| abstract
| - Success = 1 - 1 / (1 + exp(0.03 * (Attack - Defense)) where "exp" returns e raised to the power of the number that follows, the constant e equals 2.71828182845904, the base of the natural logarithm. EXP is a standard function for both Microsoft Excel and LibreOffice. From : Answer: srand - Casting spells uses a slightly different skill check curve than that used for all other skill checks. It has the same midpoint, but is steeper through the middle. So once you are over the 50/50 point, your casting gets reliable much faster than with a normal skill check curve. But conversely, under the 50/50 point your casting is much less reliable than with the normal skill check curve. I just found this out tonight, myself.
- A skill check is a check relating to use of a skill. The basic skill check = d20 + skill rank + the relevant ability modifier. Additional skill modifiers may be applicable. The DC to pass is variable with the task (see each skill's page for examples).
- A skill check is made when a character applies a skill to a task. This roll is made with a d20 (20-sided die), plus the skill level and any modifiers for this specific check. The skill check is successful if it equals or exceeds the difficulty class (DC) of the task (so high rolls are desired). The DC can either be a static property of an object, such as a trap, or be determined by the skill check (or other roll) of another character. This latter type of skill check is called an opposed check (or opposed test, opposed roll, etc.), since the task is being opposed by another character's roll. Miscellaneous modifiers can apply to a particular skill check, such as the bonus provided by using thieves' tools. This makes the roll calculated as d20 + skill level + miscellaneous modifiers or, splitting the skill level into its components, d20 + skill ranks + ability modifier + feat bonuses + skill modifiers + miscellaneous modifiers. Certain skills allow for a take 20 where a fixed value of 20 is used instead of the d20 roll when the character is not in combat. Naturally, this means skill checks cannot be automatic successes if the die comes up 20 (and conversely, rolling a 1 is not an automatic failure), unlike attack rolls and saving throws.
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