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(5.15) How abilities, resistances and boni stack                                
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(Also see (5.6) for basic information about damaage types and resistances.)

The same resistance from two or more items in your equipment don't add to each
other. For example you only need one item that provides fire resistance. If
you equip two such items you won't get better resistance than with just one
item. You cannot get "double resistance" from two items' static resistances.
This rule applies to all resistances and abilities that don't use a bonus
number to indicate their effectiveness, like faster mana replenishing or hit
point regeneration, telepathic powers, slow digestion, etc.
Intrinsic resistances and abilities gained from your class or race, or those
acquired from training a skill are also static resistances and will not stack
with other static resistances from items.

However, there is a way to further increase your base resistances (fire, cold,
acid, lightning) or poison resistance temporarily:

Use an item or spell that provides some temporary resistance. Static resistance
and temporary resistance actually stack and their effects are multiplied!
For example if you wield a shield of resist fire and you quaff a potion of
resist heat you'll have double fire resistance as long as the potion lasts,
resulting in fire damage being cut down to 1/9 instead of 1/3:
1/3 static res * 1/3 temp res = 1/9 total res.
This is quite close to having fire immunity, as far as single monster fights
are concerned.
Not only potions can boost your resistances temporarily, some items can also
be activated for temporary resistance, for example cloaks of lordly resistance
or elemental protection rings or certain artifacts. And of course there are
some spells that can be cast for temporary resistances.

Note that two temporary resistances to the same element do not stack either,
same as how two static resistances to the same element don't stack.
Only one static and one temporary resistance will stack in total, ever.

Stat increases or ability increases that are not 'flags' (flag means you either
have it or you don't) but that use bonus numbers will add to each other.
For example an orcish shield (+2) that increases your strength by +2 and a
kolla (+1) which also increases your strength (just by +1) will add up and
your character's strength will be increased by +3 in total!
Same goes for IV (Infra-Vision), luck, extra attacks, speed, etc.

There are some abilities which are not flags although they might look like it.
In fact, they add up / stack. Those are:
-Extra shots (concerning ranged weapons)
-Extra might (concerning ranged weapons)
-Drain mana ('Drains your magic'. Note that 'mana regeneration' (also called
 mana-charging) does NOT stack. So it can cancel out the effect of only ONE
 item that drains mana, not of any more). See (4.11a) for more information.
-Drain hit points ('Drains your health'. note that 'regeneration' does NOT
 stack, so it can cancel out the effect of only ONE item that drains hit
 points, not of any more. However, the 'Health' skill is able to further
 increase your regeneration rate). See (4.11a) for more information.
-Drain experience ('Drains your life force'). See (4.11a) for more information.
-Extra light radius