combi-plasma and cheap melee is your most reliable loadout.  Save CP for Veterans of the Long War and Endless Cacophony, and you can theoretically delete a Knight or other superheavy in a turn, and also guarantee that you're going to see most of the other army pour into your terminators.

Also, sorry World Eaters - you lose out on a couple of crucial pieces of this and just aren't going to be as effective, but you got Red Butchers, so lean into that instead.

Baseline Assumptions
No unit performs in a vacuum.  You're going to be hitting the field on turn two with some high-powered guns - so you're going to bring support.  By and large these units want the same thing, so we'll assume that they have it. What is 'it', you ask?

 1) Assume we give them Mark of Slaanesh so we can use the Endless Cacophony stratagem and shoot twice.

2) Assume we have an accuracy buff in there - either Prescience for +1 to hit, a nearby Chaos Lord to re-roll 1s, or possibly both - maybe you got a Demon Prince into position.  I kind of like the Lord/Prince aura because the only way to turn it off is to kill the guy, whereas psychic powers can fail or be denied.

3) Assume we are willing to drop Veterans of the Long War if we need the +1 to wound.

4) Legion Trait - I'm using the Alpha Legion trait because, y'know, I'm Alpha Legion - so we force a -1 to hit penalty against shooting if you're more than 12" away.  I'll discuss other Legion Traits in an addendum.

Terminators Part 1 - Loadout
I lean towards plasma guns and chain axes on terminators, with a chainfist or two in a larger unit.  For 390 points you can get a 10-man unit with combi-plasma, two chainfists, and 8 chain axes.

Why plasma guns?  You have access to the following guns for terminators -
Combi-bolter - fine for bargain-bin distraction terminators (26pts for combi-bolter/chainaxe - not bad) but it's a totally different roll.

Combi-flamer - you're deep-striking out of range.  Pass.

Heavy Flamer - see above, and you get 1 per 5 terminators.

Reaper autocannon - great range and volume of fire - four shots at S7, AP-1, 1 damage - but you get one per five guys, and you take a -1 to hit when you land.  Skip.

Combi-melta - here's our contender.  S8, AP-4, d6 damage?  That's pain.  Note that you get one shot at 12", though - you better hope you hit - you are vulnerable to screening (especially against units like Primaris Infiltrators and their 12" denial bubble), and odds are that you won't be able to utilize the 'shoot twice' stratagem with the melta profile unless you went after some HUGE target and/or had choice positioning.

Note also that as long as you have an accuracy buff, you're really competing with the plasma gun's overcharge mode - an extra AP at this point is mostly academic.  AP-3 or -4 are either up against an invulnerable save, a 5+ armor save max (outside of cover special rules), or you're going clean through it.  When it comes to damage, 2 damage and volume of fire wins against basically all infantry compared to melta shots, but the meltaguns do have the potential to out-damage plasma guns - they'd need a 5+ damage roll to beat both shots in rapid-fire range, and outside of 12" they're just sad.

Combi-plasma - Here's our money-maker, thanks to its range and versatility.  You get S7, AP -3, 1 damage, OR you super-charge for S8, AP-3, 2 damage.  You have a 24-inch rapid-fire gun, so in a perfect world you drop at 12" and unload, supercharging if necessary.

Note also that the 24" range means that you can still contribute if someone does still have deep-strike denial in play, OR if you nuke your first target and still want to abuse Endless Cacophony, you have options.

Why chain axes?
Really it's easy - let's keep it cheap - the chain axe / combi-plasma combo runs you 35 points a guy.  You're not here for melee, but you're probably going to end up in it.  Giving everyone power weapons is at least another 30 points or so - and understand that after the first round of shooting, no one wants to let these guys do it again.

I do recommend a chainfist on the champion (go ahead and abuse his 3 attack profile) and maybe one more in a max unit, just in case you have to punch something big to death.

Terminators Part 2 - The Damage
So, we have our ten terminators with combi-plasma.  Let's assume we drop in rapid-fire range, and get Prescience off.  That's twenty shots, and with a 2+ to hit we're going to land 16.66 shots.  Damage wise we should consider stuff with and without invulnerable saves.

Vs. T3 infantry OR T4 infantry with overcharge - Veterans of the Long War (VoTLW) is irrelevant
Wound on 2+  - 13.88 wounds
Saves vs AP-3
4+ or worse in the open - 13.88 wounds go through it
3+ in the open - 11.5 wounds go through
3+ in cover OR 2+ in the open  OR 5++ - 9.2 wounds go through
2+ in cover OR 4++ - 6.9 wounds go through
Vs. 3++ saves - 4.6 go through

The above math applies for T5-7 targets as well, assuming you use VotLW to get down to a 2+ to wound again - and it's very much worth it.

Next, let's look at the hardest targets - T8.  You are ABSOLUTELY using VoTLW so you can wound on a 3+ here with your shots.  Anything else is just a waste.

Wound on 3+ - 11.11 wounds
4+ or worse in the open - 11.11 wounds, 22.22 damage
3+ save in the open - 9.25 wounds, 18.5 damage
3+ save in cover OR 2+ in open OR 5++ - 7.4 wounds, 14.8 damage
2+ save in cover OR 4++ - 5.55 wounds, 11 damage
3++ save - 3.7 wounds, 7.4 damage

Just double that for average output w/ Endless Cacophony.  The good news is that you can do a serious number on large targets - a good deep strike, Prescience and 3CP will probably kill you a knight.

Terminator Perks -
-Plasma is pretty nasty.
-Plasma is pretty reliable, and S8 hits important break-points versus heavy targets.
-You do have the ability to split up fire in a fairly granular matter if needs be and you have the appetite for math.
-You can focus a LOT of buffs on one unit fairly easily.

Terminator Drawbacks - 
-You HAVE to drop within 12" to get the most out of your guns.
-You probably blew up 300+ points of the enemy army and you're like 12" from it - life's about to get rough.
-You have a pretty reasonable footprint - you really want guns on the ground turn one to clear a screen.
-If you don't get a to-hit buff or a way to re-roll ones, you're asking to blow up terminators.

A Note on Legion Traits
Alpha Legion - you aren't necessarily going to benefit from the legion trait based on your 12" range, but if you get charged and LIVE, you have the stratagem Feigned Retreat to fall back and shoot for 1CP.  Expect anyone who knows about this to make an effort to severely weaken you and tie you up in melee, if not kill you.

Black Legion - the trait is irrelevant. You can get some re-rolls, though, via stratagems - Let the Galaxy Burn is 1CP to re-roll 1s.  Tip of the Spear is 1CP to re-roll hit rolls for a Black Legion unit as long as it's the closest the enemy, which you probably are.

World Eaters - Skip.  You lose out on Endless Cacophony because you're stuck being marked as Khorne, and you lose Prescience because you hate psykers.  If you want terminators, run Red Butchers as S5 base melee terminators.

Word Bearers - Legion Trait is largely irrelevant to the terminators.  Of note is the stratagem Malevolent Covenant, which means you auto-pass a psychic test (Prescience, anyone?) for 1CP and a mortal wound on the psyker.  It can't be subject to Deny the Witch, either.

Night Lords - Legion trait is again irrelevant.  The stratagem In Midnight Clad is 1CP for -1 to hit vs. shooting, which can actually help.  Prey on the Weak is 1CP for +1 to hit IF your Terminator's Leadership 9 is higher than the target's - this can free up VotLW for someone else, potentially.

Iron Warriors - Ignoring cover is situational as a legion trait, but worth remembering if you're hunting heavy infantry in cover.  You do have some stratagems worth remembering - Iron Within, Iron Without is a cheap 'ignore wounds on 6+' and Dour Duty reduces the AP of enemy melee attacks, which may help you live through the drop.  Tank Hunters is about your only real damage buff, but gives you a re-roll to wounds vs. vehicles.

Emperor's Children - your legion trait is more about punching than shooting.  However, for 2CP you could use Combat Elixirs to make your terminators T5, which might be funny.  For you, anyway.  EDIT - perhaps of more importance is the stratagem 'Honor the Prince' - for one CP, one dice is a 6.  For your charge.  Can you get one 3+ on 2d6?  If so, then for one CP, you're in melee, kids!

Renegades - the Scourged get overwatch on 5+, which may help.  Otherwise, nothing really jumps out.

In Closing
The combi-plasma alpha strike is pretty sick - save it for hard targets, and make sure you clear a drop zone 12" away from the enemy to abuse it.  Save CP for Veterans of the Long War and Endless Cacophony.  Your legion may or may not offer much extra, but as long as you can get accuracy buffs and clear out ~500pts of your list for the terminators and an HQ, you're good.

Thoughts on Math-hammer - tweaked for 8th Edition Relevance

Since 40k is a dice game, it probably pays to know a bit about how the dice will behave in a given situation.  8th edition shakes up a few things (like the to-wound chart and leadership) and changes some odds (like casting psyching powers, which is easier).  It also adds the whole 're-roll ones' mechanic, which tweaks re-rolls.

A Few Disclaimers - 
1) remember that we're talking about odds.  Averages are guides for decision-making.  You'll be able to take a guess at outcomes if you're weighing options.

2) Averages emerge when you throw dice enough times - twenty throws of a dice is about average, when it comes to statistics - IE - thirty guardsmen walk into rapid-fire range and drop 100d6 looking for 4+, you'll probably see 50 hits most of the time.

3) Remember that we have a cognitive bias towards remembering outliers - we're bad at math unless we're trying.

Basic Math - looking for X+ on 1d6

Base WS/BS	Unmodified chance	Re-roll misses	Re-Roll 1's	Base with +1 Bonus
2+	83%	97%	97%	83%
3+	67%	89%	78%	83%
4+	50%	75%	58%	67%
5+	33%	56%	39%	50%
6+	17%	31%	19%	33%

I'm going with WS/BS on these because it's the most common, but this math applies to any rolls when you need X or better, such as morale and wounds.  I've added in re-rolls, re-roll 1's, and +1 bonuses.

Note that blanket re-rolls are a bit better than a +1 bonus - but they're pretty close.  The only place that really loses out on it is the 2+, as we're assuming a 1 always fails here.

Note also that re-roll ones are neat, but have diminishing returns as you need better numbers when it comes to odds.  However, some stuff (like plasma) REALLY doesn't want to deal with 1's, because explosions.

Roll at Least X on 2d6

At least X on 2d6	Odds
2	100%
3	97%
4	92%
5	83%
6	72%
7	58%
8	42%
9	28%
10	17%
11	8%
12	3%

This one's important for two big phases - the psychic phase and the assault phase.  Two obvious break points are 9+ and 10+.  

We care about 9+ for deep-striking assault troops (which means that they've got just under a 1/3 chance of assaulting off deep-strike).  Note that any deep-striking troops that can get an extra inch of charge range (IE - Trygons with adrenal glands) get a significant boost to their ability to charge out of reserves.

We care about 10+ for Smite's bonus damage.

Roll 2d6, pick the highest

Roll 2d6, pick highest	1	2	3	4	5	6
Chance of getting at least  -	3%	8%	14%	19%	25%	31%

As long as I'm doing math, went ahead and did this one.  

So, What Do I do with this?

These are all guides - if you're looking at figuring out how nasty something's going to be, crunch numbers.  

Example 1 - 5 Chaos Terminators deep-strike and fire combi-bolters into guardsmen in cover. Let's assume they're all within 12" of the targets, so their rapid-fire 2 guns are kicking out four shots each.

5 combi bolters * 4 shots each = 20 shots

20 shots at BS 3+ = 13.33 hits on average

13.33 hits that need 3+ to wound (S4 vs T3) = 8.89 wounds

Guardsmen out of cover have a 5+ save

8.89 hits vs 5+ save = 2.96 saves, so 5.9 guardsmen die.

So you could expect 5-6 guardsmen to eat it.

Example 2 - say the Chaos Lord deep-strikes in behind his Terminators, and gives them the ability to re-roll 1's

5 combi bolters * 4 shots each = 20 shots

20 shots at BS3+ with a re-roll one 1's = 15.55 hits

15.55 hits needing 3+ to wound = 10.37 wounds

10.37 wounds vs a 5+ save = 3.4 saves, so 6.9 guardsmen die

So, if you dropped the terminator lord in behind his terminators, you could guess that it'd kill 6-7 guardsmen in that context.

To bring it further - so the guard survives, and however many survivors get to rapid-fire the terminators and then probably assault (move 6 + 2d6 charge = 80-90% chance of a charge going off).

What Math can do is tell you the odds of stuff happening with dice involved - but what math CAN'T do is tell you what your opponent is going to do - does the opponent turn around and try to kill the Terminators to a man now, denying you the ability to disrupt his backfield?  Does the opponent say 'eh, screw it' and let your terminators wander around his backfield and focus firepower elsewhere?

In Closing

Having an idea of how math works gives you a decision-making tool.  The dice can always give and take away, but if you know math then you can guess how rolls will go, and ask yourself how much risk you want to accept for a given course of action.

Math-hammer and You

What Is Math-Hammer?
I'm going to use Math-hammer as a term to describe the rudimentary application of statistics to 40k in an attempt to figure out the outcome of a discrete round of harming the other guy.

Math-hammer usually takes the form of something like this:

Number of shots * chance to hit * chance to wound * failed saves = Number of casualties.

Let's put this neat little model into action: I fire my 10 Dire Avengers into your Imperial Guardsmen that are in cover. The pertinent facts are:
1) Dire Avengers are BS4
2) Their guns are 2-shot, S4, AP5 jobs
3) Guardsmen have T3, and a 4+ cover save.

Let's turn that crank with the following data:
Number of shots = (10*2) 20
Chance to hit (at BS4) = 2/3
Chance to wound (S4 vs T3) = 2/3
Failed saves (4+ cover) = 1/2

Ergo: 20 * (2/3) * (2/3) * (1/2) =...
20*(2/3) = 13.333 hits * (2/3) = 8.8886 wounds * (1/2) = 4.44 Casualties.

Hooray! We just killed some Guardsmen!

Except Not
So, what's the problem with this model? There are a few: namely, the dice, the laws of statistics, and template weapons.

The Dice
Dice are not necessarily impartial random-number generators. Some people suggest that Chessex dice (the default, little rounded-corner boggarts) lean towards the 1 a little bit. There are also some nasty tricks you can do to manipulate dice. My personal bias involves just playing with the Chessex dice, and the hell with the bad rolls you get. Actively trying to rig your rolls is a punk thing to do, and should realistically get you kicked in the dice bag.

The bottom line is that the dice do not always behave in a perfectly predictable manner, but we can still make some basic assumptions about how they'll act any given time we roll them.

Laws of Statistics
Think about most the times you roll dice in 40k. Maybe it's an ordnance shot or blast weapon; then it's 2d6 and the scatter dice (...just TRY running some math-hammer for scatter. It's pretty rough). Maybe it's your Predator Destructor kicking out 8 shots in a turn. Maybe it's your tactical squad rapid-firing someone with about 16ish bolt-weapon shots. Maybe it's terminators on the charge with 15 attacks.

What do a lot of these have in common? It's not a lot of dice. Statistics works best with large samples; a good statistical sample has a minimum of 30ish trials. Some units can indeed pull that off in a single action (IE: Orks shooting/charging, Fiends of Slaanesh in assault, 30-man guard squad w/ First Rank Fire, Second Rank Fire), but most cannot. Some units cannot throw thirty dice in the course of the game, even if all seven turns happen.

What's that mean for you? Even through the course of a game, you cannot necessarily expect 'average' performance out of a given unit.

Template Weapons
Now, if we take a basic weapon that has fixed chances of hitting, we can run the rest of our formula from there, yes? Same goes for assault. The problem lies in predicting how many hits you can slap on a target with a flamer or blast weapon. Templates have to take into account how close models are, and the formation they are arranged in. If everyone is standing shoulder to shoulder with a 2" max coherency spread, it's a much different picture for blast weapons than if they're all in base-to-base contact with each other like a fresh Deep Strike formation, for example.

The best we can do for Blast Weapons is model their scatter, armed with the knowledge that 2d6 averages about a 7, and there's a 33% chance of getting a 'hit' result on the scatter dice. So, right off the bat we know a blast weapon will hit 33% of the time. 33% of the time, scatter will then average 7-BS, so we have some idea how far the center dot might go. About the only place we can use this knowledge is when we try to apply it to vehicles and how big their hull is; we have a better chance of landing a blast template on a Land Raider than a Killa Kan, for example.

Why use Math-hammer, then?
Why, indeed? Because it gives us a starting point for making decisions. Common sense tells us that one Guardsman is unlikely to beat up a thunder hammer storm shield terminator, but it IS still possible. On the other hand, some things get a little closer. Math hammer gives us tools to make a guess at the outcome of shooting or assault, and that's at least something to base your decision on.

The numbers are not always accurate. However, it's a darn sight better than just using wishful thinking and sacrifices to the 'dice gods' as a means of making decisions with your army's firepower.

Using Math-Hammer intelligently
Here are some suggestions for using Math-hammer to your advantage:

1) Know the limits of the stats
-You need 30 rolls to get an accurate 'sample size'; if it's below that than you're not really guaranteed an 'average' result

2) Know the limits of the dice
-Dice are not perfect random-number generators, either through manufacturing processes or human interference a la practiced rolling.

3) It's Still Math
-Math, when done right and mindful of its problems, is STILL a reasonably reliable when you follow the steps.
-At least, math is a reliable tool given an understanding of the tool. It's like a computer: it can only do what you tell it to do, how you tell it to do.

4) Know what the 'Average' means
-The 'average' result is the midway point, which means that IF you roll enough dice, THIS is what happens about 50% of the time.
-What you're really dealing with is a Normal Distribution (aka bell-shaped curve)*. You're hoping that your dice will land somewhere in the middle, but it is still entirely possible to see a given set of rolls fall way the hell away from average (hey, it's possible to see 5 1's, [0.01% chance, theoretically] and you have the same chance of seeing five 6's in a row as well)

5) Know that Things Can Still Go Wrong
-The dice are still fully capable of throwing complete outliers at you. We call this 'the wheels coming off', when you fire five bolters into a single guardsman in the open, and he still lives, for example. (Worse still, he kills 2 guys on the charge, and lives.)
-In other words, you care about math, but math doesn't give a flip about you, and can screw either of you over, or both of you, or neither of you. Crap happens. Deal with it.

6) Realize the limits of Math-Hammer
There are things Math-hammer simply will not do, and they are:
-Tell you WHERE to move
-Tell you what your opponent will do
-Gauge range
-Tell you how many of your infantry will actually be in range of your target
-Tell you a blessed thing about how many people you actually will hit with a template-based weapon

Math-Hammer CAN give you an idea on:
-How much fire you need to kill a target
-How much fire you need to force a morale check
-Whether or not you might make assault (remember, you just need base-to-base with ONE guy)
-The chances of immobilizing yourself in terrain
-The chances of you winning/losing an assault, and potential morale results

Conclusion
Math-hammer is a tool. No more, no less. It's not perfect, but it's a workable enough basis for making decisions about dice in the game. As such, I suggest a working knowledge of it, since this IS a dice game, and Math-hammer DOES tell us a little how the dice work. It's a more reliable basis than all the little pre-concieved notions that your brain tends to have.

Any kind of theory makes assumptions. The more you know about the assumptions, the more use you can get out of the theory. At the end of the day, theory itself is a tool. Theory simplifies the world, loses some resolution, and usually gives you a (reasonably reliable) method of making decisions and/or learning about an aspect of life, the universe, and everything.

Math-hammer just gives you a rough idea of what can happen when you throw the dice, and that's better than nothing, in my book. There are days where the average will happen every single roll, there are days where the dice will roll sub-par on a game level for you, but in the end, across enough games, the dice will roll average.**


*Disclamer: I'm being a little lazy here and linking to Wikipedia. Note that since Wikipedia is open to anyone who wants to edit it, anyone can (and in some cases, has) tweaked the data in an incorrect manner. If you really, truly want solid info, wikipedia is a good start, but then you'd better check out the sources they've listed in the article, and move from there.

**Unless you're a bloody dice cheat. Or the other guy is.