Monday, June 28, 2010

Cheating


Warhammer 40,000 is a game – and like all games, there will be those who will feel the need to cheat. In a game like Tic-Tac-Toe, it’s easy to spot a cheater, and easy to spot a mistake. If someone puts down an extra “O”, you’ll probably see them do it, and the symmetry of the game will be thrown off (there’ll be more “Os” than “Xs”, which is impossible).


However, as a game becomes more and more complex, and has deeper and deeper layers of play, cheating can become more and more difficult to spot and differentiate from making a mistake.


Take this classic cheating move:


Model A, the furthest up model in a squad, starts 13” away from an opposing squad. After moving, however, you find that he’s within 6” assault range. The model somehow was moved up 7” instead of 6”.


The Base Jumper:

Most Commonly: New Player

Reason for Cheating: Didn’t know – Stretching the Rules

Chances of Rehabilitation: Good


The Base Jumper measures the distance to move from the front of his base, but then moves the model up to that point so the back of the base touches. Nearly 1” is gained. The Base Jumper may not even realize that they cheated – they may be thinking of it as a clever way of bending the rules.


Corrective action must be taken immediately to teach them the correct method of measuring distances from models. Usually the Base Jumper learned this mistake from a friend. If someone more experienced is doing this, though, they are trying to exploit your unawareness to gain an advantage, and then it’s truly cheating. If they try to argue it, direct them to the rulebook, it actually shows a visual representation enforcing the correct way to move models.


Warhammer 40,000 is not a computer game. There is no system that forces a game state upon players. It’s not a Magic or Poker Tournament either, where a judge watches over everything and ensures that the proper game state is maintained should a blunder be made. No, at its core Warhammer 40,000 is a casual format where the players must be their own judges.


Which brings us our next villain…


The Rules Lawyer:

Most Commonly: Experienced Player

Reason for Cheating: Win by a thousand pin-pricks

Chances of Rehabilitation: Moderate, Good with group support


The Rules Lawyer is a gamer who seems to know every rule, backwards and forwards. They despise taking out the actual book, and claim that the rules support all of their actions, and then take a fine-tooth comb to everything that you do and argue the same thing back. A great example would be Line of Sight. They’ll argue to death that the current “any part of the model is visible” rule means, for them, that they can effectively shoot your entire army – and yet at the same time will flat out deny and force a “Hand of Fate” roll to see if practically anything you have can see him – and if you can, you can bet he’ll push for 3+ and 4+ cover saves as much as possible, while you’ll get 4+ and 5+ saves in return. The rules lawyer is kind of like the Joker – he forces you to have to become something you’re not, a rules expert. However, there’s another way out. Become part of a larger gaming group that supports the actions and rules you want to take. Since Warhammer is a casual format, house-rules are a great way to settle situations that you might find odd or out of place (myself, I still love Area Terrain, since the board – to me – is simply a representation of the game state, and can never perfectly depict how the terrain really looks).


So how do you identify the cheater? It’s very difficult in Warhammer – in part because a lot of this game is occurring simultaneously, your attention may be diverted, and you may not remember the rule that’s being broken.


With cheaters, it’s like playing a game of ball-and-cups. If you miss their move for a moment, they can pull a fast one on you. I guess this is a good time to bring up the most common of all cheaters…


The Dice Master:

Most Commonly: Anyone

Reason for Cheating: Tactical Advantage

Chances of Rehabilitation: Low


The Dice Master is perhaps one of the most nefarious of all the Villains. The Dice Master is a true illusionist. While your attention is focused elsewhere, they will pull a fast one, and before you know it – a losing dice roll is now a winning dice roll. Most often this is when the opponent’s back is turned during a die roll, and they’ll just shift the die so that it succeeds rather than fails. They may also pick up failed rolls when a lot of dice are rolled, preferring to roll next to additional dice already on the table to effectively gain more rolls. The worst ones, and the ones easiest to spot, are the ones who roll a bunch of dice, and then effectively “hide” the results by scooping them up faster than you can really see them, or who roll behind something so that you can’t see how much was rolled. The only way to defeat the Dice Master is to be vigilant at all times – but you can still be friendly when doing this. Stand beside them, enjoy the excitement of the dice-rolls, and make sure they’re always present for YOUR rolls so that you create the atmosphere that EVERYONE must be present for ALL rolls.


The crux of stopping all cheating though, is to nip it at its bud. Don’t let it slide. Create a gaming atmosphere where cheating simply isn’t tolerated. If the Rules Lawyer is creating a problem, get the whole group to enforce some simple house rules. Having someone who really knows the rules truly very well is excellent to have – but don’t be afraid to deviate from the book if you want! My group allows you to ask what a squad is carrying, and motivates people to openly acknowledge confusing conversions or proxies before a game starts without prompting. At the same time, I know another group that is the polar opposite to this – keeping all information hidden at all times. Neither is truly right or wrong, but neither group would appreciate the pressures the other puts on them (one side thinking its unfair to give the opponent more information than they would actually have, and the other thinking it unfair NOT to give the information on something to avoid cheating).


Oh… one final Villain…


The Pariah:

Most Commonly: Unknown

Reason for Cheating: Extreme Ambition and Lack of Morality

Rehabilitation: Pariah status if ever caught


The Pariah brings the worst form of cheating imaginable in a dice game – tampering with the dice to make them rigged. There do exists methods for doing this – from weighing dice (drill holes in the side opposite of the one you want to land, fill with lead, paint overtop) to misshaping them (heard a rumour of melting them in a microwave or oven to just barely make them slightly rectangular). You can tell a Pariah by the fact that they reserve special “lucky dice”, that they never use any dice but their own, and never offer to let you use the lucky dice. Proving it is a different matter, and one I’ve thankfully never had to do.


If you catch the Pariah, denote them the Pariah status and never game with them again. Teach them that cheating this bad is the lowest a person can go (most effort to cheat, high effect, impossible that they did it by accident, hard to catch them again in the future, most likely to use rigged objects in other games). If you ever do find this villain, punch them in the face for me.


Hope this helps you identify future villains!


(PS. Note, I do run a Dirty Tactics article. Dirty Tactics might not win you any friends, but they are completely legal actions that do not even stretch the rules. What they do allow, however, are actions for best effect that, although perhaps not realistic, are 100% legal and highly effective.)

Monday, June 21, 2010

In-Focus: Eversor Assassin


Have you ever faced an Assassin? Warhammer 40,000 armies that are Imperial will often have the option of fielding an Assassin – a rare, and deadly, unit with a lot to fear. The first Assassin I ever faced off against was a Vindicare Assassin. Armed with his massive Sniper Rifle that could kill practically anything, this guy, to me, was more effective than a Lascannon.


Not only that, but he could pick off specific models within squads, forcing out all your sergeants, special weapons, and anything fancy.


But I didn’t lose that game – definitely not to the Assassin. At the end of the day, he still hit on 2+, and still wounded on 4+, just like any other snipers in the game (with the benefit of no armour saves allowed against him).


Now I use my own Assassin regularly as part of my Space Marine army – the Nighthawks. Assassins fit their theme very well. The Nighthawks are a stealthy Space Marine army, placing secrecy, and well-timed surgical strikes above such silly notions of honour or glory. Assassins seemed to fit the bill perfectly. My Assassin of choice? The Eversor Assassin (not in any small part because it was also the least expensive Assassin).


Through repeated uses, though, I’ve discovered that Assassins are NOT Spearhead units. They can’t just go gallivanting into enemy territory expecting to slash apart their enemies and then win the day – no matter how deadly they may at first appear.


In a way, Assassins are microcosms of Warhammer 40,000 as a whole. The Vindicare Assassin is about target priority with your shooting. The Culexus Assassin is about weird special rules that give you an edge against some opponents, but cost you against others. The Callidus Assassin is about taking out one key unit, no matter the cost. The Eversor is about brute strength of close combat.


This article will discuss the Eversor.


In many ways, the Eversor is the simplest and easiest Assassin to operate, aptly fitting its description as a human bomb. Release, and watch the carnage. This is very simple. But, as mentioned, the Eversor is a microcosm of the close combat aspect of Warhammer 40,000. In a sense, every dedicated close combat unit can be operated exactly as just mentioned – start with a squad of them, then release them at your opponent. If they get there, boom! You deal huge amounts of damage.


However, to best operate the Eversor Assassin, you must be more careful. Eversors have many strengths, and can be assigned many rolls:


- Anti-Heavy Vehicle

- Anti-Light Vehicle

- Anti-Heavy Infantry

- Anti-Light Infantry

- Character/Monstrous Creature Assassination

- Flanking


That’s a lot of options for a single unit – usually enough to classify it as a Spearhead unit. But, for as much as the Eversor represents the power of close combat units, it also represents their weaknesses. To further examine the Eversor, I think it’s prudent that we look at its unit entry a little more closely:


WS 5 (hits anything on either 3’s or 4’s)

BS 5 (S4 pistol, or Poison 4+ pistol)

S 4 (power weapon, or Poison 4+, or always glance on a 6)

T 4

W 2 (explodes when he dies)

I 5 (Infiltrate, Meltabombs)

A 3 (+1 for 2 CCWs, +1d6 instead of +1 when charging, 12” charge range)

Ld 10 (Fearless)

Sv 4+ (Invulnerable)


As you can see… a WACK-load of special abilities. Actually, he has another special ability (Fast Shot), but as of 5th Edition it’s useless (Pistols being Assault 1 now – before, he always counted as stationary for purposes of shooting, which meant he could shoot his pistol twice, now that means absolutely nothing). Like all Imperial armies, the Eversor is more defined by his equipment rather than his stats. His stats, really, aren’t that impressive.


If you’re aiming to shoot with him, you’re probably doing something really wrong. Admittedly, there’s probably nothing wrong WITH shooting with him – but chances are that the shooting will be less than effective, and is really just an icing on the cake more than it is something worthwhile. If anything, being too tempted into using his Pistol can leave you more often in a bad spot (pulling you out of assault range if he kills with it) than it will help. Yes it can wound anything on a 4+, but if it’ so tough that it necessitates you using that aspect of it, then what you’re really hoping for is to get it in assault anyways.


The greatest asset of the Eversor Assassin is his charge range and bonus attacks. Whenever the Eversor Assassin could charge, take the range he could charge, and then double it. That means that, even when going through difficult terrain, he will still bound ahead of your opponent. Keep in mind, as an Independent Character, he also can move through cover more easily than most units. A 12” charge always catches people by surprise. Just when they think they’re safe at 18”, BAM, you’re in! Combined with his Infiltration ability, and you can be assaulting on turn 1 provided he’s out of Line of Sight of ANY units.


However, for as much as the Eversor Assassin is lethal, it is also very vulnerable. With only 2 wounds, a toughness of 4, and a 4+ (albeit invulnerable) armour save, the Eversor Assassin cannot spend any time out in the open, and dies pretty quickly in close combat too. A single squad shooting at it will most likely take it out. Not only that, but if your enemy fails to break, or there’s too many of them, the Eversor will get hit by so many retaliation attacks that he’ll likely blow up.


When fighting an Eversor, keep this fragility in mind. If you don’t get the chance to shoot at it as its darting through cover, watch what happens when it charges. Any squad it touches on the charge will likely be annihilated (though, since it does NOT have offensive grenades, it will strike last if it’s assaulting into cover). If the squad it charges is annihilated, you have a prime opportunity to take it out with shooting. If the squad miraculously survives and doesn’t kill it back, counter-charge. After that initial charge, the Eversor is MUCH weaker. Yes it explodes on death, but that’s nothing to the carnage it can do if it survives the next combat round and is allowed to charge again on the subsequent turn.


For those controlling the Eversor that go the slow and steady route (waiting to charge later rather than charge right away), be very careful not to get caught in the “grand melee” that can sometimes occur, with tons of units entering into a massive multi-unit combat. The Eversor does NOT thrive in this area! Your opponents will more often get hits back on the Eversor, and if you lose due to your side taking more casualties, the Eversor’s Fearlessness will keep him there, and he’ll probably die from having to take armour saves as a result of this.


Finally, when using the Eversor, always be mindful of what you’re attacking. If the vehicle didn’t move last turn, a melta-bomb is the way to go. If it did move, getting tons of attacks with the Neuro-Gauntlet (auto-glance on a 6) will more likely damage and shake the vehicle, allowing a melta-bomb on the next turn. If your opponent is T3, turn off that gauntlet (the Eversor still has a regular power weapon that ALSO ignores armour) so that you can wound on 3’s rather than 4’s. If you’re against a Monstrous Creature (Carnifexes are great targets), turn that Neuro-gauntlet on, as it TOO ignores armour saves.


Choose your targets carefully ahead of time. The Eversor is the checkers of the Assassins. If your opponent is poorly placed, 1 Eversor assassin can chew his way through as many as 3 units in relatively short time. If you poorly place your assassin, be prepared for him to go pop turn 1.

Wednesday, June 16, 2010

Risk and Reward

Warhammer 40,000 is, largely, a game about risk management. Whenever you do something, you take a chance. On the one hand, you might succeed – on the other hand, you might fail. Chance is a fickle thing, and no matter HOW much probability study you put into it, at the end of the day, you still have to roll those dice. Sure, 91 times out of 100 you’ll succeed – but there’ll still be those 9 times that you’ll fail. This roll, this crucial roll, may be one of those times.

Then again, it may not.



The point is; you truly don’t know until you try.


Some people will claim that this completely dismisses any argument for probability studies. They say that you can’t arm-chair general a game and know from the numbers what the outcome will be. But that isn’t quite fair either – as you do know that, most of the time, a certain situation will yield a certain result. Usually, when a squad of 10 Orks charges a squad of 10 Marines, the Orks will win. If I can assume that the Orks do get into combat, at roughly that level of strength, I can assume the outcome.


But this only works for the short-run, only for stuff that’s happening, effectively, “right now”.

And “right now” for me was a decision I faced in a recent game against the Imperial Guard. (for the record, I tied the game)


Hopeless odds – a 5-man Sternguard Squad with a Chaplin, an empty Razorback with twin-link Lascannon, an Immobilized Rhino, and a Force Commander who already used up his Orbital Strike. A total of 9 models, worth roughly 500 points – most of it in 2 models.


At the board edge, a corner of the table, are 3 Armoured Fist squads in their Chimeras, one squad of an Infantry Platoon, and a Leman Russ Demolisher. I had, rather ineffectually the turn before, merely forced one Chimera and its payload to not be able to shoot this turn.



Being pinned in placed, and with time rapidly running out where the Imperial Guard could try to steal my objective in an attempt to win the game, the Guard had to move up the table – and the easiest and safest route… Tank-Shocking through my Sternguard Veterans.


Being accompanied by the Chaplin, they automatically passed their Ld test, and I had an option. I could get out of the way, or I could attempt a Death or Glory attack with my weakly S6 Krak Grenade against the fiendishly resilient Armour 12 of the Chimera. At the end of the game, we both agreed that this decision was the most important one of the game.


Most of a game of Warhammer 40,000 can be played rather simply. Unit 1 engages unit 2 because unit 1 has an excellent chance of defeating unit 2. Unit 3 could spend a turn shooting, but since it doesn’t have a very good chance of doing anything, it runs to get to a better position instead. Often at least once in a game though, you’ll be presented with a difficult decision – take the safe route that will keep you in an okay position regardless of the outcome, or take the chance that, while slim, may change everything.


I’ve mentioned the term “impact” briefly in the past. Impact, I said, is how much a certain action’s consequences will affect the game.


For example, you have an option to shoot at an enemy Heavy Support, or an enemy Troop. If it’s the beginning of the game, you’ll probably be shooting the Heavy Support. If it’s the end of the game, you’ll probably be shooting the Troop. Why? Because at the beginning of the game, removing your opponent’s Heavy Support will reduce the amount of damage that army can deal to you, whereas at the end of the game, when the Heavy Support may only be able to shoot at you once more, stopping your opponent’s troops from capturing objectives or contesting them will ensure your overall victory.


In this sense, at the beginning of the game, shooting the Heavy Support will have higher Impact, whereas shooting the Troops will have immensely higher Impact at the end of the game.

Unfortunately, as of yet, I can’t tell you a sure-fire way to determine Impact – it’s just not quantifiable. Judging points-value to points-value is a good start, but ultimately it will be the unique situation that you find yourself in that will determine the answer.


Instead, let me present you with a simple scale. Judging things by this scale can help put things into perspective so that you can make the best decision possible.


IMPACT:


1 – Very low Impact. Taking this option will result in almost no change to the game and won’t force your opponent to do things any differently.


Ex. Having a lascannon kill a single model in an opposing squad of Troops that are at full-strength, and the Troops are not being overly threatening.


2 – Low Impact. This option will marginally reduce your opponent’s strength, but not their options. In the end, your opponent’s impact against you is largely untouched, but their odds of successfully impacting you are reduced.


Ex. Shooting an Ordnance round into a 3-man squad of Devastators, the Devastators are in heavy cover (4+ cover save), and it’s Turn 4.


3 – Medium Impact. This option will either significantly reduce your opponent’s strength, or will marginally reduce their strength but will also reduce their options.


Ex. Attempting to destroy a transport that’s 1 move away from assaulting your valuable units. Chances are the unit will lose some strength, not too much, but will force your opponent to slug their way across the table, slowing them down and forcing their hand.


OR


Ex. Attempting to annihilate a Troop squad in the early game by either destroying them completely, or bringing them under 50% strength and trying to get them to fail a Ld test.


4 – High Impact. This option will almost definitely annihilate an opposing unit, and/or will put you more in control of the game by removing some of your opponent’s options. Your opponent will feel hurt after this.


Ex. Destroying your enemy’s HQ. Stopping their Troops from claiming an objective right at the end of the game. Taking out multiple units with a well-placed charge. These are all good ways to cause no end of grief for your opponents.


5 – Game-Changing Impact. This option, if successful, will change the face of the game. Not only will it destroy something that’s bugging you, but it will throw a wrench into everything that your opponent is trying to do. If you can achieve this level of impact at the beginning of the game, the game is almost as good as won.


Ex. Destroying a Tyranid player’s only Synapse creature within range of most of their army. Taking out the crucial Necron Monolith at the beginning of the game, preventing the Necron Army from gaining access to multiple “We’ll Be Back” saves. Causing your opponent’s only 2 Troop units to fall back off the table, preventing them from ever winning the game.


Preferably you want to be achieving as high Impact as possible as much of the time as possible. However, it’s not that simple – you still have that pesky problem named “chance”. Even if every Lascannon on the table turns its sights on the Monolith on turn 1, you still probably won’t take it out, and glancing it does almost nothing (1 in 6 chance of Immobilization, every other roll is effectively pointless against the Monolith).


Enemy Hive Tyrants have lots of wounds, and are often guarded by yet more gribbly creatures to absorb the blows.


Lots of Troops at the beginning of the game will be in range of Ld-modifying bonuses, or won’t even be close enough to the table edge to force them out of the game even early on.


The point is low Impact actions are often easier to achieve than high Impact actions.


And there you have your basics of risk;


High % chance that you can weakly influence your opponent.

Low % chance that you can massively influence your opponent.


If you attempt the low impact action, even if you fail, your failure won’t lie heavily on you. If you attempt a high impact action though, if you fail the consequences can be pretty bad.


So, at what point is the risk worth the potential reward?


This is what was going through my mind during the game. I had a choice – I could move clear of the tank-shocking vehicle. If I did, my opponent would have free rein of the board. They wouldn’t outright destroy my units, but they could do a lot of damage and I’d have to scramble to deal with the approaching forces.


Or, I could Death or Glory with a S6 Krak Grenade against Armour 12. I knew I would automatically hit, thanks to the Death or Glory special rules, but those same rules would force me to hit the front armour – not the back. So a 1 in 6 chance of even just a glancing hit.


Even if I got that hit, I would still need to roll either a 4 OR a 6 to stop it (a result of 5 would merely result in a destroyed weapon and the tank would continue rumbling forward).


Total % chance of success – not good (that’s all I needed to know – checking the math now, I see that I had a 5.6% chance actually – or 1 in 18).


If I failed, which was likely, I would not only have done nothing, but additionally LOST a 25 point model of a very effective squad, setting me even further behind than if I just took the safe route and stepped around the vehicle.


But if I succeeded…

Then my opponent would be boxed in. From the position I was in, if it succeeded, my Sternguard would be protected from most shooting for the turn. Furthermore, my enemy would have to bring their Chimera’s often difficult terrain to move forward. Anyone who plays with or against Mechanized Imperial Guard will know that Chimera Congestion is a problem that even “Reactin” won’t solve.


I probably spent a full 2 minutes judging what to do. In the end, I figured that it was worth the risk, and I took the option. And what do you know? Today just happened to be that 1 time after 17 failures that I succeeded.


The effect was pretty devastating to my opponent. I would rate it a 4 on the Impact scale, maybe 4.5. It wasn’t game-winning, but it certainly was game-changing. I didn’t deal a lot of damage, but in one move I had boxed my opponent in, giving my vastly inferior force (9 models remember) a chance against some 44 models (40 Guardsmen, some with special or heavy weapons, 3 Chimeras, and a Leman Russ Exterminator).


I didn’t destroy all my opponent’s forces in that area, but I stopped all by 1 Chimera and its squad of Guardsmen from reaching the objective, and then the Chaplin (still alive) proceeded to annihilate them. By keeping my opponent off my objective, I was able to turn a losing game in a draw.


How would things have turned out if they happened differently? I can only guess that the Sternguard would have faced a quicky, flamer-filled death, followed by the Chaplin bitting the dust from multiple lascannons to the face, and then having to use what was left of my Troops to fight off some 30 Guardsmen and tank. But… we’ll never know now.


So, try to judge your risk and rewards. It’s not always the right choice to take the safe route – sometimes you have to throw caution to the wind, because IF you succeed, the impact of that action will change everything.

Wednesday, June 9, 2010

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.