Editing Warhammer 40,000/9th Edition Tactics (section)

===Combat 101===
While Shooting and Fighting are separated below, they largely share rules, much like how Movement and Charging are in separate phases, but share many rules and concepts. By and large, ''any'' attack you make has 5 values: Attacks (which is rate of fire), Accuracy (typically WS or BS), Strength, AP, and Damage. These values are converted into other values in context (for example, attacks are left alone, but accuracy requires dividing by 6), then those values are multiplied together to determine how many wounds you actually expect to knock off your target. They resolve in this order, in general:

#Select a unit to make attacks.
#If these are melee attacks, determine number of attacks.
#For each model in the unit, select its target unit(s), which must be within range, and, if this is being done for shooting attacks, within line of sight.  Shooting attacks may target a different unit with each weapon and melee attacks may target a different unit with each attack, for determining how many targets to select - declare which weapons and how many attacks with each (if melee) are going against each target now. Proceed below for each model ''after'' all models have chosen targets.
#*Order of procession is pick one targeted unit at a time to be attacked, then cycle through each model that targeted that unit.
#*For each attacking model, proceed one profile at a time, grouping all attacks made with that profile together.
#If these are shooting attacks, determine number of attacks.
#Roll to hit, based on accuracy.
#Roll to wound, based on strength and toughness.
#Target rolls to save, based on its saving throws.
#*While all rolls are subject to re-rolls and modifiers, the most common modifiers in the game apply here, such as AP and Cover.
#Determine amount of damage by rolling and adding modifiers, if applicable.
#If the target has a "Feel No Pain" type rule, it rolls that against damage, much like a saving throw, on a per-damage-point basis. Feel No Pain rules cannot stack with each other - only the strongest one is applied. 

As will be discussed below, you ''always'' re-roll ''before'' applying modifiers.  Modifiers are applied in the following order: Replacement, Division & Multiplication, Subtraction & Addition, Ceiling (you always round fractions up to the next whole number).

====Attacks====
This can be random, such as 1d3, or 1d6, or 2d3, and can include an additive modifier, e.g. 1d3+3. There is a section below on dice averages, but for attacks, you can safely treat a random value as its average for the purposes of working out how much damage a given attack will do to a given target. More often, it will be a constant number- melee weapons generally use the Attacks stat of the user, while ranged weapons will specify the number of attacks they can perform in their profile.  Of special note are weapons with the Blast ability, as these weapons get a higher minimum amount of shots against larger units.

====Hitting====
By and large, this will be a WS or BS value. Regardless of the name of the stat, here called "AS" for "Accuracy Skill". 

The odds of hitting is: (7-AS-modifier)/6

*An ability to re-roll will multiply this value by (6+x)/6, where x is the number of facings on a hit roll you can re-roll, so if you re-roll 1s x is 1, re-roll 1s, 2s, 3s and 4s x is 4.
*Re-rolling all failed hits means x=7-AS, note that modifiers do not change the effect of re-rolling all failed hits, this is only affected by the AS. 
*Abaddon's ability to re-roll hit rolls even if they hit mean x=7-AS-modifier instead.

====Wounding====
Instead of requiring a fixed roll, like hit rolls, most wound rolls (WR) instead require that you compare the Strength of the weapon to the target's Toughness, although some weapons do require a fixed roll. 

Your wound roll (R) is 2+ if S ≥ 2T, 3+ if 2T > S > T, 4+ if S = T, 6+ if S ≤ T/2, and 5+ if T/2 < S < T.

The odds of wounding (oow) with a modifier to wound <math>m</math> are 
<math display=block>\begin{align}
oow &= \frac{\min\left(6,\max\left(1,7-R+m\right)\right)}{6}\\
    &= \frac{\min\left(5,\max\left(1,m + 3 + \left\lceil\log_{2}{S}-\log_{2}{T}\right\rceil + \left\lfloor\log_{2}{S}-\log_{2}{T}\right\rfloor\right)\right)}{6}
\end{align}</math>

This means S and T scale with twice the base 2 logarithm of their values, subject to the wounding caps on either end of always failing on 1 and always succeeding on 6 - for example, S8 results in a 3 in the formula twice (which will always be close to having added 6), while S4 results in a 2 twice (always close to +4).  If you were to pay for Strength on a linear scale - 1 point for S1, 2 for S2, and so on - the most cost-effective S would be 3, because it adds about 3.17 to your wound formula, and is the only S for which you add more than S to the formula.  This also means doubling your S (as many melee weapons do) is usually as good as adding +2 to the formula, but adding to your S directly (as most of them do) has very diminishing returns.

*An ability to re-roll will multiply this value by (6+x)/6, where x is the number of facings on a wound roll you can re-roll, so if you re-roll 1s x is 1, re-roll 1s, 2s, 3s and 4s x is 4.
**For re-rolling 1s, x is always 1, and so the multiplier is always 7/6.
**For re-rolling ''failures'', x is larger the more likely you are to fail; a WR of 6+ multiplies by 11/6, 5+ by 10/6, and so on down to 2+ multiplying by 7/6.  Remember, re-rolling occurs before modifiers, which is one reason why re-rolling wounds is better than re-rolling failed wounds - you can re-roll "successes" that will be failures after a modifier.
*In practice, T will usually vary between 3 and 8 - T2, T9, T1, and T10 are all very rare, and you can just assume absolutely no targets have T11+.  As S values increase, this results in diminishing returns, as the weapon becomes better at wounding T values it will never encounter.  This is generally most obvious when considering S6->S7, which is ''only'' useful against T6 and T7 in practice.

====Allocating Wounds====

After you have rolled to wound, the attack gets allocated to a model in the target unit.  Unlike in 8th edition, not only must this attack be allocated to any already wounded models, it must be allocated to whichever model in the unit has already had attacks allocated to it this phase, regardless if it actually lost any wounds or not.  Bear this in mind when it comes to weapons with different AP or damage stats.

====Penetrating Saves====
Basic saving throws work very intuitively, broadly identical to accuracy; a 6+ save works just like 6+ to hit - except that the target assigns which model takes the save in the unit and rolls the saving throw, which changes the looks of the math a little since we will be calculating how likely we are to penetrate our opponent's save rather than how likely we are to save. Many weapons have a negative AP value that increases the dice roll your opponent needs to beat to pass their saves, a cover save now adds a +1 modifier to the Sv of the unit rather than providing an alternate save like an invulnerable save like it did in the past. A saving throw roll of 1 is always a failure, but a roll of 6 is not necessarily a success. Invulnerable saves are unaffected by cover and AP but otherwise works exactly the same way as a normal save.

Your odds of penetrating (oop) are 
<math display=block>\begin{align}
oop &= \max\left(1,\frac{Sv - modifiers - AP - 1}{6}\right)\\
    &= \frac{\max\left(6,Sv - modifiers - AP - 1\right)}{6}.
\end{align}</math>
If your opponent can re-roll failed saves of x or less (so re-rolling 1s means x is 1, while re-rolling all failures on a final 5+ save means x is 4), your odds from above become:
<math display=block>\begin{align}
oop(x) &= oop + \frac{x\left(oop-1\right)}{6}\\
       &= oop\left(1+\frac{x}{6}\right)-\frac{x}{6},\\
     x &\le \max\left(6,Sv - modifiers - AP - 1\right).
\end{align}</math>

*Note that since AP is negative (-1/-2...) the outcome of AP is actually positive: -(-1)=+1. 
*AP increases damage linearly, which means having AP0 or AP-1 against a 2+ Sv and a 6+ Sv are very different things. Against a 2+ Sv AP0 will usually need 6 wounds to penetrate the save once, while AP-1 will need 3 wounds to penetrate the save once (causing 100%, i.e. 2x) more damage). Against a 6+ Sv AP0 will need 1.2 wounds to penetrate the save once, while AP-1 will need 1 wound to penetrate the save once (causing 20% more damage).
 
=====Cover=====
Light cover improves the armour save of the unit that is in cover by 1 against Shooting attacks regardless of which phase that Shooting attack is made in or whether the target or firing unit is in combat, and Heavy cover may give the same armour save bonus against close combat attacks. A model cannot claim multiple cover saves, it is either in cover and receives the bonus, or it is not, and it does not benefit. If you have a unit that is partially eligible for cover the whole unit will not benefit, but if you remove all the models from the unit that are not eligible the unit benefits immediately; therefore, it can be beneficial to roll your saves one at a time and pick off the ones outside cover first. 

*Certain units and terrain types (see terrain 101 above) have special rules which can affect chances to hit or visibility.

====Inflicting Damage====
When a model fails its saving throw it takes an amount of damage depending on the Damage characteristic of the weapon used. The model suffers that many wounds and any excess wounds are lost if not mortal; excess mortal wounds are allocated using the standard rules for allocating wounds, but since mortal wounds skip the saving throw step, you proceed immediately back to this step. If it is suffering both non-mortal and mortal wounds from the same attack, resolve non-mortal wounds first.

Feel No Pain "FNP" style abilities allow models to ignore some of the damage they take on by rolling a die and beating a number; these rules are exclusive, meaning you have to choose exactly one to use.  Some of these rules may specify that they work only on non-mortal wounds or only on mortal wounds, or in different phases, or what have you, but they generally all work the same.  This means that an FNP "save" is theoretically like an invulnerable save, but worse, as invulnerable saves are not negatively impacted by trying to resist greater damage values.  In practice, invulnerable saves are ''much'' easier to get.

Roll a die for each point of damage the model would suffer. On a roll of X or more (typically 6), ignore it.
*Sometimes, the roll is a 5+.
*A 6+++ FNP ''generally'' increases the average number of wounds you need to deal to a model to kill it by 6/5 or 20%. The chance that it will completely nullify an unsaved wound is 1/46656‬ for 6 damage, 1/7776 for 5 damage, 1/1296 for 4 damage, 1/216 for 3 damage, 1/36 for 2 damage, and 1/6 for 1 damage.
**This gets messy, quickly, because of how excess damage is wasted: while you will usually need 6 damage to kill a W5 model with a 6+++ FNP, it will actually suffer some damage between 0 and 5, as both 5 and 6 damage getting through kill it.  This means a W5 model suffering 6 damage actually takes about 4.67 on average (and has a 73.68% chance of dying outright), while a W1 model actually takes very nearly but not quite 1 damage, with the same chance (nearly 1, which is nearly 100%) of dying outright.  Meanwhile, a W6 model without an FNP takes 6 damage, with a 100% chance of dying outright (in this case, making it 'less'' durable than the W1/6+++ model).  Generally speaking, W is better for resisting lower damage (W6 can't die to D5, while W5 can, regardless of FNP), while FNP is better for resisting greater damage, relative to some starting W.  
*A 5+++ FNP increases the average number of wounds you need to deal to a model to kill it by 6/4 or 50%. The chance that it will completely nullify an unsaved wound is 1/729 for 6 damage, 1/243 for 5 damage, 1/81 for 4 damage, 1/27 for 3 damage, 1/9 for 2 damage, and 1/3 for 1 damage.

This means you can ''usually'' roll the dice for all of the non-mortal wounds a model is suffering at once, as order does not matter - enough failures to remove the model's remaining wounds kill the model, and the excess is wasted - but remember that special rules can apply (such as a model that only gains an FNP after it suffers some damage, or a weapon that lets non-mortal wounds spill over to other unit members).  You can't do this for mortal wounds in a unit with mixed FnPs, as each time a model dies, the unit's controller can choose a new model to start suffering remaining mortal wounds.