Mathammering Xenos Deathlocks

Preamble.

Today's post applies a bit of mathematics to the usage of Xenos Deathlocks that we discussed in the Horus Heresy Review on the Blackshields Rules. In brief, Xenos Deathlocks (which we will abbreviate to XD's from herein) are a type of weapon that some of the renegade space marines wielded in 30k when they went outside their command structures because of the Heresy. I really like this idea and concept. Hence, regardless of the outcome of the mathammer below, I really want to see people play these on the desktop just because they're cool. No other reason! In fact, you can see that I already convert some of my miniatures along these lines any way (with a slightly different narrative within the Alpha Legion of using reversed engineered technology).

Basics.

The Xenos Deathlocks are S=5, AP5 with assault 2 weapons. They have a half decent range for assault weapons at 18 inches as well, which is very nice -- nay attractive even, especially compared to a bolter at a similar range. But there's a price to pay for this -- not only in the points cost. They have the Lethal Exposure rule. Firing this weapon causes the unit using them to roll 2d6. If the roll is less than the number of shots fired by the unit, then one wound is taken with no armour save possible. (Overwatch is exempted from this).

So why take them at all given how downright deadly they look on paper? The answer is in the Deathlock rule. In the spirit of Volkite weapons, a unit that got hit and wounded by a XD weapon must take a leadership test modified (negatively) by the number of wounds suffers (fearless and stubborn units don't apply modifiers). Failure causes an extra 1d6 wounds that can have normal saving throws. 

So is this potentially amazing weapon worthwhile?

A trivial case.

Let's suppose a squad sergeant has a XD. He is targeting some space marines (of course!). On average, he scores 1.33 hits (from 2 shots), and of these, causes 0.89 wounds. A "typical" 3+ save in the 30k environment will reduce this down to 0.30 unsaved wounds (rounded). 

Its trivial here to see that the lethal exposure test is passed: one can never roll under 2 on 2d6, so the sergeant is always going to be safe.

How many extra wounds will the target unit take though? We will treat the enemy squad as having Ld=9 for this purpose. Hence the Ld test is taken at 8.70 for the 0.30 unsaved wounds caused already. Rounding, a roll of 8 or less therefore happens 72.2 per cent of the time. Or putting it another way: fails 27.8 per cent of the time. 

We will use this number to multiply by the 1d6 extra wounds to come up with an outcome. The average 1d6 roll is 3.5. Thus, 27.8 per cent of 3.5 extra wounds is 0.97. 

The target squad is allowed a saving throw which reduces this down to 0.32 extra wounds. That makes a total of 0.30 + 0.32 = 0.62 wounds from the two shots every turn. This is therefore rather powerful!

Complex cases.

Things get much more complex here when we have more than one shooter. Plus, there's the potential to take wounds of your own from the firing squad. In the table below, I summarise the outcomes, using the basic logic presented above in the trivial case. The final two columns are the number of lethal wounds suffered by the shooters, and the difference between the last two columns (or: how many wounds ahead the shooters are!). 

N(XDs shooting in a squad); N(Unsaved Wounds); Lethal?; Difference.

1; 0.62; No; 0.62

2; 0.92; 0.08; 0.84

3: 1.21; 0.28; 0.93

4; 1.68; 0.58; 1.10

5; 1.97; 0.83; 1.14

6; 2.27; 0.97; 1.30

7; 2.75; 1.00; 1.75

8; 3.05; 1.00; 2.05

9; 3.35; 1.00; 2.35

10; 3.64; 1.00; 2.64

As can be seen, there are a few critical turning points.

The first one is illustrated in the trivial case. There, there's no lethal wounds suffered as there's not enough shots fired for them to be lethal.

The next jump is around 6 shooters where the difference shoots up. The spread between 2 to 5 shooters is only 0.3 wounds, but the range from 2 to 6 is 0.46 wounds -- an increase of a factor of 1.53.

The jump from 6 to 7 shooters is also a big one thanks to the twin effects of increasing the number of unsaved wounds coupled with keeping the lethality relatively static. From therein, the difference increases steadily more or less; (although there is another minor jump at 11 shooters for the interested reader). 

Conclusion.

The best number of shooters for XDs is arguably 1. There's no risk to the shooter of dying from the shot. Plus they're still effective.

Beyond that, plump for 6 or 7 depending on the points available due to the rational transaction between wounds caused versus wounds taken from shooting. From therein, up to 10 shooters, the increase is linear. 

I hope this has been helpful. And I hope its accurate (I am human, and I do make mistakes, so please be kind in your comments if I have and you point them out! Thanks!). 

Which Power Weapon?

Following up from the analysis of Chaos Terminators in the New Chaos Space Marine Codex, this post deals with the thorny question of which power weapon we should select if given the choice.  Throughout the new chaos space marine codex, it does not specify any kind of power weapon to be used.  We are therefore free to model all four different types of power weapon on our miniatures.  But which one?

Let's start by looking at the stats for the power weapon varieties.

Power Swords: these have AP3 and use the user's strength.  

Power Axes: AP2, S+1, but go at Initiative=1 due to being unwieldy.

Power Mauls: AP4, S+2, and concussive.

Power Lances: AP3 and S+1 on the charge, moving to AP4 and user's strength thereafter.

But in which situation(s) should we select each?  Without knowing what kind of army we may be facing, its hard to optimize.  But, let's think about each in turn and play to its strengths.

Power Swords.  These are the basic variety with an important AP3.  These are the swords that are going to be getting rid of enemy space marines (or equivalent).  I'd suggest that they are very appropriate on squad champions for the new chaos marine codex where each champion has to challenge every turn.  If we knew with certainty that the enemy was not going to be space marines, then I'd hesitate, and probably choose a power maul instead -- they still go at initiative, but have a superior strength which will aid with taking down pesky eldar (etc.) with higher certainty.  On chaos terminators, these might need some modelling or conversion work

Power Axes. These are the only option to get back to AP2, as per 5th edition rules.  And what would we use AP2 on?  Clearly terminators, but also those occasional 2+ save regular power armour worn by some space marine commanders and their ilk (e.g. Chapter Champions, Honour Guard), as well as Blood Angels' Sanguinary Guard, Ork Mega Nobs, Tau Broadsides, Tyranid Tyrannofexes (etc.).  The main drawback is that they go at low initiative, so we need to address why we don't take power fists (or chainfists) instead. They're not so much more expensive to obtain on a chaos terminator upgrade.  But to save on points, a couple of axes inside a Chaos Terminator squad might not be a bad idea so that they can go toe-to-toe with other terminators and negate their 2+ armour save, get a better roll to wound and force invulnerable saves.  We're really taking power fists in preference to power axes as a deterrent to dreadnoughts, monstrous creatures (and similar) to tackle their high toughness or AVs. If we're talking about a character in a squad (rather than terminator squads as a whole), I'd want them to be going at initiative unless they're plague marines or other infantry that go at I less than 4 -- in which case I'd still prefer power fists instead of power axes (again, unless I'm saving on points to afford other things elsewhere and suspected they could weather going at low initiative -- just like plague champions).

Power Mauls. Higher strength, worse armour penetration such that space marines still get their armour save.  Is this better or worse than a power sword?  Here's some quick math-hammer.  Suppose we set up the target of the power maul and sword as a regular space marine, and the wielder as a nasty chaos terminator.  The probability to hit is the same in both cases (4+).  The probability to wound is 2+ for the power maul, and 4+ for the power sword.  The marine gets his regular save against the maul, but no save against the sword.  So the combined probability to cause a wound on a marine is 0.138 per attack for the power maul, and 0.250 per attack from the power sword -- approximately twice as good!  Then again, if we're facing a terminator instead, then clearly the power maul is going to be better: 0.042 vs 0.069 unsaved wounds per attack -- i.e. power mauls aren't too much better against terminators, so we might as well opt for the powerfists and chainfists instead.  So, my take on this situation is that a power sword would be better on a squad character (especially if we know we're facing other marines), but a power maul would be better if we knew we were facing (e.g.) Eldar.  In a squad of chaos terminators, a few of these are not a bad idea as a deterrent if we're facing off against lower save armies.

Power Lances. These are interesting.  I would take them in preference to power swords if I could almost guarantee that I would get the charge in and potentially finish the job in under two game turns.  This means taking them on fast moving miniatures -- such as bike-riding characters for the main part.  The other main use would be to take them on miniatures riding in assault-ramp-equipped vehicles -- land raiders and the like.  So in a squad of terminators that might be heading for combat with marines, an odd power lance might be good!  But I think I'll be only taking them on Chaos Lords on Bikes for now. 

Gift of Mutation in the New Chaos Space Marine Codex

Before continuing to review the HQ options in the New Chaos Space Marine codex, it is worthwhile pausing to examine the Gift of Mutation chaos reward.  This reward costs 10 points for many chaos lords and aspiring champions, but is the reward worth taking before deployment?

To figure this out, I'm going to go through the possible results for the Gift of Mutation results and try to attach a points value to them.  I'll then take a mean and see if that is worth more, or less, than the 10 points that it cost to purchase the upgrade. 

Firstly, I note that six of the results of the chaos boon table ends up with nothing.  We'll give that zero points.  Both spawnhood and dark apotheosis must be re-rolled, so we'll ignore them.  That gives a total of 32 possible outcomes, of which 6 result in nothing.

Let's go through the rest of the possible results. Unless otherwise stated, the points cost given has been sourced from 2 chaos codexes ago.  The points cost before the slash is what its worth to a multi-wound character, the points cost after is to a single wound (aspiring champion type) character. 

+1 attack is worth 10 / 5 points, in line with the old mark of Khorne (rather than daemonic mutation which costs more);

+1 strength is worth 10 / 5 points;

+1 weapon skill is tough to judge, but we'll simply call it 5 points and be done with it;

+1 ballistic skill is like WS, so again, we'll just call it 5 points;

+1 initiative is approximately the same as a mark of Slaanesh, so we'll give that 10 / 5 points;

+1 wound is worth 15 points;

+1 toughness is worth 10 points;

+1 armour save is worth 20 / 10 points ... I feel this might be slightly over-costed, but let's roll with it;

+1 strength on a ranged weapon is an oddity, so we'll give it 10 points, inline with the +1 melee

strength;

fleshbane is an interesting one, a bit like an enhanced poison attack, or daemon's noxious touch.  Let's give that 10 points;

adamantium will helps with deny the witch, but its not over powerful.  How about 5 points?;

shrouded gives a solid cover save (or cover save improvement) which we'll apply 15 / 10 points to;

eternal warrior is like the old daemonic rune ability which was worth 35 points.  I think that's over-costed now, so we'll lower it to 20 points;

witch-eater is an oddity that circumstantially punishes enemy psykers. Probably about 10 points;

re-roll failed armour saves is very good. We're certainly looking at 20 / 15 points I'd suggest;

poisoned attacks - we'll apply a level 5 points to;

crusader - longer run moves are not too great, so how about 5 points;

hammer of wrath - an additional attack at I=10 is good - we'll adopt the same points cost as +1A which gives 10 / 5 points;

icy aura is a low initiative strike effect that amounts to +1A, so again, 10 / 5 points;

hatred means re-rolling misses in round one of combat, 15 / 10 points I think;

shred re-rolls failed wounds, and is certainly worthy of 15 / 10 points as above;

instant death attacks are okay, so we'll give them 10 points;

stubborn is not so great on a character since they're almost exclusively fearless, but on a squad leader it might prove okay once in a while: 0 / 5 points;

fleet is not as great as it was in 5th edition, so we'll append 5 points to that;

feel no pain is good and we'll go for 15 / 10 points on that one.

The final option is multiple boons which results in an average of 2.5 more boons.  The average of all the above (including null results) is approx. 21 / 17 points.

What are the means of all the above?

Answer: 9 / 7 points.

It therefore seems that the gift of mutation boon is not quite worth taking.  Let's suppose I've been a bit mean with some low points costs though.  I'd need to find an extra approx.40 points for character abilities in the above reckoning.  So maybe I've undercosted poisoned attacks ... there's 5 poitns.  But then I'm struggling a little bit.  At best, gift of mutation appears to be a break-even proposition for independant characters.  But for regular squad leaders, I think we're going to forget about it.

Rise of the Screamers

Brent's article on BoLS got me thinking more about Screamers of Tzeentch and their rising role in daemons armies.  Since the new rules debuted in White Dwarf, I think its fair to say that all us daemons players have been gushing over the flamers and screamers once more.  Where they were once limited, I think both of these daemons are coming back with a vengeance.

For the Screamers of Tzeentch, the changes mean that they are much more survivable than they were before.  The extra wound means that we will no longer be losing some (most? / all!) of a squad due to exploding vehicles (yess... that's happened to me).  But perhaps the biggest change is the replacement of warp jaws with Lamprey's Bite.  Against vehicles, that means that they probably aren't as good as they used to be (pen = 8+2d6 in the old version, vs 5 + 2d6 in the new version).  That said, they do gain more attacks (1 in the old version, vs. 3 in the new version).  Hence, they can still readily tackle light tanks, but the probability of penetrating an AV=14 tank has gone from 83.33% to 16.66% per attack. At AV=10, the probability has changed from 97.22% to 72.22%.  Given the 3 attacks, light tanks are probably in even more danger from screamers than they used to be.  But gone are the days of Land Raider hunting methinks.  I'll leave that to the monstrous creatures now.

Lets have a look against infantry.  To kill a marine, the screamers now hit on 4+, and wound (with no save) on 3+.  That compares to 4+, 4+ followed by a save previously.  And this is where the price increase is at, I think.  Screamer of Tzeentch can really put a whole lot of pain on all armies.  Striking at I=4, they should devastate the typical tactical squad in exchange for minimal damage in return.  For 100 points, 4 screamers on the charge will typically inflict 5.33 unsavable wounds on a marine squad.  That really hurts and is up there with the damage potential of a 5th edition bloodletter.  But more significantly, they can also rob terminators of their 2+ armour save, forcing them to use their invulnerable save.  At 25 points each, I contend that Screamers are going to become a mainstay of daemons forces for the immediate future.  I'll save talking about flamers to another time.....

Icarus Lascannon: Model Making and Statistical Evaluation

One of the nice features about the Bastion and Aegis Defence Line sets are that they come with a couple of "upgrades" in the box.  In the case of the Bastion, the Icarus Lascannon comes supplied. 

Making the Icarus was reasonably straight forward -- it is not the most complex (nor most fiddlesome) model to assemble (I think that award might go to the Shadowsword).  Some of the sprues do leave appreciable nubs on the main plastic once removed, so I found that some time invested in clean up work is essential to get the model looking good.  I think my only minor quibble is that the front end of the lascannon itself comes in two parts.  I'd prefer just one part please!  (equally, I am happy drilling my own barrel holes on miniatures; some other people may not be, so I can see how it is seen as an advantage).

Rules-wise, the Icarus lascannon is not too different to a regular lascannon except for being able to take on deep-striking and flying units nicely.  Assuming a typical (marine) BS of 4, the chances of scoring a penetrating hit on a flyer are then:

AV=10: 3+ to hit; penetrate on 2+ => 56% (with 33% chance of explosion if hit => 18.5% cumulative)

AV=11: 3+ to hit; penetrate on 3+ => 44% (with 33% chance of explosion if hit => 14.8% cumulative)

AV=12: 3+ to hit; penetrate on 4+ => 33% (with 33% chance of explosion if hit => 11.1% cumulative)

AV=13: 3+ to hit; penetrate on 5+ => 22% (with 33% chance of explosion if hit => 7.4% cumulative)

AV=14: 3+ to hit; penetrate on 6+ => 11% (with 33% chance of explosion if hit => 3.7% cumulative)

So, whilst appearing nice against low AV units, I probably wouldn't use it over the quad gun.  The gain is at the high AV end where the quad gun won't dent anything.  But then again, considering the low probabilities involved, why was I shooting at a land raider again?

Dark Eldar: A Cause for Re-Thinking Marks of Chaos on Raptors?

For a squad of chaos raptors, an icon of Khorne seems optimal from a previous analysis (see: parts I and II).

However, in recent times, the advent of dark eldar has got me re-thinking this conclusion.  Lots more players are taking dark eldar (and there's still the die-hard eldar fans ... much like I'm a die-hard chaos marine and daemons player - kindred spirits). So, should I reconsider the Icon of Khorne?

I'll resurrect the three options that I was toying with originally: the raptor champion armed with a power fist, twin lightning claws, or simple baseline raptors.  I'll put them up against ten dark eldar cabalite warriors instead of the usual space marines).

Let's look at each Icons in turn, and assuming that the raptors get the charge in.

Khorne.

With a Khorne Icon, the raptors gain an extra attack each, but they strike second.

Khorne Case 1: Baseline Raptors.

The kabalite warriors need 4+ to hit and 5+ to wound from 9 attacks.  This results in 1.5 wounds, of which, 0.5 stick.  The sybarite has a power weapon with 2 attacks.  S/He also hits on 4+ and wounds (without a save) on 5+.  That results in 0.33 more wounds, making 0.83 total.

The raptors hit on 4+ and wound on 3+ from 41 "normal" attacks (total) if everyone was still alive.  Let's assume one is dead from the dark eldar.  That means there are (only!) 37 attacks.  That gives 8.22 wounds.  (i.e. dW = 7.39).

Khorne Case 2: Power Fist.

Again, 0.83 wounds incoming from the first-striking dark eldar kabalite warriors.  Assuming that one of the regular raptors perished, they get 8x4 attacks on the charge that results in a total of 7.11 wounds. The aspiring raptor champion gets 4 attacks (2 base, 1 charging, 1 from the icon), of which 2 hit and 1.67 kill.  This gives 8.78 wounds (and dW = 7.95).

Khorne Case 3: Lightning Claws.

As above, but the champion has 5 attacks and 2.5 hit. They wound on 3+ with a re-roll for failed wounding rolls. This gives 2.22 more wounds for a total of 9.33 (and dW = 8.5).

Slaanesh.

For a Slaaneshi Icon, the chaos raptors strike simultaneously with the dark eldar.

Slaanesh Case 1: Baseline Raptors.

The raptors are still taking 0.83 wounds, but now strike back without losing anyone.  On the charge, they get (9x3)+4 = 31 attacks.  That gives 6.89 wounds (and dW = 6.06).

Slaanesh Case 2: Power Fist.

Assuming the aspiring champion survives, the raptors get 9x3 regular attacks, plus 3 power fist attacks.  The regular attacks cause 6 wounds; the power fist yields 1.25 wounds.  That's 7.25 wounds in total (dW = 6.42).

Slaanesh Case 3: Lightning Claws.

Again, we'll assume the champion survives.  The regular attacks again cause 6 wounds. The lightning claws have 4 attacks, of which 2 hit and 1.78 kill.  That gives 7.78 wounds (and dW = 6.95).

Conclusion.

The Icon of Khone is still superior.  The extra attack still outweighs the increased initiative.  Good job since I've already modelled the Icon of Khorne and don't particularly want to change!

How Many Tesla Carbine Shots Are Required to kill Plague Marines?

Nurgle's plague marines are tough; no doubt about it.  But how worried are plague marines when taking incoming fire from Tesla Carbines (as used by Necron Immortals)?  Let's look at some statistics.

An immortal will hit a plague marine on a 3+ (probability = 0.67).  

The tesla carbine will wound on a 4+ (new combined probability = 0.33).

The plague marine saves the wound on a 3+, followed by a feel no pain roll of 4+ if required.  Hence the probability of the wound being saved is 2+.  Therefore an unsaved wound has a probability of 0.056.

But the Tesla special rule will activate on a hit roll of 6.

So we'll modify the above calculation to count for only a roll to hit of 3, 4, or 5.  That yields a probability of an unsaved wound of 0.042.  

Now let's add in the roll to hit of 6 (probability of 1/6 = 0.167).  This causes an automatic 2 extra hits.

So we're taking 3 hits with a wound caused on 4+.  That's 1.5 wounds * 0.167 = 0.25 wounds.

Each wound is saved (as above) on 2+.  This gets reduced to 0.042 unsaved wounds if the necron rolls a 6.

Combining the two results (0.042 unsaved wounds on a hit roll of 3,4,5 with 0.042 unsaved wounds on a hit roll of a 6) yields 0.083 unsaved wounds per incoming tesla carbine shot.  That means 12 tesla carbine shots are required to down a plague marine, on average.  That compares to 27 bolter shots (or indeed, gauss flayer shots) to down a plague marine.  So an immortal armed with a tesla carbine is more than twice as deadly as a regular necron or space marine to my plague marines.

How Many Khorne Berzerkers does it take to Down a Necron?

Berzerkers of Khorne are (were?) noted for their close combat prowess.  So, today I wanted to look at how many berzerkers it will take to kill a necron warrior in close combat.  I am assuming that the berzerkers managed to charge and also got off a bolt pistol shot prior to charging.

The simplifying assumption here is how to deal with the necron's natural save of 4+ followed by the 5+ reanimation save.  Combining them together grants the necron an effective save of 3+ (i.e. it saves half of all regular wounds, followed by ignoring one third of those that get through).

Let's resolve the bolt pistol shot first.  It hits on 3+ and wounds on 4+.  In other words a 0.33 chance of wounding.  Using the effective save of 3+ (as above), the necron will suffer 0.11 wounds per shooting, charging Khorne berzerker.

When the berzerker makes close combat, he will have furious charge (assuming that this hasn't been denied to him thanks to the adaptive tactical genius that is Nemesor Zahndrekh).  The berzerker attacks first and is hitting on 3+ and wounding on 3+.  That means 0.44 wounds per attack.  The berzerker has 4 attacks on the charge, which will lead to 1.76 wounds landing.  Of these, the necron will fail to save 0.59.

Combining this melee result with the above shooting means that a singular, regular Khorne berzerker will cause 0.7 unsaved (and non-reanimated) wound when charging.  Phew!  I was worried that that would work out a lot worse!

Statistics: How Many Seekers of Slaanesh

This article should have been posted alongside my earlier series on the statistics of various daemon units, but got omitted due to being lost in the warp for a little while.  The question for this post is how many seekers of Slaanesh do I need in a unit to take care of various situations?

Against Infantry.

In common with daemonettes, the seekers of Slaanesh have rending claws, a bucket load of attacks and high maneuverability.  But they are also fragile with a toughness of 3 and a regular 5+ invulnerable save (the latter is looking even more fragile in light of the Grey Knights release).  So how many seekers will be needed to alpha strike (that is kill on the first turn of melee) a ten man marine squad?

Firstly, I'm going to assume that the experienced daemons player can avoid getting shot at with these cavalry before they get in to combat, and that they manage to charge the space marines.  If this is not the case, then we can assume 3 could potentially be cast back to the warp due to bolter fire -- see the daemonette's statistics for a justification of this point.

The seekers have 5 attacks each on the charge, hitting on 4+ and wounding on 5+ (rending on a 6).  Therefore the marine will take 0.417 "normal" wounds and 0.417 rending wounds.  On average, 0.556 marines will die per seeker of Slaanesh that charged.  Therefore, fully 18 seekers of Slaanesh are required to alpha strike a marine squad (or 9 seekers for a 5 man combat squad). This is less than daemonettes thanks to the extra attack, but its not all that efficient even so.

Light Tank Busting.

As with daemonettes, the rending nature of the claws of Seekers mean that they threaten light (AV=10) tanks quite readily.  Even two Seekers will pose a problem for an AV=10 tank thanks to their rending ability -- that'll result in at least 1 glancing hit, probably more.

Statistics: How Many Screamers of Tzeentch?

Screamers of Tzeentch are rightly thought of as flying melta bombs.  Hence the role that I have for screamers in my daemons army is to target enemy tanks, zoom quickly toward them and blow them in to scrap metal.  I don't intend for the screamers to survive this attempt in general for two reasons: they readily die to small arms fire, and even if they get to complete their task successfully, my experience is that they get caught up in the subsequent explosion of the tank they've just busted!  Hence they're something of a glass hammer in the same way that the flamers of Tzeentch are.

Tank Busting.

Let's suppose that they fly in to contact with a target vehicle.  They then use their warp jaws to plant a melta bomb.  In the case of a stationary vehicle, each screamer will plant one melta each.  For a moving vehicle, 2 screamers will be needed to statistically guarantee one melta bomb being planted.  And for a flat out vehicle, six will be needed.

For many vehicles, even a single melta bomb means a lot of trouble.  This is especially true for rear armour = 10 or 11 tanks like rhinos and similar.  I typically need about three successful meltas being planted to ensure a reasonably good chance of wrecking vehicles like rhinos (or better).  Hence, that's 3 screamers for stationary vehicles, or six for moving vehicles.  I won't even bother thinking about flat out vehicles from here on in as I reckon that would be a desperation move to try to target them with screamers.

Now let's add in a bit of jeopardy.  Consider 10 standard bolter shots coming in at the screamers, fired by BS=4 troops (i.e. space marines).  Of them, 6.67 hit, and 3.33 wound.  Half will be saved, resulting in 1.67 unsaved wounds.  Hence if the screamers are going to be taking incoming fire, we need to add and extra one or two to the squad to compensate.

Overall, I'd therefore suggest about 5 screamers for targeting stationary rhino-like vehicles, and about 7 or 8 for moving rhino-like vehicles.  Land raiders and necron monoliths are a different matter entirely!  I'd probably suggest up to doubling the number of recommended screamers for taking down land raiders.  But with the price for each screamer being somewhat above the average ork, I think the daemons player should think about alternative methods to down land raiders (e.g. through Heralds of Tzeentch, soul grinders, or greater daemons).

In the unlikely scenario the screamers survive, I will then use them to swoop in on objectives (depending on the game) to contest them.  Clearly this is a late turn gambit as they will readily fall to moderate close combat squads.  I recall a game against some Guard in a tournament some two years ago where Ogryns shot them up and ripped them to bits in the mid-game.  It wasn't pretty!

Statistics: How Many Flesh Hounds of Khorne?

Flesh hounds of Khorne are typically used to rapidly hunt down opposing troops.  They're not vehicle killers and they're not monstrous creature slayers if we're being honest.  But they could do both of these roles (e.g. rhino killing) if other daemon troops have already been wiped away and one is desperate.  But there should be superior daemons choices for either of these roles.  I regard their primary role as to engage opposing units rapidly, and tie them up.  Hopefully they might score a few wounds as well.  But how many should be used?

Against Space Marines.

Let's put some flesh hounds up against space marines and see how they perform.  An experienced daemons player should be able to take advantage of the flesh hounds and ensure that they take few (zero?) shots on their way in to combat and that they get the all-important charge in.

If they get the charge in, then they will strike first due to the furious charge special rule.  They will get three attacks each, hitting on 4+, wounding on 3+ and killing when the marines fail their 3+ armour save.  Hence each flesh hound will cause a statistical average of 0.33 wounds on the charge.  Therefore three flesh hounds will be required to take down a space marine.  

At this point, we can see that we're going to need a lot of flesh hounds to take care of the space marines, even with Karanak coming along to help.  At 15 points each, I think that the points spent on flesh hounds will only tie up opponents rather than deliver a killing blow.  I therefore think the points would be better spent elsewhere, unless you're playing a mono-Khorne army.  And even in a mono-Khorne army, I think I'd only have a unit of flesh hounds in it for their speed to tie opposing units up.  And their fluffiness.  They're simply not that good in my opinion otherwise!  (Sorry to sound so negative!)

Statistics: How Many Bloodcrushers of Khorne?

And to finish off our examination of the elites section of the daemons codex, we finally turn to the Bloodcrushers of Khorne. Once again, in order to answer the question we will consider what role we want the bloodcrushers to play on the battlefield. For me, it boils down to icon-bearing, anti-infantry, anti-monstrous creature, and anti-elite troops, with perhaps a smattering of light tank busting. Let's have a look at each of them.

Icon Bearing.
This purpose boils down to survivability. How many standard bolter shots (fired by marines) can an icon-bearing bloodcrusher take? Well, the marine will need 3+ to hit, 5+ to wound and then the bloodcrusher to fail its 3+ armour saving throw. That amounts to 0.074 wounds per standard shot. Or put another way: 27 standard shots will be required to take two wounds away from the bloodcrusher and remove him from the game (on average). Plaguebearers eat you hearts out! (yuck on second thoughts). Even against plasma shots, they'll take 5.4 shots to kill. So the bottom line is that bloodcrushers can make reasonable icon bearers.

Anti-infantry.
As usual, we'll put a bloodcrusher up against a squad of 10 space marines, with a power fist equipped sergeant. We will assume that the bloodcrushers get to charge in (which I hope is the case for you experienced players out there), meaning that furious charge is active. Given they might take some bolter fire on the way in, they have probably lost 1 wound already.

The bloodcrushers strike first with 4 attacks, hitting on 3+, and killing on 2+ (hell blades are power weapons!). That results in 2.22 wounds taken by the marines from a single bloodcrusher. Hence an unit of 4 or 5 should be readily able to alpha strike a tactical squad.

If the marines get to strike back, then they hit on 4+, wound on 5+ and cause a wound when the bloodcrusher fails its 3+ save. That means 0.11 unsaved wounds per regular space marine trooper. The bloodcrushers are not bothered at that level of pain. End of story.

Anti-Monsters.
Let's put a bloodcrusher up against a daemon prince of Nurgle to see what happens. They strike simultaneously (assuming the bloodcrusher charged in). The Khornate daemon hits on 4+, wounds on 3+ and makes it stick when the prince fails its 5+ invulnerable save. That gives 0.89 wounds on the charge.

The prince hits on 3+, wounds on 4+ and makes it stick when the bloodcrusher fails a 5+ invulnerable saving throw. With 4 attacks, the bloodcrusher takes a similar (0.89) amount of wounds in exchange. They're evenly matched, remarkably.

To take out the daemon prince in an alpha-strike, 4.5 bloodcrushers would be needed. Two would be needed to win the combat on the charging round.

Anti-Elite troops.
What about terminators? What about with a storm shield? Let's have a look.

The bloodcrushers strike first, hitting on 3+, wounding on 2+ and downing terminators when they fail their 3+ invulnerable save. With 4 attacks on the charge, that means 0.74 wounds. Therefore 7 bloodcrushers will be needed against a squad of 5 storm shield terminators to alpha strike them. Striking back, the terminators would hit on 4+, wound on 2+ and make it stick on failing the bloodcrushers 5+ invulnerable save. They take 0.55 wounds from 2 such attacks. Hence to statistically go better than a draw against 5 terminators, we will need at least 4 bloodcrushers.

Light tank busting.
Against AV=10, the bloodcrusher on the charge will have 4 Strength=6 attacks hitting (assuming the vehicle was not moving). Half of them will at least glance. Without going too much further, it is safe to say that even a modest number of bloodcrushers can pose a threat to light weight tanks.

Summary.
It looks like 4 or 5 bloodcrushers in a squad should be enough to handle most situations described above. Their only draw-back is that they don't move as fast as fiends of Slaanesh. But hey, in a daemons army: you can have both and play tag-team.

Statistics: How Many Flamers of Tzeentch?

Flamers of Tzeentch are known to be a "glass hammer". That is usually meant in the sense that you'll get one hit out of them before they disintegrate (due to enemy fire!).

So, what role do I have for flamers on the battle field? There's two broad roles really. Firstly: tank hunting, and secondly: elite troops hunting. Combined with their jump infantry status, they should be able to let rip one volley before perishing horribly. So let's have a look at how they do.

Anti-Tank.
Their main weapon is the template attack. It will automatically glance anything with an armour value on a 4+. Take two flamers, and I will statistically glance once. To get a reasonable chance of a high glancing result, about 6 flamers will suffice.

Anti-Elite Troops.
When people think of elite troops, they will often think about terminators. But plague marines are also a kind of elite troops due to their quasi-terminator saving throw and high toughness.

In one of the Warpstone Flux contests a while ago, we saw that flamers of Tzeentch were simply excellent against plague marines, even in small numbers (poetic justice or what?!).

Against terminators, they fare slightly worse due to the 5+ invulnerable save that the terminators have. Even so, a small squad of flamers can really take the fight out of a squad of terminators due to the breath of chaos. The statistics are a little hard to work out given the vagaries of template weapons, but from play experience, slightly less flamers than the terminator squad will be needed (i.e. about 4 flamers is often enough to take out or severely weaken 5 terminators, assuming optimal flamer template placement).

Survivability.
How many bolter rounds can flamers of Tzeentch take? Fired by marines, standard bolter rounds hit on 3+, wound on 4+ and kill on 4+. That's 0.167 dead flamers per shot; or 6 standard shots to down them. So in some ways, yes: they are something of a glass hammer.

Summary.
Even 3 flamers can pose problems for tightly packed marine squads. Taking a few more for anti-tank and anti-elite jobs ... and I think that 4 or so flamers is about the right number.

Statistics: How Many Beasts of Nurgle?

Beast of Nurgle are tough. And it's also tough to know how to play them unless we're using a mono-Nurgle Epidemius list.

Overview.
There are two basic, interlocking points that need to be made about beasts of Nurgle.

(1) Firstly, they are like having 2 plaguebearers on the board, wrapped in in one miniature. That is to say, they have the same statistics line apart from the wounds column and attacks column. They have 2 wounds instead of 1, and d6 attacks instead of 1. Point for point therefore, they are more deadly than plaguebearers in combat due to the extra attacks.

(2) The downside is that they're not troops. They cannot sit back on an objective and hold it -- they can only contest. But they are very good at sitting and contesting! To see this, simply check back on my plaguebearer analysis. Three beasts of Nurgle will suffice for an entire game of contesting (as long as they don't get charged).

For tar-pitting, three or four beasts will be needed against a typical space marine squad (again going by the plaguebearer analysis).

Anti-Monstrous Creature Role?
So, do beasts of Nurgle have a role to play against monsters? Let's put them up against a daemon prince of Nurgle and see what they can do.

The daemon prince will attack first with 4 attacks, of which 2.66 hit, and 1.33 wound. The beast will save a third of them with the invulnerable save (feel no pain won't work against monstrous creatures), leaving 0.89 unsaved wounds. If the prince charged, then let's round up and say 1 wound total.

The beast will get an average of 3.5 attacks against the daemon prince. Of them, 1.17 hit, 0.58 wound (no poisoned re-rolling here!) and 0.19 stick. Hence 5 or so beasts will be needed to just draw even. I think I prefer a large pack of plaguebearers to be honest.

Summary.
They're like plaguebearers, but have slightly more attacks at the expense of not being able to hold objectives. If I'm going to take them, I'll do so only in a mono-Nurgle list. But if I were to take them in a mixed daemons list, then I would take about 4 or 5 -- i.e. about half of the number of plaguebearers that I would put in a pack, due to their similarity to plaguebearers.

Statistics: How Many Fiends of Slaanesh?

Continuing the daemons codex review, today we turn to the Fiends of Slaanesh. Many daemon players swear by them and many opponents swear at them. Why is that? Let's have a closer look and address the question of how many fiends should a daemons player include in a squad?

What is it that I want to achieve with Fiends? Well, there's the anti-infantry role (obviously), the anti-tank role, the anti-monstrous creature role, the all round anti-other army role (almost joking), the hit and run role, and the moving fast to contest objectives role. I'm going to ignore that last point and take it for granted that you're going to move fiends quickly. That is one of their best points and one of the strongest reasons to field them. Combined with the hit and run rule, these guys can pose a problem for many opponents across the board.

Anti-Infantry.
I'm going to take my usual approach of setting them up against a squad of 10 marine. They will take a round of bolter fire before charging in to the squad (whose sergeant has a power fist, of course). The marines will hit on 3+, wound on 4+ and take a wound off a fiend on a failed 5+ save. That means an average of 2.22 wounds before the fiends get the charge off. That translates as one dead fiend. On the other hand, if the daemon player is worth his or her salt, they should take zero wounds on the way in due to their immense movement and charge range potential.

In melee, the fiends will strike first with a remarkable 6 attacks each. They will hit on 4+, wound on 3+ (rending on a 6) and the marines will make armour saves where appropriate. The results in 2 wounds, 0.5 of which will be rending.

The marines get a 3+ save against the 1.5 normal wounds, resulting in 1 wound caused in total per fiend. In exchange, they will suffer attacks from 8 regular marines (assuming the 9th regular marine perished rather than the sergeant), resulting in 4 hits, of which 2 will wound and 1.33 will stick. The power fist is likely to cause an additional 0.55 wounds. That's almost a dead fiend in exchange.

Therefore the fiends need to number more than 1 in a unit to win a combat...! Ten are needed for an alpha strike. But a few less than that is usually a good number. Dare I say that six(!) is about the right balance for this anti-infantry role. The fiends stand a good chance of killing plenty of marines and taking very few wounds in exchange. Don't forget to hit and run at the right moment once you're done!

Anti-Tank.
With a strength of 5 and rending, the fiends can be very damaging to opposing tanks. They can penetrate AV=13 and glance AV=14 at best, so there's not a tank in the game that is invulnerable to their claws (at some level).

Below, I give a table of probabilities to glance and penetrate a given AV value, assuming that there's a single fiend that gets 6 attacks on the charge to the (non moving) vehicle.

AV=10: 6 hits, resulting in 1 glancing and 1 penetrating hit
AV=11: 6 hits, resulting in 1 penetrating hit
AV=12: 6 hits, resulting in 0.33 glancing and 0.66 penetrating hits
AV=13: 6 hits, resulting in 0.33 glancing and 0.33 penetrating hits
AV=14: 6 hits, resulting in 0.33 glancing hits

Of course, it is very unlikely that the fiends will go for stationary or immobile tanks. So the above values should be halved if the tanks have been moving (but not flat out). I wouldn't recommend targeting flat-out tanks unless it is near the end of the game.

So if I want to penetrate AV=13 that is moving, I will require 6 fiends. But since the fiends will target the rear armour of a tank, we're mostly looking at AV=10, 11 or 12. The chances of penetrating these tanks therefore increases, but again (and from play experience) 6 fiends is about right. And did I already mention that's a fluffy number to have?

Anti-Monstrous Creature.
The main problem with figuring out how good fiends are against monstrous creatures is what creature should I put them up against? With infantry, I like to consider marines as the opposition (and therefore assume that eldar and guard miniatures will be easier!). In the absence of a good and obvious choice, I elect to put them up against a daemon prince. This is because it appears in two codices and is probably more common than carnifexes. Trygons might also be a good alternative, but let's stick with daemon princes.

The two creatures strike simultaneously (I=5).
The daemon prince strikes on 3+, wounds on 3+ and the fiend has a save of 5+. From 4 attacks, the fiends will suffer 1.19 wounds.

The fiends hit on 4+ and wound on 3+. But let's be evil and say that it is a daemon prince of Nurgle with T=5. They now wound on 4+ (rending on 6). The prince has a 3+ save against normal attacks (assuming an iron hide for a daemon's codex daemon prince) and a 5+ save against rends.
From 6 attacks, 3 will hit. Of those 3, 1.5 will wound (0.5 rending). After taking saving throws, the prince suffers 0.67 wounds.

If the prince has 4 wounds, 5.97 fiends are required to take it out on an alpha strike (let's round that up to SIX!). About three will be needed to win the combat. So again, not only is 6 fluffy, but it also works against monsters!

Summary.
Take six of them for flexibility: they can alpha strike a Nurgle daemon prince (and pose serious problems to other high toughness targets), they can penetrate tanks readily and they will easily win against standard marines. And six is fluffy.

And finally, none of the above assumes the unholy strength upgrade. Said upgrade will only improve the situation! Remember also that it is the sheer speed of these guys that can hurt opponents -- maximize this advantage!

Statistics: How Many Nurglings?

A full discussion of daemon troops wouldn't be complete without those naughty little nurglings. I have admittedly struggled to find a place for them in my mixed daemon forces (not so mono-Nurgle lists with Epidemius). But if they are to have a role, then is should be analogous to ripper swarms: a screening unit and a tar pit. Screening is tough to evaluate and it clearly follows the rule of thumb of the more the better. Let's have a look at the other role.

Tar-pitting.
With some luck, the nurglings will not lose a single base by the time they reach hand to hand combat with their target tar-pit unit (a squad of marines, of course). They might have taken a wound or two or one base though. So the question then becomes how many nurgling bases do I need to force a draw with the space marines in close combat?

In close combat, the marines strike first, hitting on 3+, wounding on 3+ and making the wound stick by avoiding 5+ save. For 9 marines, that means 2.67 unsaved wounds -- just about enough to take off a base of nurglings. The power fist sergeant will cause an additional 0.74 wounds, taking the total up to 3.41 wounds.

In exchange, one base of nurglings hits on 4+, wounds on 5+ and makes it stick a third of the time. With 3 attacks per base, (4 on the charge) that comes to 0.167 wounds per base (or 0.33 wounds on the charge). That means I will need at least 18 bases without charging (hahaha) and at least 9 or 10 on the charge.

So the answer to my question is that I will need to take a large (maximized) squad if I want the nurglings to do a half decent tar pitting job. Otherwise, they can simply die fast and provide a screen to my other more valuable troops!

Statistics: How Many Pink Horrors?

Pink horrors are clearly not close combat exponents. They shoot things. Repeatedly. And fast (assault 3). They want to get in range, shoot things and avoid being charged. It's that simple. Add in a little bit of tank hunter, Changeling mischief, and icon bearing and we're done.
Shooting.
So, if they're going to shoot things, then how many horrors do I need to take care of a (say) squad of 5 marines?

Each horror gets 3 shots at BS=3. Hence 1.5 shots will hit. Fifty per cent of that will wound (S4 against T4). That means 0.75 wounds, on average. And then the space marine gets a 3+ armour saving throw. So, 0.25 unsaved wounds per horror.

Hence I need 4 horrors to statistically take care of a single space marine. Therefore a squad of 5 marines need only fear a full pack of 20 pink horrors of Tzeentch. This seems like a very large number realistically. Especially given the points value of the horrors.

Survivability.
Let's have a quick look at their survivability whilst we're here. How many standard shots (i.e. bolter shots fired by a marine ... or BS=4, S=4 shots) can they take?

They'll get hit on 3+, get wounded on 3+ and save on 4+. Hence they stand a 22 per cent probability of being removed from a standard shot. Therefore 4.5 standard shots are required to remove them on average. This means that space marines shooting at them will kill less horrors than horrors will kill marines in a firefight! This is a somewhat surprising result that is often overlooked by marine players. Equally, it is half of the survivability of plaguebearers. Hence I will often take units of 10 or more horrors for my purposes of icon bearing, backed up with a little shooting ability to make eldar (etc.) think twice, before encouraging them to hop along to claim an objective on turn 4 or so.

Further Discussion.
BUT, there is a different reason that I will take horror packs: the Bolt of Tzeentch. A good set up I've found is simply to take a minimum sized squad and equip one horror with the Bolt of Tzeentch for extra anti-tank ability in the daemons army.

And then there's the Changeling. I've discussed this fellow in the past, so I'll simply provide a link to those earlier thoughts.

Statistics: How Many Plaguebearers?

Today, I'll continue my examination of lesser daemon statistics by having a closer look at Nurgle's tallymen: the plaguebearers. They are one of my favourite units in a mixed daemons army list and I don't usually leave home without them.But what do I want my plaguebearers to achieve in a typical mixed daemons army list? Well, they're certainly not there to get their points back through close combat with opposition units. I use them in two primary roles:
(a) Objective securing;
(b) Tar-pitting opposing units (and monstrous creatures).

Before we get in to it, I will also note that I use plaguebearers to hold chaos icons in my mixed army lists given their survivability and have long ago concluded that they're the only lesser daemons that are worth while taking a chaos instrument for. That can also make for some neat wound allocation shenannigans, but I won't get in to that!

Objective Grabbing.
Usually, I will sit a unit of plaguebearers on an objective (if it is an objective game), hunker down and sit there for the entire game. Perhaps some other units might deep strike off their icon to support them; perhaps not. I will usually aim to place an icon in a piece of terrain as well, so they'll get approximately a 4+ cover save.

Let's assume that they get 10 incoming shots per turn. How many plaguebearers do I need for a 5, 6, or 7 turn game so that at least 1 of them survives (statistically)?

We'll assume the shots are from marines (hitting on 3+) and wounding on 5+ (thanks to the daemons high toughness rating). For 10 shots, there are 2.22 wounds resulting.

Their cover save means 1.11 wounds stick and the feel no pain special rule reduces that down even further to 0.55 wounds. Hence over 5 or 6 game turns, there are approximately 3 daemons sent back to the warp. Four in a 7 turn game. Hence I could get away with a minimum sized squad if I believed that they would be mostly left alone apart from a puny 10 bolter rounds per turn!

Tar-pitting.
Let's have a look at the other role I have for them -- tar-pitting other units. What do I mean by tar-pitting? Simply making sure that other units are in close combat with the plaguebearers and not attending to other units that might be better targets for shooting (etc.).

We'll assume that the situation is that I want to tie-up 10 space marines in close combat for most of the game (thereby keeping them away from objectives and preventing them from shooting my more fragile daemonettes or bloodletters). One of the marines is a sergeant with a power fist.

Given that the plaguebearers enter play via deep-strike, we'll assume that they take some incoming firepower from the marines. This will result in approximately 1 plaguebearer heading back to the warp (give or take a little margin of error).

The marines strike first, hitting on 4+ and wounding on 5+ (with 2 attacks each, let's assume). If the plaguebearers charged in, they will take 3.33 wounds, of which 1.11 stick after their saves and feel-no-pain rolls. In return, the plaguebearers will hit and wound on 4+ (with re-rolls to wound due to poisoned attacks). For every plaguebearer, that results in 0.25 unsaved wounds on the charge. The sergeant with the power fist will then cause 1.11 wounds of which 0.74 stick. So, the plaguebearers need to number at least 8 strong to get better than even odds of a draw (which my instrument of chaos then means I'll convert in to a won close combat). Add in a few extras to survive the incoming fire, and about 9 or 10 plaguebearers will be needed. This number again feels about right from play experience.

Statistics: How Many Daemonettes?

With daemonettes of Slaanesh, I want them to primarily be rapid moving infantry killers, with a secondary suite in light tank busting. So how many of them do I need to accomplish each of those tasks with a reasonable chance of success?Against Infantry.
We'll use the same situation as with the bloodletters: a ten man strong space marine squad armed with bolters, a multi-melta and a flamer. How many daemonettes might I lose before they reach their target? Well, firstly I'm going to suggest that they can completely avoid the flamer due to their fleet special rule. With luck, they may also be able to avoid rapid fire range of the bolters (depending on the opponent and the gaming situation at hand). Hence, we have 8 bolter shots and a multi-melta shot to weather before close combat ensues. The bolters hit on 3+ and wound on 3+. The multi-melta wounds on 2+. In total, I might expect an average of 3.56 + 0.11 = 3.67 wounds. Each daemonette gets a 5+ invulnerable save, leading to 2.45 unsaved wounds. Let's round that up and say 3 daemonettes may die before getting in to melee with the space marines.

In close combat, the daemonettes strike first due to their high initiative. They have 4 attacks each on the charge, hitting on 4+. Hence 2 attacks will hit on average. Of those hits, one in six will cause a wound and a further one in six will rend (i.e. no save). Therefore the marines take 0.33 "normal" wounds and 0.33 rending wounds, on average. With a 3+ save against the normal wound, the typical daemonette causes 0.44 unsaved wounds on the charge. Even with 20 daemonettes, I'm not going to be able to alpha strike the space marines out of existence. But for a smaller squad of, say 5 marines, 12 daemonettes will take care of them in an alpha strike on average. From experience, this feels about right given that I usually have to back my daemonettes up in close combat with another unit.
Light Tank Busting.
Remarkably, daemonettes can pose a problem to AV=10 tanks. This is due to the rending special rule. If they roll a 6 on their armour penetration, it means they get an extra d3 to roll. That extra d3 results in at least a glancing hit (penetrating two thirds of the time). Assuming that the daemonettes charge the tank, they will get 4 attacks each. Hence even two daemonettes should be statistcally enough to result in a glancing hit if the tank has not moved. Three daemonettes would be needed if they are only hitting on 4+ to cause a glancing hit. At flat out speed, they will be hitting on 6+. To cause a glance (statistically), we will then need 9 daemonettes.

Of course, I haven't spoken about the result of the glance or penetrating hit. That's another die roll entirely. But against tanks that haven't moved, or have only moved a "normal" amount, daemonettes in small numbers can pose problems. Hence I think I will take about 12 daemonettes in a squad: not only is it fluffy, but they can also handle a small combat against marines and pose issues to light tanks.

Statistics: How Many Bloodletters?

This week, I'm going to be writing a series of four articles looking at the troops choices for the four main chaos powers in Codex: Chaos Daemons in a similar way that I looked at the advantages of plague marines and noise marines in the past. Today, we're starting with Bloodletters of Khorne.Not so long ago, Raptor1313 wrote an article on how evaluating units by making their own points cost back is overly simplistic. So, what is it that I want bloodletters in my (mixed daemons) armies to do exactly? I personally think that the answer to that is to do what they do best: kill infantry quickly and efficiently. I'm not bothered if they don't make back their points. I just want to be certain that they do their job.

The situation.
Most commonly, I use bloodletters to take out squads of space marines. So in my considerations below, I will assume that I want my bloodletters to take on a squad of 10 marines. I will assume that one of the marines is a sergeant with a power fist. Perhaps one of the more typical set-ups that I come across is multi-melta plus flamer special weapons in these squads, so I will assume that as well.

In game terms, my bloodletters have to deep strike in. I will assume that this goes reasonably well and then I run them to ensure not too many bloodletters get whacked by templates and to get closer to their quarry. The marines will sit still and rapid fire them. After that, I will have my bloodletters assault the marines. (Of course, sometimes the marines may choose to charge them rather than the other way around, so this situation is necessarily simplistic!).

The question is this: how many bloodletters do I need to (statistically) achieve the goal of destroying the opposition (without having to rely upon them fleeing and the bloodletters catching up with them)?

Calculations.
The first step in this calculation is to determine how many wounds are caused by the space marines on the bloodletters before they can get in to combat. That's 8 rapid firing bolters, 1 flamer and 1 multi-melta. I'm going to assume that the flamer template hits 2 bloodletters (which may or may not be accurate in a real game - this is purely a thought experiment!).

How many hits do the bloodletters take on average from this volley? Firstly, there are 16 bolter rounds to consider. Two-thirds of them will hits -- meaning 11 hits (rounded up). We'll add 2 hits from the flamer, which makes for 13 strength 4 hits. I'm simply going to be pessimistic (from my bloodletter's point of view) and assume that the multi-melta also hits them.

How many wounds result from that? Well, half of the strength 4 hits will wound. That means approximately 7 wounds ... and we'll just assume the multi-melta causes a wound as well. So 8 wounds in total.

How many bloodletters survive? Their 5+ save is invulnerable, so they get a save from everything (just not a terribly good one). About 3 of those 8 wounded will survive.

For the win.
To fulfil my wants for the bloodletters, I must take out the entire marine squad in one round of combat. How many are needed?

The bloodletters on the charge have the benefit of the furious charge universal special rule. They're hitting and wounding on 3+. Moreover, they're killing on 3+ thanks to their hellblades. Moreover, they're charging, so they get 3 attacks each. That means 1.33 marines removed per bloodletter. I'd need 7.5 bloodletters to assure myself (statistically) that the marines would be removed entirely. Since they strike first (due to the higher initiative) the marines don't even strike back(!)

How many?
I lose about 5 bloodletters to the rapid firing marines. I need 7.5 to survive in order to wipe them out. Hence 5 + 7.5 = 12.5. Rounding up - this means about 13 bloodletters to achieve my aims. Although I will note that I've been pessimistic along the way (regarding the multi-melta which may not hit or wound, but I assumed it would!). Twelve bloodletters should be fine.

Shortcomings and caveats.
Of course, I've ignored the fact that sweeping advances could work just as well (against chaos marines!). Or if my opponent is near the board edge, they could certainly flee away and off the battlefield. And there could always be faults in my logic above! (let me know!). But overall, and from experience, I know that 10 bloodletters sometimes pulls up short, hence a unit of 12 or so bloodletters feels like it is about the right answer to my original question.