*Our friends at Nights at the Game Table have an article on knowing the odds for us.*

Welcome to this week’s Warhammer Tactics! Today, we’re going to be diving into everything you could ever want to know about dice odds.

If you’re curious about the effects of re rolls, bonuses or minuses to dice, or the odds of charging out of deep strike, then look no further, because we’re going to cover it all today.

Knowledge is power, and with this newfound knowledge, you’ll have the power to make all the right decisions, both before the game while writing a list, and during a game! Get out your calculators, because we’re going to be doing a ton of math today. Don’t worry, I’ve done everything I can to make it as easy to follow as possible, so you won’t be needing any college level math here today!

I suggest bookmarking this specific article somewhere on your browser so you can come back to it later, since you may find yourself wanting to check this information out again! I’ll also be dividing this article into clean sections that are easily identifiable, so you can quickly jump to the section you want to read up on again with little to no searching required.

Before we begin, we need to establish something. 40K is a very random game, and part of the game is responding to that randomness. Frankly, it’s also a large part of the fun. Dice can dictate that a lone Tactical Sergeant takes down a mighty Demon Prince, and those moments are worth their weight in gold.

However, when it comes to making informed decisions, we assume perfectly average dice, and not lucky or unlucky rolls. This is because, in aggregate, assuming your dice aren’t loaded or very poorly made, they should more or less work out to be average across the tens of thousands of times that you will roll them. Anyone familiar with Math-hammer will already know this, but for those who are new to this, it’s important to establish.

## Re-Rolling 1s:

To kick us off, let’s look at one of the most common abilities in the game: the ability to re roll 1’s to hit. Most armies in the game have access to it, but how much of a difference does it really make?

Let’s assume we have a Space Marine shooting his bolter. Normally, he is hitting on 3+. That means that he hits 2/3rd’s of the time, or ~67% of the time. We know he hits 2/3rd’s of the time since a d6 has 6 facings, 4 of which (3 4,5,6) that result in a success, out of 6 possible results. However, the ability to re-roll 1’s changes the result of a 1. Normally, it’s a failure, but now it’s a second shot, with a 2/3rds success rate.

Effectively, this means that out of the 6 possible results on a D6, now our Marine has 4 facings that are a success, one facing that is 2/3rds of a success, and one facing that’s a failure. 4 and 2/3rds out of 6 is a pretty awkward result, since it’s a fraction in a fraction! Luckily, it’s easy to fix. If we multiple 4 and 2/3rd’s by 6, we get 28/36, or ~78%. That’s a ~17% increase in accuracy, 16.666 repeating to be precise, and that’s not too shabby!

If you found that example a little hard to follow because of all the fractions, let’s look at this another way. Imagine you have 36 Space Marines now, all shooting their bolters. Because we have perfect dice, we make 36 attack rolls and get 6 1’s, 6 2’s, etc. We have 24/36 hits, and 6 1’s to re roll. We grab the 6 1’s and re-roll them, and we get 1, 2,3,4,5, and 6, because again perfect dice. We have 4 more hits, which we add to our pool of 24 for a total of 28/36 hits, which is the same number we got with our fractions. This is a more visual example of the mathematical example above.

Now, here’s where this gets really interesting. It doesn’t actually matter what you’re hitting on. Whether you have a Ballistic Skill of 6+ or 2+, you will ALWAYS be ~17% more accurate, and therefore ~17% more damaging! I’ll show you with those two numbers to demonstrate. Let’s start with a BS 2+ model, let’s say Custodes.

Just for the sake of clean math, we have 36 Custodes shooting one shot each. That’s 36 shots, 30 of which hit, 6 of which we re-roll, scoring another 5 hits, for a final hit total of 35/36. If we divide 35 by 30, we get 16.666 repeating, which I round up to ~17%, the same as with our Space Marine example. If we do the same thing with 36 attacks hitting on 6’s, we get 6 hits and 6 re-rolls, and we get one more hit from our re rolls for a total of 7. 7/6 is, you guessed it, 1.166 repeating, or ~17% improvement.

Not only is re-rolling 1’s to hit the same regardless of your Ballistic Skill, but it’s also a flat ~17% improvement to your damage whether you get to re roll 1’s to hit, or 1’s to wound. Obviously, most armies have access to re-rolls 1’s to hit, but there are a couple models that bestow re-roll 1’s to wound, like Necron Lords.

Consider 36 Necron Warriors shooting at some Imperial Guard. Normally, they hit on 3+ and wound on 3+. That means we should get 24 hits, and 16 wounds. We won’t worry about saves for this since it doesn’t affect our results. If these 36 Warriors are near a Necron Lord, they get to re roll 1’s to wound.

Since we have perfect dice, our 24 hits are 4 1’s, 4 2’s, so on and so forth. Our 4 re rolls go on to score us an additional 2.667 wounds, for a total of 18.667. Dividing 18.666 repeating by 16 gives us 1.1666 repeating, or an extra 16.666 repeating percent more wounds. And if you’re curious, having a re-roll 1’s buff to both hit and wound is a 1.1667*1.1667 improvement to overall damage, or a 1.36111 (~36% ) improvement!

So, the lesson here is that you should never leave your re-roll buff’s at home! They are noticeable damage multipliers that are easy to include into most armies. Since it’s related, I’ll also quickly touch on abilities that allow you to re-roll everything to hit. It’s super easy compared to just looking at re-rolling 1’s. Just figure out what your failure rate is, square it, and you have your new failure rate. Subtract that from 1, and you have your new success rate.

For example, going with Marines, they have a 1-3 failure rate, or 1/3rd. 1/3rd squared is 1/9, which is their failure rate if they re-roll all misses. 1/9th failure rate means they have a 8/9th’s hit rate. Divide that hit rate by their old hit rate, and we see it’s a ~33% increase to accuracy. Nice and easy!

## Dice Modifiers:

Let’s move on to dice modifiers. These come up all the time in the game, but their value is rarely discussed.

To properly understand dice modifiers, we need to break down the attack process, which is something you’re already probably very familiar with. A lot of this will be pretty basic, but it’s important because it’s going to establish a couple of ground rules for dice modification.

Attacking can generally be broken down into a 4 step process: Rolling to Hit, Rolling to Wound, Rolling to Save, and Inflicting Damage. Since practically all dice modifiers affect one of the first 2 steps, we’re going to focus on them.

When rolling to hit, as a player we are really concerned with how many hits we get, not how many misses we get. The same is true when rolling to wound. We care about how many successful wounds we get, not how many dice fail to wound.

The opposite however, is true when our opponent rolls to save. We care about how many saves our opponent fails, not how many they pass, since failed saves go on to inflict damage. Just keep that in mind, although we won’t be talking about saves much from here.

This is important because it gives us a sense of direction when talking about dice modifiers and the effects that they have. Specifically, it establishes that we are concerned with how many hits or wounds that we get (or our opponent gets), and how many saves our opponent fails (or that we will fail).

So, the logical extension here is that we should look at dice modifiers in terms of successful hits caused, successful wounds caused, or failed saves caused. Now that we have established how we talk about dice modifiers and why, let’s dive into modifiers themselves!

Imagine for a bit, if you will, that you have 6d6 in front of you. These 6 dice are turned to count from 1-6. These 6 dice represent all of the possible results that you can roll on a d6. We can now look at any situation in the game that we want to and evaluate it.

Let’s take a basic example: A Chaos Space Marine shooting at another Chaos Space Marine before and after Veterans of the Long War (a stratagem that provides +1 to wound) with a bolter.

Normally, our Marine wounds on a 4+, since Bolters are Strength 4 and Chaos Marines are T4. That means that we score a success on a roll of a 4, 5, or 6. Looking back to our visual example, we can see that this is a 3/6th’s success rate. For the purposes of this lesson, we won’t simplify fractions just to make the numbers cleaner, even though normally 3/6th’s would get simplified to ½. If we use Vets, we now succeed on a 3+ as well, meaning we now have a total of 4 successes. We’ve gone from 3/6th’s to 4/6th’s, which is a ~33.33% increase in damage!

Now, you may be looking at this and scratching your head a bit. We went from 3/6th’s (50%) to 4/6th’s (66.667%), and I said we had a 33% increase in damage. Yet, our wound rate went up only 16.667%, from 50 to 66.667, so what’s the deal? Well, this is why earlier we established we’re only concerned about our successes, not overall. Yes, the value of 1/6th is only 16.667. But this improvement of 16.667% doesn’t exist in a bubble by itself. It’s in relation to another number, in this case, 3/6th’s, or 50%.

So, when we talk about an increase in damage, we talk about in relation to our previous figure, not in an abstract sense. Since 4/6th’s is 33% bigger than 3/6th’s, it means we get 33% more damage. You can test out yourself, if you want. You’ll find that regardless of your base figures, a clean +1 to hit or wound will never actually give you a 16.667% increase in overall damage!

This leads to an important conclusion regarding dice modifiers, which is that the better your hit/wound rate is, the less impactful modifiers to your dice are in either direction, while the worse your hit and wound rate is, the more impactful those modifiers are. I’ll illustrate to explain. Let’s say we have a hypothetical player with some Imperial Guard and Custodes fighting some Alatoic Eldar.

Normally, Imperial Guard hit on 4+ and Custodes on a 2+. That’s a 3/6th and 5/6th hit rate, respectively. Alatoic imposes a -1 to hit outside of 12”. Let’s just assume that the -1 to hit is active. This means that Imperial Guard drop to a 2/6th hit rate, and Custodes to a 4/6th hit rate. Going from a 3/6th hit rate to a 2/6th hit rate is a 33% reduction in accuracy (2/3=.667) for our Imperial Guard, while for Custodes they go to a 4/6th hit rate from a 5/6th hit rate, which is a 20% reduction in accuracy (4/5=.8)

So, the immediate conclusion here is that buffs to dice modifiers on models that are less accurate or less likely to wound are more impactful than models that are more likely to hit or wound, and this is a good rule of thumb.

If you’re in the middle of a game and don’t have time to do a bunch of math, than defaulting to this rule of thumb is pretty reliable. However, there are rare occasions where this isn’t the case, so make sure to put in some time doing math on the units in your army that you can buff to find the best units to use certain buffs on and against what targets!

## Charge Roles:

And at last, this brings us to charge rolls. Specifically, we’re going to talk about the odds for charging out of deep strike. I’ll cover regular charges (simple 2d6), planning on investing a CP re-roll to re-roll a die, being able to re-roll a failed charge, and being able to re-roll a failed charge while also planning on investing a CP on said charge, effectively being able to re-roll either or both dice.

As if that doesn’t sound like enough, I’ll also cover having a +1 to charge rolls, since some armies like Demons have that bonus for all of those different permutations, AND being able to roll 3d6 for all of the above situations I described for 2d6, both with and without a +1.

So no matter what your specific army is capable of, you now have a resource to tell you exactly how likely you are to land a charge or two out of deep strike to help you make the most informed decisions possible regarding to list creation and game play decisions.

Before we begin, we need to have another visual in mind. Originally, this section was going to have a bunch of graphs depicting this information. But, I think it will be a lot simpler for everyone if we simply visualize a graph in our heads a bit, and we simply reference this imaginary graph.

Imagine a 6 by 6 grid, where both the rows and columns are labeled 1-6. Our rows are our 10’s place, and our columns are our 1’s place. This gives us 36 squares representing the 36 possible results on 2d6. To figure out our odds of rolling 2d6 and getting a 9 or better, you simply write out the 36 possibilities, and figure out how many add up to 9 or better. As it turns out, there are 10 results out of a possible 36 on 2d6 that add up to a 9 or better. So, we have a 10/36 success rate, which is about 28% (27.777 repeating, specifically).

But what if we can re-roll our charge? Well, the easy way to handle that is to find out how likely we are to fail a charge twice in a row. Since we have a 28% success rate, that means we have a 72% failure rate. 72% squared is ~.52, or 52%. Since we have a 52% failure rate, that means we have a 48% success rate.

Let’s move to something that’s actually a bit more complicated, which is planning on investing a CP to re roll a single dice. I won’t be dragging you down with piles of math for this, and instead I’ll be describing the math I did in a broad sense, give a couple examples, and the total.

Pretty much from here on out, I’ll be following that kind of set up. This way, you can get the information without drowning in multiplication and addition. So, I wrote out my 6×6 grid, and assigned each result a score from 0-100. If the result had no chance to succeed, even with a CP re-roll, it received a score of 0.

For example the result 1/1 gets a 0, because even if I re-roll a 1 and get a 6, for a new result of 6/1, that’s only a 7, which is a failure. If the result was a success without a CP re-roll, it got a score of 100. For example, the result 6/3 is a score of 100, since it’s already a success. For every other result, it received a score based on its likelihood to succeed with a CP re-roll. Its score is be equal to its likelihood to succeed as a percentage.

For example, let’s take the result 5/3. This adds up to 8, which is a failure. However, it has a 50% chance to succeed with a CP re-roll, since re-rolling the 3 will add up to 9 or better half of the time (4+). This result gets a score of 50. After scoring all 36 results and adding them together, we get a score of 1854/3600, which is a 51.5%. That means that we have a 51.5% chance to succeed on a charge from deep strike, if we want to invest a CP on the roll.

Next, what if we can re-roll either or both dice? This is especially applicable to Ork and Khorne players, since they have easy access to the ability to re-roll failed charge rolls. Well, I followed the same method as I did for the CP re-roll, but factored the ability to re roll either or both dice. In most situations, it’s actually more beneficial in terms of getting a success to spend a CP and re-roll one die, rather than re-roll both.

In fact, there are only 9 results (11/12/13, 21/22/23, and 31/32/33) where straight up re-rolling both dice is better than re-rolling one. Anyways, I did the same thing, assigning every result a score, except every result now has a minimum score of 28, since you can always opt to re roll both dice and try again, which has a 28% success rate. This gave the score of 2021/3600, or 56%.

Let’s move on to charges with +1 to their charge results. This is very common for any Demon player, since they have an upgrade that provides +1 to advance and charge rolls. This moves our requirement to succeed down to an 8, since 8+1 is 9. Basically, I followed the exact same steps that I did for needing a 9, and simply moved my target number to 8, which of course greatly increases our number of successes.

If you’re just making a straight 2d6 roll, you’ve got a 15/36 success rate, or ~42%. If you can re-roll your charge, you jump up to a ~66% success rate. Interestingly, if you score out all of your possibilities with a CP re roll like I did before, you get a score of 2370/3600, or ~67%, which is practically the same as being able to re roll your charge. If you can do either or both, your score jumps up to 2549/3600, or ~71%.

And now this is where things get fun, which is the 3d6 charge roll. The way I handled this was creating 6 more 6×6 grids, just like the first one, except after I was done, I went one grid at a time and added a number to every single result. The first grid I added a 1, the second a 2, and so on. This gives me a total of 216 results, for the 216 possibilities on 3d6. From here, the process was mostly the same, albeit more difficult.

First, I tallied the number of success to find the odds of a straight 3d6 roll. I found that there are 160/216 success on 3d6, which is about a 74% success rate. If you can re-roll that, you jump up to a ~93% success rate, which is pretty high!

Finding out the odds of a CP re-roll was difficult, but I found a way. I simply went through each grid, one at a time, and scored each grid individually like I did the 2d6 rolls. I then added all 6 scores together, and got a total of 19,381/21,600 or just shy of ~90%. If you can re-roll the entire 3d6, or one dice, that bumps the score up to an impressive 20,336/21,600, or ~94%!

Time to close out with the last possibility, which is the 3d6 charge roll, with +1 to charge. This is almost exclusively pertinent to Khorne Daemon players, however, we leave no stone unturned here at Nights At The Game Table! First, let’s start with the basic odds of success on a 3d6 roll needing an 8. We succeed 181/216 times, which is a ~84% success rate. If we can re-roll that charge roll, it jumps to a whopping ~97% success rate. Digging into the nitty gritty with some CP re rolls, we find that with only the CP re-roll option, we have a rather surprising total: 20,336/21,600, the same total as having to make a 9” charge, with the ability to re roll the failed charge and investing a CP into the roll.

I’m not sure why in terms of the math why these numbers are the same, but I double checked my scoring and got the same totals.

Finally closing this out is the option to re roll a failure, or CP re roll one dice, with a score of 21,024/21,600, or a whopping ~97% success rate on that charge. The reason this number isn’t improved from just being able to re-roll is because in every circumstance, you’re more likely to succeed by just re-rolling everything than re-rolling one dice.

Phew! I know this was an extremely long read if you sat and read the entire article, but remember that this article is also intended as a reference document for players in the future in case they have questions about how to calculate most common math questions that come up in 40K. Well, that finally brings us to a close. Our last couple articles have been more theoretical nature, discussing things like math or tournament play. Make sure to turn in next week, where I’ll be going over something far more practical: what you can do to be victorious against Agents of Vect!

*To see more great articles like this, along with battle reports, painting tutorials, and lots more, click here to check out Nights At The Game Table!*

**And remember, Frontline Gaming sells gaming products at a discount, every day in their webcart!**

“3+. That means that he hits 2/3rd’s of the time, or ~67%”

“(After reroll 1 )we get 28/36, or ~78%”

“That’s a ~17% increase in accuracy!”

Looks like a 11% increase to me, from 67 to 78 %

You always reroll 17% of your roll. That dosent make you 17% more accurate since you still need to hit with the second roll. Thus, the better the original mark, the greater the benefit to rerolling 1’s.

or am I missing something?

The article unfortunately does not do enough to differentiate terminology between percentages (X out of 100), and percentage points (comparing percentages against each other as whole numbers, ie 67% vs 78%).

Confused me as well. He doesn’t mean the absolute increase in percentage points, he means the actual percent difference between 67% and 78%

when it comes to rerolling ones, the easiest method is to say EXPECTED VALUE (with no rerolls) multiplied by 7/6ths.

That amounts to a ~17% increase in accuracy

If you have 6 space marines you are trying to kill in one shooting attack, I like to work backwards rather than from the POV of the potential shooters. To kill 5 Iron Hand Tactical Space Marines I go,

I need 6 wounds, + 1/6 of their total for FNP, so 7 wounds to meet the likely minimum to wipe the unit out.

7 wounds on 3+ saves, means 21 wounds to save.

21 wounds Str 4 vs T4 I need 42 hits.

42 hits, with no rerolls I need 63 (BS3) shots; with reroll ones, take 63 divided by 7/6 or (63*6)/7 which amounts to 9*6, or 54 shots fired.

And you can see how Marines suck at killing other Marines! Anyway if you only have 10 shots incoming rerolling ones, you can then anticipate killing 1 marine, 2 if you are lucky. You would think the Horus Heresy to decades, like two granite boulders throwing pebbles at each other

> 67%

> 78%

>17% increase

I’m not sure I have confidence in the math behind this article.

10 marine shots, because round numbers are nice.

67% hit rate produces 6.66 hits and 3.33 misses, 1.66 of those misses are ones.

Of the 1.66 ones, the rerolls have a 67% chance to hit. 1.66 * .67 = 1.11

This takes your total hits from 6.66 to 7.77, or (as you correctly math out) a 67% chance to hit changes to a 78% chance if we round

78 – 67 = 11

That’s an 11% increase in efficiency, not a 17% increase.

When talking about an increase in efficiency you do not take the absolute difference of 11.111(repeating). You take the 11.1111(repeating and divide it by the original value of 66.6666(repeating) which gives you the 16.66666 (repeating) increase.

While not wrong, its a useless metric.

when I matHammer, I want to know my end result.

In this case, my end result is 78% instead of 67%, an 11% increase.

By that mean we find out that reroll 1 are far more valuable on 2+ and 3+ models, and fall steadilly after that.

I made no statement on it usefulness, which by the way it does have one, just how it was derived.

To show how it is useful,

I hit on 5s re-rolling 1s, I take 1/3 (the original hit percentage) of 16.66666% (the efficiency increase) and get 5.5555% (half of the increase if you hit on 3s go figure) and add it to the original 33.3333% for a sum of 38.88888% total chance to hit. Or I hit on 4s and take (.5*16.6666%)+.5=58.333333% chance. Or I hit on 3s 2/3*16.66666+2/3=77.77777%, etc.

Saw the same thing.

I think he means 78 is 17% bigger than 67., thus the result is improved by 17%

Which is useless!

Reroll 1 has gains in value as your BS increases.

Or, it more directly shows the same thing: Since your expected number of Hits for a given number of Shots always goes up by the same percentage, it’s clearly a greater absolute increase when that same percentage is applied to a larger base value.

Clarity and usefulness are subjective. While the fundamental math is objective, there are multiple valid ways of presenting it, some of which are more or less useful for certain audiences and/or purposes.

Rerolling 1s always give you a 17% more “attempts” to score a hit (so it really increases your chance of success in a 17%), but a 17% of 17% is not the same as a 17% of a 83%.

Asuming you reroll 1s:

Hitting on 6+ you’ll get 7/36 hits, instead of 6/36.

Hitting on 5+ you’ll get 14/36 hits, instead of 12/36

Hitting on 4+ you’ll get 21/36 hits, instead of 18/36

Hitting on 3+ you’ll get 28/36 hits, instead of 24/36

Hitting on 2+ you’ll get 35/36 hits, instead of 30/36

Rerolling 1s, you don’t get the same value hitting on 5+ than hitting on 3+. It increases the better chances you have to hit.

It always increases the damage by 16.66666666%, regardless of BS

Whilst the discussion on charges is interesting, I’m not sure it’s valid – the WH40k Rulebook FAQ clarified that if we reroll a result of multiple ice (eg, 2d6 or 3d6 for a charge), we have to reroll all dice. Unless there’s special stratagems that allow rerolling only a single die within a charge roll?

Actually, the Command Re-Roll stratagem specifically states that it allows the “re-roll of any single dice” – so you definitely can’t use it to re-roll your entire charge roll. The Ork ‘Ere We Go rule allows you to “re-roll failed charge rolls” – so you have to re-roll the entire roll if you use that rule.

I take advantage of this all the time with my Orks. If I roll a 1 and a 2 for a charge, I’ll just re-roll the whole darn thing using ‘Ere We Go. If I roll a 1 and a 6, I’ll spend a command point and re-roll just the 1.

Hope that helps!

Finally, big thanks to the author of the article. I LOVE this level of analysis. This is really great stuff!

Ah, love me some mathhammer. You haven’t had your head twisted around until you’ve tried to calculate the expected damage of a Farseer casting Executioner versus W2 using its selective cast reroll ability with a +1 to cast. Or a Death Jester with Luck of the Laughing God and Curtainfall plus the Shrieking Doom and that other shoot twice stratagem versus Terminators with storm shields. Or Haywire jetbikes shooting a Doomed Knight.

Anyway one of the most useful mathhammer tidbits I’ve found is that rerolling 1s to hit, to wound, or to damage, as well as bonus attacks on 6 to hit, all have the exact same effect numerically: multiply expected output by 7/6. …Which the guy who designed the Scythes of Tyran presumably didn’t know.

This comment section makes me lose hope in humanity. If you correct someone who took his time to write a huge article, do the calculations 10 times to see if maybe… just maybe… you’re in the wrong.

It is a 16.666% damage increase when you re-roll 1s. Always. Your balistic skill does not matter in the slightest.

And if you say “increase doesn’t matter, end result does”, well it is really simple: You get the most efficient shooting unit you have and you put this aura on it and your most efficient unit is 16.666% better. If you want to find out if the character with this aura is efficient – you compare his damage to normal units (per point) and you reduce his points until he’s about in line with other units. Then you know how many points he needs to buff to redeem himself. So you take the unit he is buffing and take 16.666% of the unit’s cost. This way you know the breakpoint on when you should take the character so you don’t get into the HQ tax territory. Ofc this a simplified way of looking at it but it’s a good jumping off point.

Thank you! As a math teacher I was losing hope there with all those comments about how the math of the article is wrong. 😉

People always struggle with % and probabilities, that’s why Las Vegas exists.

Your example with the “aura” is a good one.

17% increase of something that’s really good, is really good.

17% increase of something that’s not really good, is not really good.

While the percentages don’t lie, the effect that this increase will have on the game compared to how much you pay in points for this increase will greatly matter.

Guess I should also state… this is why +1’s are really helpful! They can turn something that’s really not good into something that’s really good.

You’re not exactly wrong, but it’s not the whole story either. Rerolling 1s to hit will get you more hits total with better BS, but the same marginal gain (proportional increase in damage, 7/6). This means that better BS doesn’t necessarily benefit more from a reroll 1s effect, instead it depends on the total average damage of the attack.

For instance, take two different units, one shooting at BS3+ with a damage 1 weapon and another at BS5+ with a damage 2 weapon, both versus a W2 target, with every other parameter being the same. They will, on average, do the same damage (with a smoother distribution for the first since it hits more often but does less damage per hit, but that’s another topic). For convenience’s sake, say you shoot 36 times with each, netting you an average of 24 hits at BS3+ and 12 hits at BS5+. If you add a reroll 1s effect, the first now hits 28 times and the second 14. BS3+ got a bigger increase in total hits (4 vs 2), but the proportional increase is the same (16.7%), and the average damage remains equal (28 D1 hits versus 14 D2 hits).

So, to recap, it is true that a better attack gets a bigger boost, but that counts for every attribute (number of attacks, S, AP, D, abilities), not just BS. However, your second post is also right — contrary to reroll 1s effects, you do get a bigger marginal increase from flat bonuses to hit/wound as well as reroll all failures the worse the original BS or wound roll is. Ao, for example, a Tau Commander and a Fire Warrior get the same proportional bonus from one Markerlight, but the Fire Warrior gets a much bigger one from five of them.

Hey guys, one of the main authors here. There’s a lot of you that commented about the 11%/17% issue from re-rolling 1’s. It definitely would have been better to include a blurb explaining more about why it’s 17(16.667) and not 11, sorry about that!

The specific applications of these were left out because that’s rather army specific, and the article was long as it was. The intent is just to help you make more informed list construction and gameplay decisions.

As many have pointed out, the 17% is derived from 78 being 17% bigger than 67. As many people here have demonstrated, your total damage dealt does go up (on average of course) 17%, not 11%.

Hopefully this helps clear up any confusion! Thanks to everyone else that stepped in and explained it in the comments.

There will also be a ton of upgrade trees.