Tag Archives: Warhammer 40000

Alpha Legion Operatives

As a change of pace, I’m foregoing probability for the sake of a proper hobby update.  My main army is Alpha Legion (using codex chaos space marines) but I really miss having the use of cultists as human operatives.  I’ve had a hankering to run a renegade guard list with Alpha Legion operatives for a while now, and with that in mind I’ve been slowly amassing some forgeworld renegades over the last 12 months.

The forgeworld models are fantastic and here’s what I’ve picked up so far.
9 enforcers Image

50 bods and 3 weapon teams Image
command squad Image

6 tank crew Image

7 psykers Image

Obviously I’ll need to get a lot of vehicles to make a viable guard army, but I’m looking at using some fairly heavy conversion to set the army apart from a ‘normal’ Imperial Guard army.  More updates soon, and there are pictures available on the accompanying FaceBook page.

Stacking the Odds Part II

The previous post on the probabilities for making lots of saves generated a bit of interest, and (as usual) some clever readers pointed out scenarios that should bear further analysis.  Altmann from the Penny Arcade forums asked:

“Can you work in the probability of making 4+ feel no pains as well? I know we’re getting into NASA shit but I’m curious”

Followed by Joe “Maynard” Cullen (of WarHeads fame) who pointed out that some wargear items also add complexities:

“The Wolf Tail Talisman gives a 5+ invulnerable save that happens before the armour save”

So in a similar fashion to my ultimate Ballistic Skill chart, I took it upon myself to rank the performance of a variety of armour types with rerolls, with Feel No Pain (FNP), and just plain regular saves.  This will give some insight into the relative merit of the saving throws we normally encounter in 40k.

As with Stacking the Odds Part I, the chart shows how likely each type of save is to take no casualties from an increasing number of saves.

So chart number one:

This charts the various types of save (and combinations) showing the odds of taking no casualties for up to 6 saves (I cut it off at 6 as about half of them approach zero at this point).  The legend on the right shows the ranking from best to worst with a 2+ rerollable save being the best, and a regular 6+ save being the worst.  The sharper eyed in the audience may notice that some of the save types listed in the legend don’t show up in the graph – namely “5+ FNP” and “3+ FNP”.  Rest assured this isn’t an error, it is simply that they are coincidentally covered by other save types that perform identically.  So a 5+ with Feel No Pain save works out the same as a regular 3+ save, and a 3+ with Feel No Pain save works out the same as a regular 2+ save.

Or do they?

The calculations are correct, but you need to interpret the data in the context if the game itself.  So saving on a 5+ followed by a 4+ for FNP is statistically the same as a 3+, until you get hit by an AP5 or AP4 weapon, at which point all you get is the FNP, which is just a 4+ save (as you can see from the chart is a lot worse than a 3+).  The FNP could also be blocked by a high strength AP- weapon, leaving you with just a 5+.

In a similar vein, the 3+ with FNP is the same as a 2+, but what if they got hit by a battle cannon? the 3+ is negated by AP3, and (assuming we’re talking about T4 units) the FNP is negated by the instant death rule.  So no saves of any kind!  But a squad of terminators would still get their 2+ and (assuming that 5 are wounded by the blast) they have a 40% chance of taking no casualties at all!

So what about those opening questions?  Well Altmann was interested in the effect of FNP on terminators, and to show the difference I’ve scaled the number of saves taken up to 30, and dropped the weaker save types.

The effect is actually pretty strong, if we take say 20 saves, a regular terminator squad has only a 3% chance of being unharmed while the FNP terminators have an 18% chance (again assuming that they aren’t hit by something that negates FNP!)

Joe’s suggestion of the Wolf Tail Talisman (WTT) is charted below. Assuming the squad has power armour, then it works out quite close to (but slightly better than) a 4+ reroll, and worse than a 2+ save.

This should let you compare the various save types available to you, but don’t forget the context of how saves and FNP get negated! If there are any other save types you want to see included, then please do leave a comment.

Poster Boy

As a quick break from the usual TheoryHammer, and just to show it’s not all about statistics, I’ve added some images to the resources section for those of you who are into terrain building.  It’s a set of miniature posters for the 40k/necromunda setting.

Gabriel_Pitt at the excellent Penny Arcade forums provided the source material – though he did mention that they apparently come from GW site (not that I can find them there now).

Here’s an example of how they were used in one of his terrain projects:

Downloads available here.

The Joy of Penetration

5th edition games often feature a lot of vehicles, and understanding how best to crack open that armour and feast on the goo inside can be a crucial skill for any player.  With that in mind, here’s a question:

After some poor manouevring by your normally brilliant tank commander, your shiny new Leman Russ gets hit by a Lascannon, and by a Battle Cannon.  Which is more likely to penetrate?

The ambush continues, and the Russ is hit by a Demolisher Siege Cannon, and a Multimelta at close range.  Which of these is more likely to penetrate?

For most weapons, armour penetration is relatively straightforward, i.e. weapon strength + D6.  So, for example, a Krak missile can get results from 9 to 14 (not bad against a Rhino, but smacks of desperation against a LandRaider).  However many of the best Anti-Vehicle weapons don’t follow such a simple pattern.

For example, ordnance weapons roll two dice and pick the highest to add to the weapon strength, and melta weapons at half range get to add 2d6 to the weapon strength. This produces results that aren’t as simple, and can have a couple of quirks.

How does this apply to our terrified tank commander?

The interesting thing about the opening questions, is that it depends on what side the tank is hit from.

Let’s take the lascannon versus battle cannon first.  For a rear shot (AV10) the lascannon is more likely to at least glance, but the battle cannon is more likely to penerate.  For a side shot (AV13) the battle cannon is more likely to at least glance, but the lascannon is more likely to penetrate.  From the front (AV14) the Lascannon is the clear winner and is more likely to glance, and more likely to penetrate.  Not that the lascannon is remarkable against AV14 (with <20% chance of penetrating) it’s more that the battlecannon can’t pen Av14 at all!

It wouldn’t be a WarHamSandwich without some charts so let’s take a look at the comparison.  The graph shows the odds of getting at least ‘X’ for an armour penetration roll with each weapon.  So to get the odds of penetrating AV13, we look at the 14 result as this gives us the odds of getting at least 14 (the 13 result would get the odds of at least glancing).

So we can see a crossover from 10 to 11, and from 13 to 14 where the relative efficacy of each weapon against that AV switches.

So what about that second volley of shooting?
Again it depends on the angle. The Demolisher is more likely to penetrate against side and rear, but once we get to the front this flips and the multimelta becomes more likely to penetrate.  The crossover is clearly shown in the chart, below.

So what’s the point Vanessa?  There certainly are some comparisons where you can unequivocally say weapon X is better at anti-vehicle than weapon Y, but often it’s not so black and white.  With a bit of analysis you can pick the best tool for the job at hand.  Here’s a comparison of some of the common anti-vehicle weapons so you can gauge the relative merits against various armour values.

That said, this analysis doesn’t look at the end-to-end process, from hitting to penning to what you get on the damage chart.  I guess that will have to wait for next time…

Size matters

One of my earlier posts talked about the importance of estimating range, and some techniques to help you guess distances on the fly.  Naturally I’m not the first nor the last person to have considered this part of the game, and I thought it might be useful to share some of the better articles I’ve seen on the topic.  Hopefully you can find an approach in the mix below that will help you on the field of battle:




A further piece of work on my ‘to do’ list is to publish the dimensions of some fairly standard tabletop stuff.  This will help by giving some references on the board that you can use to estimate distance.  I’ve started here with standard base sizes:

When I get the opportunity I’ll add the dimensions of some common vehicles, e.g. Rhino, Landraider, Chimera etc and put them all up in a single document in my Resource section.

That’s all for now; I’ve been travelling round the world for the past while, but that should calm down from this October onward – so hopefully I can get back to a more regular update schedule!

PS if anyone has the time and inclination, then please do post up any vehicle dimensions that you know in the comment section, and I’ll collate them.

Cut the BS

My last analysis on rerolls brought up a couple of questions from the audience, with comments mainly focusing on Ballistic Skill.  One in particular about the merits of the Vindicare assassin got me thinking about the how to evaluate shooting ability.  In line with my usual form, here’s a question:

A lowly guardsman stands in the open, he faces on one side, the mighty Eldar Phoenix Lord Fuegan Burning Lance (BS7) and on the other side Krazy Kullen (BS4) the weapon operator on a Chaos Rhino.  Fuegan’s melta weapon is obviously more potent than Kevin’s twin-linked bolter.  But who is more likely to miss?

Crazy Kevin

So my earlier treatise on rerolls only considered ‘normal’ rerolls where whatever you needed to get the first time was the same for the reroll.  Cunning commenter Caolan pointed out that at very high BS the shooter gets a reroll on a miss, but it’s not the same as the initial roll.  So a BS of 6 gets you a hit on a 2+, and  a 6+ reroll if you miss; BS7 gets the same 2+ to hit, with a 5+ reroll on a miss; BS8 is 2+ 4+; BS9 is 2+ 3+; and finally BS10 is 2+ 2+.

Rather than running the numbers in this post, have a look at my response to his comment at the bottom of this post.  But where I took it a step further this time is to calculate the odds to hit for BS1 to BS10 and for BS1 to BS5 with rerolls.  This gives us an interesting ranking of the relative accuracy of the BS values, and the impact of rerolls.  I’ve highlighted the rerolls in green to set them apart from the regular BS values.  The dark blue is the additional accuracy provided by the reroll (so under the dark blue is the basic odds to hit, the dark blue is the reroll, and the whole bar is the total accuracy).

Lo and behold the answer to our starting question appears before our very eyes.  It turns out that Eldar Phoenix Lords at BS7, are only as accurate as Chaos Rhinos with BS4 twin-linked bolters.  They are equally accurate. Who knew that Krazy Kullen was such a marksman?

What really comes through for me is how good BS4 rerolls are.  I’m known to have a fondness for Obliterators, and with twin-linked plasma AND melta at BS4 you can really see why.  More generally we can see that a reroll is better than a 1 point improvement (or more!) in BS for all cases except BS1 – but I think that’s a fairly well known thing already.

That said, you now have the definitive list from BS10 to 1 with rerolls, use it well my friends.

Undo! Undo!

Sometimes things just don’t go your way.  We’ve all had that situation where you really wish you could do that roll again.  Thanks to wonders such as twin-linking, or lightning claws, sometimes we can.  Today we are talking about re-rolls, and (as is my habit) here’s a question:

A bolter shot hits and wounds a Warlock on a Jetbike, he needs to make a 3+ armour save to survive.  If the farseer had cast Fortune to give him a reroll on that save, how much more likely would he be to survive? and would he have been better off in Terminator armour instead?

Rerolls don’t change the range of possible results (i.e. 1-6) but they do change odds of a particular result.  I’m following the usual format for the percentage odds here so I won’t labour the discussion with what each row means.

1 2 3 4 5 6
= 2.78% 8.33% 13.89% 19.44% 25.00% 30.56%
< 0.00% 2.78% 11.11% 25.00% 44.44% 69.44%
> 97.22% 88.89% 75.00% 55.56% 30.56% 0.00%
<= 2.78% 11.11% 25.00% 44.44% 69.44% 100.00%
>= 100.00% 97.22% 88.89% 75.00% 55.56% 30.56%

Well actually … it is a little different this time so perhaps I should give some explanation to the more interesting bits.

  • The ‘equals’ row gives the odds of a particular result if you were to roll two dice and pick the highest.
  • The ‘less than’ row shows the odds of failing a particular result, e.g. theres a 25% probability of failing a 4+ (rerollable).
  • The ‘greater than or equal to’ row shows the odds of succeeding on a particular result, e.g. the odds of succeeding in a 5+ (rerollable) is 55.56%

“So what?” says you.  In isolation it’s not that insightful, but if we compare it to the odds of a ‘normal’ (i.e. not re-rollable) outcome it gets very interesting.  The odds for a normal roll are covered here, but I’ve graphed the odds of success for normal vs rerollable to really show the difference.

Ok so the odds of getting a 1 or better is 100% in both cases … duhBut what about that Warlock from the beginning?

The jetbike Warlock has a 33.33% chance of failing that save (with no reroll).  If the Farseer has done his job and put Fortune on that Warlock, then the reroll brings the probability of failure down to 11.11%.  The reroll makes him three times less likely to fail! and what about that terminator armour? it has a 16.67% chance of failing that save – that’s twice as good as the basic Warlock, but one and a half times worse than the Fortuned Warlock!

A fortuned jetbike Warlock has significantly better saving throws than a Terminator with a Stormshield – think about that before you try gunning down a Seer Council.

Take a moment to really look at the chart.  The rerollable 6+ is almost as good as a basic 5+, and is about twice as likely as a normal 6+.  The 5+ reroll is better than a basic 4+, and so on until they converge at 1.  Also notice those trendlines I’ve added, the basic rolls get linearly less likely, but the rerolls stay high and then gradually fall off as you hit 6.

Of course, not all re-rolls are there to mitigate failure – sometimes you can be forced to reroll a success, but that analysis will have to wait for next time…

Two Dee Six

Now that we’re fully versed in the probabilities of the humble d6, let’s see what happens when we roll two of them together.  Yes that’s right, we’re talking 2d6 baby, yeah!

Ok, like last time I’ll kick it off with a question, actually this time it’s a couple of questions:

A squad of Chaos terminators has basic leadership 10.  In an epic career of 1,000 unmodified leadership checks, how many would you expect to fail?  Their Chaos marine brethren have leadership 9; if a squad of Chaos marines also had to take 1,000 unmodified leadership checks in their career how many would you expect them to fail?

On 2d6 we can get results from 2 to 12, but unlike the d6 scenario the results are not all equally likely.  The chart below follows the same format as this post so I won’t be as laborious in describing what each row means.  (Note I’ve rounded to one decimal place to keep the chart smaller).

2 3 4 5 6 7 8 9 10 11 12
= 2.8% 5.6% 8.3% 11.1% 13.9% 16.7% 13.9% 11.1% 8.3% 5.6% 2.8%
< 0.0% 2.8% 8.3% 16.7% 27.8% 41.7% 58.3% 72.2% 83.3% 91.7% 97.2%
> 97.2% 91.7% 83.3% 72.2% 58.3% 41.7% 27.8% 16.7% 8.3% 2.8% 0.0%
<= 2.8% 8.3% 16.7% 27.8% 41.7% 58.3% 72.2% 83.3% 91.7% 97.2% 100%
>= 100% 97.2% 91.7% 83.3% 72.2% 58.3% 41.7% 27.8% 16.7% 8.3% 2.8%

Ok, so the ‘equals’ row shows the odds of any particular result from 2 to 12, and as I noted above this is not the same for all results.  In fact it’s quite different; as an extreme example you are 6 times more likely to get a 7 as a 2.  7 is the most likely result, and results get less likely the further you go above or below 7 (so 2 and 12 are the least likely results at 2.8% each).  It’s worth noting that the odds of getting a 7 is 16.67%, which is the same odds as getting any particular result on a single d6 (i.e. the odds of getting 7 on 2d6 is one in six).  This means that while 7 is the most likely single result, there’s only a one in six chance of getting a 7 (clear as mud eh?).

What does this all mean in game terms? The most common use of 2d6 is for leadership checks of various types (there’s also scatter dice but I’ll cover those in a separate post in the near future).  Interestingly enough, while most of the time we hope for high rolls in 40k, for leadership we want to roll low.  So the most useful row in the above chart is the ‘greater than’ row; it gives us the odds of failing a leadership check for a given Ld value.

The odds of failing a leadership check decrease fairly rapidly as Ld increases, but what’s most interesting is the step changes at the higher end of the leadership scale.  In the long run, Ld9 fails twice as many leadership checks as Ld10; Ld 8 fails over three times as many times as Ld10, and Ld 7 fails five times as many times as Ld10.

Or to put it in absolute terms: Ld 9 fails one in six times (yes that includes you, Fateweaver), Ld 10 fails one in twelve times.

This gets us the answer to our opening questions fairly quickly.  The Chaos terminators at Ld10 will expect to fail 83 of their 1000 leadership checks, whereas the Chaos marines at Ld9 will expect to fail 167!  So in practical terms, for an unmodified roll, Ld10 is twice as good as Ld9. Adding an Ld10 aspiring champion to the Chaos marine squad means they would expect to fail half as many leadership checks.

That’s enough for now, any comments or questions welcome!

Take your chances

With the outcome of almost every ingame event determined by the toss of dice, a grasp of probability is an essential tool in Warhammer 40,000. How do you give yourself the best chances if you can’t work out the odds? This post will give you basics of the probabilities associated with common rolls. But for now, I’ll open with a question:

5 space marines rapid fire their bolters at a chaos marine – what is the probability that the chaos marine dies? Scribble down (or just remember) your gut instinct answer now, and check it against the results at the end, it may be quite different…

1d6 – What are the odds?

On a 1d6 roll you can get results from 1 to 6, and each result is as likely as any other i.e. ones are as likely as sixes (though sometimes it doesn’t feel that way!). Here’s a chart showing the odds:

1 2 3 4 5 6
= 16.67% 16.67% 16.67% 16.67% 16.67% 16.67%
< 0.00% 16.67% 33.33% 50.00% 66.67% 83.33%
> 83.33% 66.67% 50.00% 33.33% 16.67% 0.00%
<= 16.67% 33.33% 50.00% 66.67% 83.33% 100.00%
>= 100.00% 83.33% 66.67% 50.00% 33.33% 16.67%

This may look confusing at first, but let’s take a moment to examine the chart. The 1 to 6 across the top is the number on the die, and each row below shows the odds of a particular type of outcome.

The row starting with the = (equals) symbol is the odds of that particular result. So as we read across we see that all of them are the same odds (16.67% or 1 in 6, which makes sense if you think about it).

The row starting with the (greater than) symbol shows the odds of a result that is higher than the number at the top of the column. So, for example, the odds of getting greater than 3 on a d6 is 50%, which makes sense as half the possible results are higher than 3.

The row starting with the <= (less than or equal to) symbol shows the odds of a result that is equal to or lower than the number at the top of the column. So while the odds of getting a 2 is 16.67% (check the = row), the odds of getting a 2 or less is 33.33% (check the = (greater than or equal to) symbol. This shows the odds of getting a particular number or above. So the odds of getting a 3 or more on a d6 is 66.67%. This bottom row is the most interesting for Warhammer 40,000 as this is generally how we think of the game, e.g. 4 or higher to hit at BS3, or 3+ to wound on Strength 5 vs Toughness 4.

At this point you are either thinking ‘duh this is bloody obvious’ or you are utterly confused. Perhaps it’s time for an example.

A space marine shoots his bolter at a chaos marine. He is BS4 so he hits on a 3 or better (66.67% from our bottom row). The bolter is strength 4 and the chaos marine is toughness 4 so it’s 4 or higher to wound (50% from the bottom row). The odds of the chaos marine making his save is 66.67% as his save is a 3+. BUT if we want to calculate the probability of the kill, then we need to look at the odds of the chaos marine FAILING his save. To do that we simply look up the odds of him getting less than (<) 3, which our table shows as 33.33%.

How do we add it all up to get a result? Well for a start you don’t add them, you MULTIPLY them:

(odds of hitting) x (odds of wounding) x (odds of failing the save) = odds of kill

So based on our example above (66.67%) x (50%) x (33.33%) = 11.11%

But what about that opening question? There are 5 marines in rapid fire range of that lone chaos marine. So we get 10 bolter shots. Most players will multiply the odds of the kill (11.11%) for one shot, by the number of shots (10). This is wrong! the fact that it gives an answer over 100% should be your first clue (nothing can have odds greater than 100%).

So how do we work out the real answer? You have to look at the odds of the chaos marine surviving. The odds of him surviving one shot is 100% minus the odds of the kill (11.11%) so the odds of survival for one shot is 88.89%. The odds of him surviving all 10 shots is:

88.89% x 88.89% x 88.89% x 88.89% x 88.89% x 88.89% x 88.89% x 88.89% x 88.89% x 88.89%=30.79%

This means 10 bolter shots has (100%-30.79%) = 69.21% chance of killing that marine. So it’s quite likely, but definitely not certain!

Hopefully I’ve explained this all clearly – but if anything is unclear then say so in the comments section and I’ll clarify.

Next time I’ll cover the nuances of the 2d6 roll.

1 2 3 4 5 6
= 16.67% 16.67% 16.67% 16.67% 16.67% 16.67%
< 0.00% 16.67% 33.33% 50.00% 66.67% 83.33%
> 83.33% 66.67% 50.00% 33.33% 16.67% 0.00%
<= 16.67% 33.33% 50.00% 66.67% 83.33% 100.00%
>= 100.00% 83.33% 66.67% 50.00% 33.33% 16.67%

Going the distance

Starting with the simple stuff.

For the game of Warhammer 40,000 the normal play area is 6′x4′, more usefully in inches 72″x48″.

Most of the game activities revolve around actions that depend on distance (e,g, moving, shooting, assaulting) and these actions almost always have distances that are 6″ or a multiple thereof (e.g. 6″ moves, d6″ run, 12″ rapid fire etc). So, before the game starts, it is useful to imagine the tabletop in 6″x6″ squares (so the playing area will be 12 squares wide by 8 squares deep).

This grid will guide your judgement of distance

This will help gauge weapon ranges, how long it will take to get from point A to point B etc. It won’t give accurate results, but it will give you a ballpark, and will let you know if something is definitely impossible. It’s inexact because a) you’re guessing, and b) most of what you do will be diagonal – so the orthogonal distances that square counting gets you won’t be right.

To overcome A requires experience, good spatial reasoning, and some practice (ie set up a tabletop and guess the various ranges, measure and see how you did).

To overcome B I’d suggest the following – imagine the rectangle that has one corner on your starting point, and the opposite corner on your end point. Add the longest side of the rectangle to half the shortest side and you will get a good approximation of the true distance.

So when assessing the battlefield, consider the deployment zones, terrain, and objectives – imagine your 6″x6x grid and start to consider what you can do, not just in this turn – but right through to game end. Just as an example, say at turn 2 you want to decide which units to send to which objectives; it is easy to underestimate how long it will take to get there – the grid will let you know if reaching that point is possible at all within the time available. For example a footslogging unit walking on turn 1 in a dawn of war scenario will not be able to make it to the opponents edge of the table even if they go in a straight line with no obstacles – unless they forego shooting for running.

Before the game starts, and during every turn, look at distances and consider them in terms of game turns to get there, or ranges required to shoot there, etc etc. Look at your opponent’s position and do the same to gauge what he can do, and what he may be going for. Don’t forget to use legal measurement to check your estimates during the game, for example movement and range after declaring shooting (yours and your opponents!)

Now stop reading this, and go practice eyeballing the tabletop.

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