Upon further thought, stacking is too important to not devote an article to.
How Things Stack
Stacking is one of the most important concepts in 3rd Edition Dungeons & Dragons, as they apply any time dice are rolled. As a player, if you don’t want to just accept a raw d20 when attempting to do something, learn the stacking system. As a DM, the two most important duties for you are adjudicating DCs and what bonuses apply to a situation.
Types of Bonuses
Generally speaking, each type of numerical bonus you can get is only good once: you don’t get two Armor bonuses from what you’re wearing, you don’t get four attributes bonuses on the same die roll, et cetera
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Armor
This is the type of bonus armor gives you. Mage Armor gives you this bonus, too.
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Attribute
This is the bonus you get due to a good (or bad) attribute score. Strength bonuses to attack in melee are of this type. Magic generally will affect the attribute itself, not directly affecting the attribute bonus.
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Circumstance
This bonus is based on some situational factor to the advantage of the object or subject of an action. Gaining higher ground in melee grants this bonus.
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Competence
Some spells and magic items grant a competence bonus. This means they just plain make you better at doing that action. Guidance gives this bonus
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Deflection
These pretty much just apply to Armor Class. A Deflection Bonus is normally a magical effect that actually redirects incoming attacks
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Dodge
Dodge bonuses mostly come from abilities such as… the Dodge feat! No magic items or spells should grant Dodge bonuses, as this is one of the few bonus types that actually stacks, and this would be abused otherwise.
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Enhancement
Enhancement bonuses are what magic weapons always get (+2 Longsword gets a +2 Enhancement bonus to attack and damage). Magic Weapon and Cat’s Grace both give this kind of bonus.
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Enlargement
Bigger can be better. When a character is by whatever means made significantly larger than normal, some characteristics such as Strength or Constitution are increased.
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Flanking
You get this when you’ve got an opponent flanked, and that’s the only time you should only get this bonus as the result of flanking your opponent.
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Haste
Speedups from magic items, fluctuations in the time-space continuum, or spells grant their own kind of bonus: basically you’re moving faster than everybody else so you get another bonus. This normally applies to Initiative and AC.
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Inherent
This would be an increase in the core characteristics of the beneficiary of the bonus. A Wish spell increasing a stat grants an Inherent bonus. Any given stat can only have +5 worth of Inherent bonuses at any given time, but otherwise they stack.
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Insight
An insight bonus is when some magical effect gives a supernatural, precognitive advantage. True Sight is the most straightforward example of this.
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Luck
It’s luck. What can you say. Divine Favor and Luckstones tend to grant this, as does being born a Halfling.
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Morale
These come from that warm tingly feeling when God is on your side, the wind is at your back, and you’ve got that new-socks feeling.
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Natural Armor
Thick-skinned critters with a naked AC of over 10 have Natural Armor. It stacks with normal armor and doesn’t count for the purpose of touch attacks.
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Profane
This is just a creepy “evil” bonus for when you need that extra-evil feeling in the morning.
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Resistance
A resistance bonus provides protection from some form of harm, generally absorbing damage.
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Sacred
This is the fluffy-bunnies goodie goodie feeling that Paladins pick their toenails with every day. It’s the opposite of a Profane bonus and generally exists to put some oomph into what would otherwise be for dramatic visual effect.
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Synergy
Some skills come together very nicely. Disguise complements Bluff, Tumble benefits Jump, and so forth. These actually stack if they come from different sources.
Wow, that’s a lot when you look at it. Most of these bonus types have adequately descriptive names, so it’s only the special exceptions that need to be remembered. Everything else is more of a “heck, I can have a lot of bonuses” effect.