The Sliding Scale of 2-dice Probabilities

Warhammer 40,000 is a game built on rules and probabilities. Those who designed the game wanted it to be balanced, fair, but with enough complexities that the game would allow almost any situation to occur and be carried out. Not only that, but the game had to be designed with a certain flavour. This flavour is called “telescoping”.

Telescoping is how the game goes from small scale to large scale, or large scale to small scale, by orders of magnitude. A 500 point game lasts about 30min, start to finish. A 1000 point game lasts about an hour and a half though, 3 times as much time for only twice as many points. A 3000 point game can last the whole day if things start getting off course.

(note, the reason for the jump is that you are dealing with more models. A 1500pt game of two Grey Knights players will still go swiftly, a 1500pt game of two troop-heavy Ork players will take much, much longer)

However, telescoping also applies to the math and structure behind the game. The simplest reason is due to the properties of the dice.

A single die roll does not produce many variations. It’s an exact equal chance of the numbers 1 through 6 being rolled. However, when you roll two dice together (like in a Ld test), you can achieve an ARRAY of results:

Ld	2	3	4	5	6	7	8	9	10
Pass %	3%	8%	17%	28%	42%	58%	72%	83%	92%
% Change	-	+5%	+9%	+11%	+14%	+16%	+14%	+11%	+9%

Notice the % change column. In a single d6 roll, each roll is 16.7% greater or less than the ones next to it. If you need a 4+, it’s 50%, but 5+ is 66.7% and 3+ is 33.3%. The change is even.

Not so with 2 dice…

If you’re measuring something like Leadership, going up from Ld7 to Ld8 (+14% increase) gives you a bigger jump in your chance of success than going from Ld8 to Ld9 (+11%). Keep that in mind the next time you’re deciding how far away from that Junior Officer you’re going to be moving your Infantry Platoon.

Leadership is not the only situation where a single attribute change makes a larger than normal difference. The same applies to twin-linked weapons.

BS	5	4	3	2	1
Normal	83%	66%	50%	33%	17%
Twin-Linked	97%	89%	75%	54%	30%
% Change	+14%	+23%	+25%	+21%	+13%

As you can see here, it’s clearly a huge advantage to be twin-linked (a Twin-Linked BS2 weapon has an even better chance to hit than a normal BS3 weapon) – but that the amount that it’s worth changes from point to point. A BS5 weapon only gets a 14% increase in effectiveness from being Twin-Linked, but a BS3 weapon gets a staggering +25% increase in effectiveness.

The laws of probability affecting the roll of 2 (or more) dice is a great example of something called the Normal Distribution.

Normal Distributions are used by probability experts to determine just how likely, or unlikely something is. Essentially, it says that if you do something a whole bunch, 68% of the answers will be more or less within 1 Standard Deviation of each other. A Standard Deviation is a short way of saying “the square root of the average distance of any point in the study from the average of the study”.

Or in other words… with a d6, the average roll is 3.5, with a standard deviation of 1.5.

(To calculate standard deviations quickly, but not exactly accurate, find the difference between the average result, and then the higher or lower result, and divide by 3. Three standard deviations account for 98% of results, which for us effectively can be said to be all, or 100%, of the possible results. This makes the working deviation for a d6 1.2, not 1.5, as you can take 3 steps down from 3.5 to 0 at 1.2, and 3 steps up to 6 at 1.2.)

So, if you shoot 10 bolter shots, your average result will be that 6.6 will hit (upper SD = 1.1, lower SD = 2.2). That means that 68% of the time 4 or more or 8 or less will hit.

Also with Normal Distributions, we can see further and further into the probabilities. Go a SECOND standard deviation away from the norm, and you encounter 95% of all occurrences.

Knowing the standard deviation of a dice roll is very important. In the last probability analysis posted here, I said that if 24 shots came from Space Marine Bolters you can count on 12 hitting. Why 12? Why not 8? Surely you can count on hitting with 8 more than you can count on 12. Why not just 1?

I don’t count on these, because they’re too far away from the average (16). If I WERE to estimate a fast and dirty standard deviation, I’d say it were 2. I know it’s not, but 2’s an easy number to work with. I can say that I’m 68% confident (mostly confident) that I’ll hit anywhere between 14 and 18 times. If I hit more or less than that, then I really have encountered bad luck.

How is this useful to you? Once again, when judging a situation. Before we said, with the very basics, that you could count on killing 2 Space Marines with 24 bolter shots, but now we can say that we’re confident that we’ll kill between 2 and 4.

***PERSONAL NOTE:

While doing this example, 24 Space Marine Bolter Shots, I ran a quick probability study. I averaged the number of shots hit from the mean and 1 standard deviation away from the mean. In other words, I took all the possibilities that are likely to happen at each step in the way, and calculated the average of that.

Thus, 24 shots, average 16 hit, possibly 18.7 hit, possibly 10.7 hit. Then, 10.7 hit, average 5.3 wound, possibly 3.6 wound, possibly 7.1 wound. And so on.

Once finished, I arrived at an answer that was 68% of the time you’ll kill between 2 and 8 Space Marines. I knew this was wrong. Why? Because experience tells me that 24 shots will often kill 2 Space Marines. That’s just what I’ve noticed over the years, no math about it. I then looked through the equations and found where I was wrong.

Redone, the calculations show what likely happens, 68% of the time between 3.7 and 1.9 Space Marines will die from 24 Bolter shots.

Morale of the Story: Never let numbers dominate your thinking. If you KNOW something, and your calculated answers say differently, chances are your numbers are wrong. All too often people get caught up in the equations, but the fail to anticipate the outcome in order to really gauge how accurate it is. If I say 6 – 2 = 3, you know it’s wrong, because you already expected a different answer. If I ask what 529 – 315 equals, you might not know the exact answer, but you’ll know that an answer above 300 or lower than 100 has GOT to be wrong. Develop these instincts, they’re incredibly powerful tools when dealing with math.

***

Want to see this in practice? Here’s the 24-Shot experiment. Find a dice roller online (type “dice roller” into google, first one should be the D&D one, that’s fine). Now, pretend to roll the dice for 24 Bolter Shots at BS4 against a Space Marine squad (3+ save).

Keep track of how many Space Marines died each time.

Do these experiments 10 times.

Now, average out the number of space marines died (total space marines died divided by 10). I can guarantee you (98% certain) that this number lies between 3.7 and 1.8.

Want even more precise? 68% of you will have a value between 3.2 and 2.5.

Your most common scores for number of Space Marines died will be 2 and 3. You will have either one or two results of 1 or 4 Space Marines dying (most likely you’ll have more 4’s than 1’s, but I can’t be quite as confident). One or two rolls will be completely outside this (like 7 dying, or 0 dying).

When you understand probabilities, you can really give yourself an advantage by predicting the outcomes of near-future events.

USB Escapism

Well, once again I’m missing my USB stick. That little bugger just keeps escaping me. So, I’ll have to present you with something off the cuff.

Today, I’m going to talk about Magic: The Gathering, and how you can relate it to Warhammer 40,000. Why Magic? Because, after picking up Magic Online (a digital version of the game – pretty much just an interface for playing the game), I’ve had many more chances to play Magic than Warhammer.

Overall, in fact, it’s much easier to become “good” at Magic than it is to become “good” at Warhammer. This has nothing to do with the game’s complexity or difficulty though. The big reason is the fact that you do get more chances to play Magic than Warhammer. In Magic, you can play a match in as short a time-span as 5 minutes, although a common length for the game would be 10 or 15 minutes. Warhammer, on the other hand, takes a good 2 and a half hours even for a straight-up, 1-on-1, 1500 point match. You need to set up terrain, place armies, go through 5 or 6 turns of back and forth action/reaction, and your tactical decisions take longer to execute.

So, in the time that it takes you to have 1 battle, you could probably have played 10 games of Magic. You’ll learn a lot more about how Magic works from those 10 games than you will from that 1 game.

But, regardless of the differences, Magic and Warhammer are built on very similar concepts. In both you have a pre-determined pool of resources that you choose to play with. In Warhammer this is your army list, and in Magic this is your deck list. You both play a game, trying to maximize your use of limited resources. Warhammer is much more a game of controlled loses, as your army tends to be diminished, whereas Magic is more about gaining and growing your power-base in order to have a superior lead over your opponent (although games can be won without doing this; see “Red Deck Wins” philosophies about trying to win before you run out of gas).

In the end, every game in the world comes down to a similar basic resource – time. In Warhammer, think of everything you could do if you could take 2 turns in a row – think of how destructive that would be for your enemy. In Magic, you literally can take an extra turn with cards like (((Time Warp))). Even games like Monopoly or Chess have a basis of gaining ground on your opponent – using moves, cards, or actions to make your moves count for more and making your opponent’s count for less, effectively gaining fractions of a turn on your opponents.

In Magic, gaining a turn on your opponent is much easier – and not just because of cards like Time Warp. The crux of the matter comes down to what does it mean to gain a turn? Magic theory states this as laying down an extra land (bypassing the one-land a turn rule), or drawing extra cards (bypassing the one-card drawn per turn rule). There are some other ways (like having extra Upkeeps (Paradox Haze), Attack Phases (Relentless Assault), etc.) but they’re much, much more rare.

So, if you can do things like return a land to their hand (Boomerang), you can “gain” a turn on your opponent. If you destroy multiple creatures with a single card (Consume the Meek), you “gain” a turn on your opponent. If you cast a spell that does a lot of different things (Cruel Ultimatum), you “gain a turn” (or in this case, multiple turns) on your opponent.

Warhammer, meanwhile, is a lot more difficult for gaining ground on your opponent. There are no special abilities that give a whole extra turn, nothing that stops your opponent from moving their entire army, and zilch that can call in an extra unit to appear in the game.

Instead, you have to rely on tactics and strategy to gain ground. Every turn that you merely Stun an enemy vehicle, you gain ground as the vehicle is effectively destroyed for one more turn. Every time you force your opponent through difficult terrain, you slow them down, giving you more time to get into a better position or send another volley of Pulse Rifles into their ranks. Every time you make an assault with the intention of preventing them from moving on their next turn, you take ground away from them.

In Warhammer this is called “controlling the flow of the game”. Are you the one who is dictating what happens in the game, or is your opponent dictating what happens? In short, if you’re controlling it, then you’re likely winning. If your opponent is controlling it, then you’re likely losing.

Take this situation; you have a Seer Council and are facing up against Grey Knights. You really want to get your Seer Council into combat with their Terminators. It’s your best chance at slowing them down if you can get a “Doom” psychic power off on them. However, there’s a Land Raider nearby that will just take apart your army if you let it live, and only your Seer Council is in a position to tackle it.

In a sense, at this point, you may think that you’re in control. You have your choice of targets, and can go for the best chance-to-profit move (attacking the Land Raider). But really, you’re probably out of control. In the time it takes you to attack the Land Raider, the Terminators will have moved away from you, meaning that to attack them back again will take twice as much effort as it did before. The same goes for the Land Raider. Yes you have a choice, but neither of them are good.

Overall, it’s easier for a close-combat style army to control the flow of the game than it is for the shooting army. Shooting armies get a bonus at the start of the game through army placement, but once on the table they’ll be stuck in their initial deployments – while the close combat army still has lots of options for taking you apart.

When the game is between two shooting armies, placement is even more important – as shooting and destroying one unit can allow you to gain ground on your opponent as they can’t fire back.

Things are most complicated when the game is between two close combat armies. It’s all too easy for the game to collapse into one grand melee somewhere on the table – with forces pilling in on all sides. If it looks like this is about to happen, carefully judge the strength of all units that likely will get involved. The winner of the grand melee often wins the game. Remember a backup plan should your forces fail. If it looks like your opponent has the advantage, turn tail and run for cover and reinforcements. You may be giving some ground to your opponent, but you can gain a lot of it back by deciding where and when the grand melee takes place.

And now, you're moment of Zen...

Snazzgunz: Relentless, Eternal Warrior, Furious Charge

Universal Special Rules. They simply sound terrifying. They’re Universal (big), they’re Special (awesome), and they’re a Rule (ticketable offense).

In Snazzgunz, I’ll be looking over the special rules that are ever-present throughout Warhammer 40,000. From the Universal Special Rules, to the Eldar Jetbikes special rules, to Tyranid special rules (wow there’s a lot there).

It’s interesting to look at the framework of Warhammer 40,000. Everywhere in the game we are presented with rules. Really, though, the game just has a few basics:

Infantry move 6”, assault 6”, you roll twice to see if you might deal damage to your opponent, and they roll once to see if they’re okay. That’s it. So in many ways, Warhammer 40,000 is a game about BREAKING the rules. Yes Infantry move 6”… but Infantry with Jump Packs move 12”! Yes you roll twice to see if you deal damage… but if you’re twin-linked you get to reroll some dice! Yes they get to roll to see if they’re okay… but NOT if you dealt the wound with a Power Weapon.

Universal Special Rules are rules that are likely to be found in multiple armies. The most common is the Invulnerable Save. It breaks the rule that, even when you don’t get a save, you still get a save (Boss Klopz: “Da metal skelliez don’t count!”).

Presented here are 3 other Special Rules that you’ll often run into. Maybe not all the time (these rules are usually found on Elite, HQ, or Heavy Support units), but you’ll still run into them quite often.

Relentless

The first is the Relentless Rule. This easy-to-learn rule allows a model to move, fire any weapons, and still assault. Most commonly you will encounter this rule when fighting Space Marines (all Terminator models gain this rule), or Tyranids (their Monstrous Creatures have this rule).

Relentless units are often all-round good Spearhead units. A Hive Tyrant is a powerful foe, but it remains deadly throughout the game largely due to the fact that every turn it’s on the table, it can cause some serious damage. In close combat, the Tyrant is a beast of Epic Proportions that even few Assault units can stand up to. At a range, the Tyrant can also be a menace, killing scores of light infantry, or punishing light vehicles. And every single turn, the Tyrant is moving towards its objective or enemy.

In this way, Relentless is a special Movement rule, since that is where it has its greatest impact. It allows units to keep moving, even if they would normally have to stand still. When using a Relentless unit, keep it on the move – either moving to a more advantageous position, moving to cover, moving to assault, or moving to the objective.

When facing a Relentless unit, try to control where the unit will move. The best direction is probably AWAY from you. As a Spearhead unit, if you break the spear’s tip, the rest can be blunted. Relentless units are often slow – so if they spend 1 turn going the opposite direction, they’ll need a whole 2^nd turn just to end back where they started… and since a game will likely only last 6 turns, you’ve just dealt with a deadly unit for 1/3^rd of the game.

Eternal Warrior

This uncommon special rule is most often found on HQ units, but also entirely throughout the Daemons codex. This rule makes you immune to the dreaded Instant Death clause. You may not see many Eternal Warriors out there, but it’s important to remember this rule when you do. The greatest players, sports stars, and chess champions in the world do as well as they do because they can exploit an opponent’s mistake.

Don’t be one of those people that make this mistake!

When you go into combat against an enemy, and you plan to take them out with a decisive Power Fist, Force Weapon, or similar attack – remember to consider Eternal Warrior. Instant Death does not come up often, but there are many armies that focus on using their Instant-Death causing characters/units to take out opposing characters. If that character turns out to have Eternal Warrior, then the attack falls flat.

By the same token, you can use your Eternal Warriors offensively in this matter, by pitting them against some of the deadliest enemies in the game and still expect to see them walk out of the fight alive.

Furious Charge

This is the real meat and potatoes I wanted to get at. This Universal Special Rule has been getting more spotlights recently from Games Workshop, mostly because every single Ork boy has it – and it is nothing to laugh at! At +1S and +1 Initiative, Furious Charge can make any assault-orientated unit doubly, or triply effective on the charge.

Nothing pisses off an Eldar Wraithlord more than when it gets charged by a Blood Angel Librarian with Furious Charge and a Force Weapon. They think they have it made, but then they realize that the Librarian only needs to do 1 wound to completely annihilate their Wraithlord. This would not be possible without Furious Charge.

It’s important to remember that Furious Charge takes effect after all other modifiers. So Ork Nobz with Power Klawz that charge are S9, not S10.

It’s often easy to forget the impact of Furious Charge. In Warhammer 40,000 we tend to think of Attacks and AP as the two biggest influencers of a weapon/model’s ability. However, Strength is probably the most important attribute after Toughness to a model. Toughness 4 is barely touched by S3 attacks (5+), able to shrug off S4 attacks (4+), vulnerable to S5 (3+) and akin to tissue paper at S6 (2+). No matter where you stand along the S3 to S5 curve, receiving +1 to your strength increases your unit’s deadliness.

That means a unit that hits on 4’s experiences a 33% increase in the number of wounds it would likely score if its attacks have the bonus from Furious Charge.

(Units that hit on 3’s experience only a 25% increase… still very sizable)

That’s like adding 3 extra models to a 9-man squad.

But you also have to remember the Initiative difference. That +1I can give you a further edge. Striking first in combat is a huge advantage, as you get to strike at full power, and your opponent will only strike back with whatever’s left (if there is even anything left).

When using Furious Charge, try to take advantage of it as often as possible. ALWAYS remember to use Hit & Run units where possible to regain the attack, initiative, and strength advantages of charging.

When fighting against units with Furious Charge, try to minimize its effects. Orks are most dangerous on the charge – so if they’re going to get to you the turn after they leave close combat, charge them instead! Deny them that advantage. Being stuck in the same combat turn after turn is the last thing units with Furious Charge want.

Always remember the impact that this can make on other rules as well. An Ork Warboss with a Big Choppa already receives a +2 bonus to Strength on top of S5. When that Furious Charge is added in, this brings the Boss up to S8 – often enough to deal Instant-Killing blows to HQs, and ruination to vehicles.

Starcraft 2 Stuff

Well, I don’t have a Warhammer article for you today… my USB stick is somewhere else. I promise, as soon as I can I will upload the next Warhammer tactics blog.

However, in the meantime, I’ll share some of my other obsessions with you.

Starcraft 2 is awesome.

I’m really happy I pre-ordered the game, as you receive a Beta key when you do (good marketing). I’ve been busy this last week playing matches against others just like me. And when I say “just like me”, I mean it! Most other players out there are just as bad.

Okay, that’s not true – but what IS true is that Starcraft 2’s match-making system works like a charm. The game has a system that matches you up against opponents who will be right about your skill level. In this way, you’re never facing anyone too much better or worse than you are.

Let me bring you through my intro games so far, letting you know of my discovery of the game through them:

Match 1: Zerg vs Zerg: Victory!

First game ever. It’s suggested you start in the Novice Leagues. The Novice Leagues are LIKE real-play, with some differences. First, the maps are modified to slow down aggressive players. You’ll need to pound through 6000 hp worth of destructible rocks before you can hit either your opponent’s base or even their first natural expansion.

In this match, we both powered out as many zerglings and “roaches” as we could. Roaches are sort of the new Hydralisk (despite the Hydralisk still existing). They take up the same tech-position, but cannot hit air units with their ranged attack. They do, however, possess a remarkable healing factor – but this only applies when burrowed (which is researchable only at Tier 2, the Lair).

Match 2: Terran vs Terran: Victory!

I completely eschew the ground in favour of running my tech up to Starports. Terran air-power is second only to Protoss (very balanced, actually). I learn that Terran add-ons are essential. Taking the Tech Lab for the Starport allows for some really amazing units (Banshee, and their new Science Vessel), but taking the Reactor for mass-producing Vikings (an effective anti-air unit with anti-ground capabilities as well) really is the way to go with Terrans if you have access to enough resources.

Match 3: Protoss vs Protoss: Defeat :-(

Every race in Starcraft 2 is incredibly different from every other one. I highly suggest playing at least 1 game as each rather in the Novice Leagues just to get familiar with the way each race builds. The Protoss are even MORE “Protoss”-y. Like before the Probes can set up a work order and then go do something more important (like harvesting minerals), but the new ability of the Nexus can NOT be forgotten (which is difficult, since you’re so busy in Starcraft 2). The Nexus can increase the build-speed of any building (factory or research) by 50%. Big difference in the long-match, as it can increase your Probe count early, and help power units out the Stargate, or speed you through tech upgrades when you really need them.

My opponent here powered out more stuff than myself, and I was taken down easily.

Match 4: Protoss vs Protoss: Victory!

Discovered the awesome power of the Void Ray. I think this unit’s going to be retweaked before the game is released. At the moment, players have access to them too soon – as soon as they build a Stargate they can build these Tier 3 Siege units. 2 or 3 of these beasts are okay, but as soon as you get 4 or more, they always will power up to max-damage (their damage has 3 outputs, increasing from 1 to 3 the longer they’re firing, very devastating considering that once fully-powered, they stay powered as long as there’s little down-time between switching targets).

The game ends with a race to destroy each other’s final building first – with my Void Rays demolishing everything at lightning speed while his invisible Dark Templar go uncountered.

Match 5: Terran vs Protoss: Victory!

My Protoss opponent attempts to rush me with Carriers, and nearly succeeds. However, I quickly build some Terran Thors (a monstrously large mega-unit with anti-air and anti-ground), and support it Vikings. My opponent never expands, and I win the resource race as his main base starts running out of minerals while I have 3 expansions pulling in their weight.

There’s lots more to tell, it’d take too long. The down and short of it is that now that I’ve played 5 additional games meant to “rank” me into a league, I’ve been put into the Copper League. This league, I believe, is one step up from the Novice Leagues and holds about 100 positions. I currently hold spot # 32, after beating a player higher than me (in the score screen it actually shows who was favoured to win, yeah me!). However, I’m still REALLY low in the league system.

UPDATE:

In the days after writing this article, I played 3 games of Starcraft 2. The first one I lost, and then, on my second try (once again, with Protoss, my worst race as I’ve discovered), I think I stumbled across the secret to playing competitively from a strategic point of view.

As the game currently stands, rushing is the answer. Not necessarily a victorious rush, but just something so jarring to your opponent that it gives you the breathing space to start expanding. My mistake before was being a chronic aggressive expansionist. I would prioritize expanding over everything else. Why? It’s my style. I absolutely love soaking up wealth. Unfortunately, that means I’m not really BUILDING anything.

Often, this meant that I would start expanding before I even had any real groups of units to defend myself with or, more importantly, attack with.

In that second game, though, I played Protoss once again, and this time I focused first on pumping out as many Zealots as early as possible. With the new Protoss build-system, this is frighteningly easy – you don’t even need any vespene gas. You just hold off of using your Chrono-boost on your Nexus so that you can use it almost non-stop on your 2 Gateways. Continue producing Probes at this time – even past the point that you would normally stop. You need maximum income during this period with little investment. Then, once you have about 6 Zealots, you attack. Unless your opponent was also rushing for units, you’ll find yourself dominating your opponent’s 2 or 3 units – and then you can go to town against their workers.

The nice thing about this is that, with maximum income, you’ll still be edging ahead in saved minerals – enough to build a Nexus somewhere else (preferably at the map’s gold fields – mineral fields that are yellowish in colour and provide 10 minerals each trip instead of just 5). Even if your opponent defeats your rush, you’ll be a sizable leg up on them – since you’ll have used that time to continue building, but you’ll now have a greater income potential.

For Terrans:

Same idea, but build Barracks with Reactors. It’s absolutely terrifying to see 4 Marines being produced so quickly. I actually made a mistake in my third game with this in building a Reactor before really getting ahead with the second Barracks. Build BOTH Barracks’ first, then put out a few Marines, then upgrade. Note, you’ll need gas to build a Reactor – but you’ll also need some other bonuses to get a leg up on your opponent. Build an Engineering Bay to start researching both offensive upgrades early. I’d also suggest (though I didn’t in my game, and I think I regretted it) building a third Barracks with a Tech Lab so that you can upgrade your Marines further with Combat Shields and Stimpacks, and also start producing either Reapers or Mauraders, depending on your situation (I’m thinking Mauraders due to their ability to slow down enemies – but Reapers could be useful in cases where you want a back-door into their base to force your opponent to double-back while you advance).

For Zerg:

I have no idea yet. The Zerg’s weakness is also a strength – and they’re the reason I LOVE expanding. To build more units simultaneously (after using the Queen, do NOT forget about her Spawn Creep Tumour ability – Zerg move faster on creep, so it’s important to cover large areas of the map with it) you will NEED a second Hatchery – but this will also go at an expansion point.

So I don’t know what to do yet. You need that second Hatchery, and it should build another Queen right away, but when do you switch from expansion to aggression – I do not know. It may turn out that rushing Roaches and Hydras should be best… but that’s a lot of upgrading before you start attacking. I’ll keep you informed.

Building Your Army List

Boyz before Toyz.

That sentence sums up all that is Ork about an army list. Boyz before Toyz says, “You need a strong presence of troops before you start putting points into more fancy stuff. Ork Boyz are strong infantry, but can be whittled down easily. You need enough of them to not only have an impact late-game, but also to capture objectives.”

That’s a lot of words summed up by Boyz before Toyz.

Army building is one of the most important tasks in the game, and you have to make a load of strategic decisions often before you even know who you’re playing against. As such, a lot of people really stress about their “lists”. Frankly, they’re worried it’s simply not good enough. Players go far and wide to seek approval for their lists. They go to friends, the internet, and tactical articles like this.

What you have to remember first is that no list is perfect. The game is designed and balanced so thoroughly that for every power-list out there, there is at least an equally powerful list somewhere else that also has the added bonus of trouncing the first one.

For example, an army of all tanks with ordnance (like 6 Demolishers in a 1000 point teams match) should be great against another force that takes just a few elite anti-troop killers (like Grey Knights that have eschewed heavy weapons for stronger close combat), but will do very poorly against a huge Ork Troops force backed by some Kustom Force Fields (can’t kill enough boyz, and once they get into close combat, they’re hitting the rear armour).

In my experience, designing an “all-comers” list with some kind of specialization is often the best way to go for a tournament. An all-comers list has a lot of power to it, mostly because so many people undervalue the effectiveness of well-placed Troop choices. The basic troop of almost any force in the game is a powerful unit for very little points – but they simply don’t have the bells and whistles that draw people to the more advanced stuff. As mentioned in a previous article, a Space Marine Tactical Squad is a DEAL for 10 models (offering you 10 tough-as-nails units with a special weapon, heavy weapon, a sergeant for close combat, and the ability to split them into 2 dedicated squads).

However, even with lots of troops, you shouldn’t forget some of those bells and whistles because, in the right environment, they will do amazing stuff. An Assault Squad is useless if it’s engaging a Dreadnaught (assuming the squad has no power fist), but shines brilliantly when assaulting enemy light infantry and ranged specialists. If you take 3 squads of them, you likely won’t see them all performing at their best, since you’ll need them in different spots on the board. If you take just 1 squad, you can set it on a goal right at the start of the game, and it will almost assuredly complete that task. That’s the strength of taking just 1 of something (but you probably want a second one, or another with the same goal that does it a little differently).

If, by some chance, you DO know who you’ll be fighting, or you at least have a good idea of the people/forces that will be playing, don’t be afraid to “meta-game”. Meta-gaming is something I’ll cover in the future. To put it shortly, if you know for a fact that people in your area play with lots of tanks, put in more tank-killers. If you know for a fact that people in your area bring lots of Spearhead units to tournaments in the form of beefed up characters and Monstrous Creatures, bring character and monstrous creature killers.

So, when building an army list, keep in mind each unit’s goal. In general, static units should only ever be given one or two goals, whereas dedicated assault units or very mobile units can be given 3 goals. The only exceptions to this are static units that are truly able to handle 3 different types of goals (an Imperial Guard Leman Russ Battle Tank can contest an objective, and blast light or heavy infantry apart at the same time), or dedicated assault units that are likely to die too swiftly and should never be given more than 1 goal (Tyranid Hormagaunts die too quickly to assign anything other than being disruptive or taking out light infantry, but they do that one task very well).

Here’s a list of goals to consider assigning to your units

• Character & Monstrous Creature Assassination
• CC Anti-Heavy Vehicle (Land Raider, Falcon Grav-Tank, Ork Battlewagon, etc.)
  
• CC Anti-Light Vehicle (Ork Trukk, IG Sentinels, Tau Devilfish, etc.)
  
• Ranged Anti-Heavy Vehicle
• Ranged Anti-Light Vehicle
• CC Anti-Infantry
  
• CC Anti-Heavy Infantry
• Ranged Anti-Infantry
  
• Ranged Anti-Heavy Infantry
  
• Contesting Objectives
  
• Claiming Objectives
  
• Outflanking
  
• Infantry Support
  
• Tank Support
  
• Spearhead (often anti-anything, like a Daemon Prince, but never a Troop)
  
• Disruption

So, for example, consider this small army:

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HQ: Ork Big Mek w/Shokk Attack Gun, Heavy Armour, and Cybork Body

Elites: Kommandos w/ 2 Skorchas

Troops: 2x 20 Ork Boyz, w/Shootas and Nob w/Power Klaw and Boss Pole

Fast Attack: Warbuggie w/Twin-linked Rokkit Launcha

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This small army probably costs around 500 points, and has 5 units. The Big Mek is designed for Anti-Heavy Infantry and Anti-Light Vehicle. He’s a standalone model that is meant to quickly deal with any major threat first-turn. Some people would call this unit a Spearhead unit, as it “can” deal with anything. However, especially in the case of the Shokk Attack Gun, “can” doesn’t necessarily mean “will”. The most common roll is a S7, AP2 large blast – great for dealing with Heavy Infantry, and able to stand up to a light vehicle – but woefully inadequate for heavy tanks. Even at lower strengths it’s good against heavy infantry, and it’s useful against light vehicles a little over 50% of the time.

The Kommandos are Outflankers, Anti-Infantry, and Anti-Heavy Infantry (thanks to the Skorchas that can also act as Power-Weapons).

The Boyz are for Claiming Objectives and CC Anti-Infantry. Their Power Klaw enables them to do more though, as they could run into almost anything as they make their way to the objective. The Bosspoles will help keep the squads in the fight if their numbers get low.

Finally, the Warbuggie is for Anti-Light Vehicle and Outflanking. It does not have the Outflank special rule, but its speed allows it to engage almost any enemy quickly, and the twin-linked Rokkits help it deal with problem enemies with consistency.

Thus, this army has the following capabilities:

Ranged Anti-Heavy Infantry (x1)

Ranged Anti-Light Vehicle (x2)

CC Anti-Infantry (x3)

Outflanking (x2)

CC Anti-Heavy Infantry (x1)

Notice the curve-pattern. The army has a specialty, close-combat anti-infantry. This is what this army is best at (pretty common for Orks). The army is also somewhat adept at dealing with light-vehicles (like enemy transports), and can get into some advantageous positions with its Outflankers. Finally, the army has the ability to deal with Heavy Infantry, both at range, or up close. For 500 points, that’s a really well-rounded army, with a troop-killing specialty.

However, the army lacks the ability to easily deal with Characters/Monstrous Creatures, Heavy Tanks, a Spearhead unit, and has no way of supporting its troops or vehicle to make them better. These flaws could be exploited by any army in the game, from a Tau Hammerhead, to a Tyranid Carnifex, to a Terminator Assault Squad (okay, I don’t know if you’d see that in a 500 point match).

When you design your army, you’ll also have to choose between a top-down and a bottom-up design. Do you design for a specialty first, then build around that, or do you take the cool stuff you want first, then see what needs to be tweaked after? The above list was top-down, starting with wanting a Big Mek with Shokk Attack Gun and Burna Boyz for some Heavy-Infantry killing power, and then putting in the troops and a Warbuggie to round the list out.

Choosing your army is a very difficult strategic decision, and there’s SO much more that we can go into! Hopefully this helpful hint will aid you in designing winning lists in the future!

Probabilities made Easy

How I Stopped Guessing and Learned to Love the Fraction:

Throughout this Strategy and Tactic’s blog, you’ll see me referencing numbers, percentages, and probabilities. Sitting down typing, I’ll be a lot more tempted to work out the exact probabilities of what you want (or what you don’t want) occurring, and I might even get into some more complex stuff too (like saying “you can be 95% confident that you’ll score between 3 and 5 hits).

However, for most of us involved in the fast-paced games where stuff actually happens, or those of us playing a tournament, you're not going to have the luxury of time and paper or a graphing calculator.

So much of the time I see people discussing probabilities online. They say that a certain event is so exactly probable. Like, a bolter shot fired from a Space Marine Tactical Squad has a 66.6% chance of hitting. If the Marine fires 2 shots, he has a 50% chance that both hit and a 75% chance that at least 1 hit. Etc., etc.

This ISN’T helpful for the majority of people, mostly because it’s too in-depth. A lot of people just want to know if what they want to happen has a favourable chance of happening, or not. Heck, most people don’t even know what a favourable chance is.

So, I’m going to give you a quick and dirty run-down of how to judge your chances on the fly. This method should help you size up your chances within 10 seconds. If it takes longer than this, then you probably don’t have a favourable chance, or you’re dealing with a very complex situation.

Effectively, to do this you are going to break the rules of standard probability calculations. You’re going to wind up with numbers over 100%, which normally is not allowed, you’re going to add when you should multiply, and you’re going to estimate when you should calculate.

Step 1: Know the Odds

Memorize this.

6+ = 16% or 1/6
5+ = 33% or 1/3
4+ = 50% or 1/2
3+ = 66% or 2/3
2+ = 83% or 5/6
1+ = you never have a 1+, but it’s 100%

It’s imperative that you know these numbers or fractions. I put down both, because I like working with fractions (seriously, when you understand fractions and can do them in your head, all of math becomes easier to handle).

Step 2: Add

Any time that you have a chance of doing something, add these together. If I fire two bolter shots from a Space Marine Tactical Squad, I have a 130% chance of hitting with at least one. Or, in other words, often 1 hits, sometimes 2 hit, but rarely will none hit. Why? Well, 100% means that you have a good chance of it happening. It’s not perfect (perfect does not exist in this system) 100% merely means a good chance that at least 1 of what you are trying to determine will happen. 30% means that sometimes, though not often, 1 MORE will hit. Now, you know that there’s a chance that neither shot will hit, but that’s a different chance calculation (specifically, 33% + 33% = 66%, is less than 100%, so not a good chance, but it’s there).

When dealing with larger shots, knowing fractions will help. Say it’s 24 shots. Well, 24 * (2/3) will give you 48/3. Don’t worry if you can’t do that division, you can guess that 3 goes into 48 at least 12 times. That’s quite a bit lower than in reality, but you don’t need to know that it’s exactly 16 times (besides, exact figures are misleading). 12 is a figure you can count on – meaning that you should be able to hit 12 times. You may get more, but it’s unlikely that you’ll get less since you under-estimated.

If you do shoot for exact estimations (like 16 in this case), you will find that 50% of the time you score this or more, and 50% of the time you’ll score this or less. This isn’t a probability study, this is a tactical survey.

Step 3: Determine Best Decision

So you know that you should hit more than 12 times. Will that be enough? At this point you should be able to know (shooting at Gaunts, you’ll kill a good number of them, 7 or 8 probably, shooting at Space Marines, you’ll get maybe 1 or 2… maybe none at all). If not, continue you’re fast calculations.

Guants: 12 * (2/3) = 24/3 = 8, no saves, 8 dead

Space Marines: 12 * (1/2) * (1/3) = 12/2 * (1/3) = 6 * (1/3) = 6/3 = 2 dead

What will this accomplish? Will the Gaunts be neutered? Will the Space Marines be forced to make a Ld test? Will this even the odds in Assault? That tactical decision will still be up to you, but you are now armed with info that can be compared to other information and your strategy in order to determine the best choice.

Remember, however, that this system is for BASICS only. Things get MUCH more complicated than this, but your understanding of this basic concept is rather critical. You need to know this math in order to make statistically good decisions. Just remember, for best comparisons, guess on the low side. This game involves a strong element of chance. Sometimes, even a statistically favourable event will go catastrophically wrong.

For example, one time I had a squad of genestealers assault a Land Raider back when Rending gave you an extra D6 (not an extra D3). By all probability, the Land Raider should have been toast – but it didn’t, and its hurricane bolters then proceeded to munch apart my Genestealers – a devastating blow to my army (I was already getting low on units that could deal death-blows to my enemy).

A Note on Unfavourable Situations:

Sometimes an event is unfavourable, but you should take it anyways. A great example of this is when shooting at tanks. Technically speaking, a single Lascannon has a poor chance of killing any vehicle, simply because over half of the Vehicle Damage table gives a result that is NOT destroyed. Even the dreaded Tau Railgun has a less than 50% chance of destroying even an Armour 10 vehicle (1/2 to hit, 1/2 to destroy… remember that being AP1 gives it +1 to its damage roll = 1/4, or 25%... and we’re not even counting the vehicle as hull-down for an additional 1/2 chance that it shrugs off the hit).

However, it still makes sense to include these in your army because, when it DOES destroy a tank, it will often deal a very large blow to the enemy. Tactically speaking, it has the best chance-to-impact ratio out of your whole army by targeting the enemy’s vehicles. Impact is the tactical blow that losing that unit will cause to your opponent. It cannot be directly measured (destroying that Demolisher in range of your Terminators is a much greater blow than destroying that Demolisher that’s 48” away from anything).

Determining that ratio will largely be determined by you, as a tactical decision governed by your strategy.