The Core Mechanic
These rules assume a standardized system for determining the success or failure of any given task. That system is:
d20 + Modifiers vs. Target Number
The Modifiers and Target Number are determined by the type of task.
If the result of the d20 roll + the Modifiers equals or exceeds the Target Number, the test is successful. Any other result is a failure.
A “natural 20” on the die roll is not an automatic success. A “natural 1” on the die roll is not an automatic failure, unless the rules state otherwise.
Dice
These rules use the following die notations:
d4 = four sided die
d6 = six sided die
d8 = eight sided die
d10 = ten sided die
d12 = twelve sided die
d20 = twenty sided die
d% = percentile dice
Die rolls are expressed in the format:
[#] die type [+/- modifiers]
Dice rolls are described with expressions such as “3d4+3,” which means “roll three four-sided dice and add 3” (resulting in a number between 6 and 15). The first number tells you how many dice to roll (adding the results together). The number immediately after the “d” tells you the type of die to use. Any number after that indicates a quantity that is added or subtracted from the result.
d%
Percentile dice work a little differently. You generate a number between 1 and 100 by rolling two different ten-sided dice. One (designated before you roll) is the tens digit. The other is the ones digit. Two 0s represent 100.
Modifiers
A modifier is any bonus or penalty applying to a die roll. A positive modifier is a bonus, and a negative modifier is a penalty.
Stacking
In most cases, modifiers to a given check or roll stack (combine for a cumulative effect) if they come from different sources and have different types (or no type at all), but do not stack if they have the same type or come from the same source (such as the same spell cast twice in succession). If the modifiers to a particular roll do not stack, only the best bonus and worst penalty applies. Dodge bonuses and circumstance bonuses however, do stack with one another unless otherwise specified.
Modifier Types
Ability Modifier
The bonus or penalty associated with a particular ability score. Ability modifiers apply to die rolls for character actions involving the corresponding abilities.
Armor Bonus
An armor bonus applies to Armor Class and is granted by armor or by a spell or magical effect that mimics armor. Armor bonuses stack with all other bonuses to Armor Class except other armor or natural armor bonuses. An armor bonus doesn’t apply against touch attacks.
Deflection Bonus
A Deflection bonus affects defense rolls and is granted by an ability score, fear, spell or magic effect that makes attacks veer off harmlessly. Deflection bonuses stack with all other bonuses to Deflection defense rolls. A deflection bonus applies only to Deflection defense rolls.
Dodge Bonus
A Dodge bonus improves defense rolls resulting from physical skill at avoiding blows and other ill effects. Dodge bonuses stack with all other bonuses to Dodge defense rolls.
Natural Armor Bonus
A natural armor bonus improves Armor Class resulting from a creature’s naturally tough hide. Natural armor bonuses stack with all other bonuses to Armor Class except other armor or natural armor bonuses. Some magical effects grant a bonus to the creature’s existing natural armor bonus. A natural armor bonus applies against touch attacks.
Rounding Fractions
In general, if you wind up with a fraction, round down, even if the fraction is one-half or larger.
Exception: Certain rolls, such as damage and hit points, have a minimum of 1.
Multiplying
Sometimes a rule makes you multiply a number or a die roll. As long as you’re applying a single multiplier, multiply the number normally. When two or more multipliers apply to any abstract value (such as a modifier or a die roll), however, combine them into a single multiple, with each extra multiple adding 1 less than its value to the first multiple. Thus, a double (×2) and a double (×2) applied to the same number results in a triple (×3, because 2 + 1 = 3).
When applying multipliers to real-world values (such as weight or distance), normal rules of math apply instead. A creature whose size doubles (thus multiplying its weight by 8) and then is turned to stone (which would multiply its weight by a factor of roughly 3) now weighs about 24 times normal, not 10 times normal.