For many 40k gamers, painting minis and buying books is only the beginning. At some point, they’re bound to start thinking about how they can start improving their play to win more of their games. While there’s no substitute for practice, there are a number of things players can learn to improve their play and army-building skills, which we’ll be covering in our series of articles. In this article, I’ll go over the basics of probability, and how understanding basic probability and statistics can help better predict outcomes and evaluate units in 40k, leading to smarter tactical decisions and better outcomes. And while I know that for some, the thought of digging into a bunch of math brings back unpleasant memories, I’ll try to distill this down to just the most important aspects and make it clear how you can apply all of this to your games (and the rest of your life, really!)

Warhammer 40k book note font? Sep 09, 2013 at 16:21. I'm looking for this, for my boyfriend - it's driving him insane. Most of the math and statistics we’ll apply to Warhammer 40k will revolve around dice, since that’s the primary font of randomness in the game. So here’s pretty much everything you need to know about calculating probabilities around dice in 40k: Calculating a Weapon’s Output. I've noticed that this site uses the same font and graphical design for its logo as Warhammer Online's logo, and Warhammer fantasy in general. That is to say, this logo: I've also noticed many people on these forums use that very same graphical text design for their signatures. Download Caslon Antique Font Family Free for commercial use From Wikipedia:Caslon Antique is a decorative American typeface that was designed in 1894 by Berne Nadall. Warhammer 40,000: Dawn of War demonstrates in its transformation from video game to book how written text intrudes into the text by narrating experience and internality, fixing the point of view and dictating sensory reception where the game does not.

Basic Statistics

One of my favorite parts of Warhammer 40k is how it allows you to finally put to use some of those parts of your grade school education you thought you’d never use “in the real world.” In this case, math. Well, more accurately statistics and probability. Properly assessing units, wargear, strategies, and board states is key to improving your game in 40k and doing so well often requires a basic understanding of statistics, or at least the common probabilities involved in the game.

Before we can properly dig in to probabilities in Warhammer 40k, we need to go over a few common statistics terms that we’ll be using and are important in statistics.

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The Probability of an event is the measure of the likelihood that the event will occur. Most of the time we talk about dice math, the probability of an outcome is equal to the number of ways it can happen divided by the number of possible outcomes. So the probability of rolling a 6 on a D6 is 1 (you can only roll a 6 one way) divided by 6 (there are 6 possible results), so the probability is ⅙, or about 16.7%.
The Complement Rule for probability states that the likelihood of an event happening is the same as the opposite event not happening, i.e. the chance of getting a hit is the same as the chance of NOT missing. In math terms, this means the probability of an event is also equal to 1 – the probability of it not happening. So going back to our last example, the probability of rolling a 6 on a D6 is the same as the probability of not rolling a 1 to 5 on a D6. This seems trivial, but we’ll use this a lot in subtle ways.
Independent Events in statistics are events where the probability of one occurring in no way affects the probability of the other occurring. When events are independent, the chances of both happening is just the product of the likelihood of each. So any given die roll doesn’t affect the next die roll (the die doesn’t know what just happened), so the chances of rolling two fours in a row is equal to (⅙) * (⅙), or (1/36). Note that this is not the same as the chances of rolling an 8 on 2D6, which can happen several other ways.*
*NOTE: All dice rolls are independent events! Your chances of rolling a result on a die are the same every time, no matter what you just rolled or how many 1s or 6s you rolled previously. You are never “due” for a break — this is called “The Gambler’s Fallacy”
The Expected Value for some process is basically what we’d expect the average outcome of that process to be in the long term. You can get the expected value for a process by summing all the possible values and multiplying each by the likelihood that it will occur. So the expected value of a roll of a D6 is (1 * ⅙) + (2 * ⅙) + (3 * ⅙) + (4*⅙) + (5 * ⅙) + (6 * ⅙) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5. The expected value of a roll of a D3 is 2, and the expected value of a roll of 2D3 is 4 (just add the two together).
Variance is a measure of how far results of an event can vary from their average or expected value. For our purposes, we’ll use variance to describe how broad or spread out the possible outcomes of an event are. So going back to our expected value example above, while the expected value of a single roll of a D6 is 3.5, results can go from 1 to 6, meaning that on an individual roll, we can get all kinds of outcomes. Because of this, it can often be preferable to have a flat value of 3 for damage over a D6, even though the expected value is lower – being able to predict the result can make planning much easier. A lot of the work we’ll do building armies and using stratagems will be with the goal of reducing variance.

We’ll use these concepts over and over in 40k as we use them to evaluate units and wargear and to determine the likelihood of success for some actions. One of the most common ways we’ll use statistics to do this is to calculate the damage output of a weapon based on its likelihood of wounding a target. The way you’ll see this expressed most often is as the weapon’s ability to hurt MEqs, or Marine-Equivalent targets, i.e. Toughness 4, 3+ armor save targets.

Pictured: Me rolling anything important in a game against Campbell

Dice Math

Most of the math and statistics we’ll apply to Warhammer 40k will revolve around dice, since that’s the primary font of randomness in the game. So here’s pretty much everything you need to know about calculating probabilities around dice in 40k:

Calculating a Weapon’s Output

Generally, we can calculate a weapon’s Wound output by calculating the chance that the weapon will hit, then score a wound, then go unsaved. Taken together, this looks like:

Wound probability = (hit probability) * (wound probability) * (1 – save probability)

Then, because we may have multiple shots and do multiple points of damage per shot, we want to add those in as well.

Wound output = shots * (hit probability) * (wound probability) * (1 – save probability) * damage

If we have a weapon with variable shots or damage, we can use expected value to substitute for those values, so we can use 2 for D3 and 3.5 for D6.

While this isn’t perfect — it doesn’t take into account factors like range for example, but it does let us do easy comparisons for weapons when we control for other factors. If say, we wanted to figure out how much damage a rapid-firing group of intercessors might do to a knight, we can do that:

5 intercessors = 10 total shots, S4 AP-1 D1

With a 3+ BS, we have a ⅔ chance to hit – there are 4 results on a D6 that will give us a hit result (3, 4, 5, and 6), which would be 4/6 and that reduces to ⅔. And at S4 vs. T8, we’ve got a ⅙ chance to Wound. At AP-1, the knight’s save is 4+, so there are 3 results that will give him a save, giving us a 3/6 or ½ chance to deal a wound.

Ok so with all of that, our math becomes:

Wound output = 10 * (⅔) * (⅙) * (½) = 10 * (1/18) = 0.56

So your intercessors rapid-firing at the knight will, on average, do about half a wound. While you might not have needed this math to tell you that shooting bolters at a knight was a bad idea, what you can use it for

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