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

====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.