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Determining Success with 1d20
Most success chances in Age of Enlightnement are determined by rolling 1d20, adding modifiers, and comparing it to the Difficulty Class [DC] of the action being attempted. Some actions have a set DC (such as climbing a wall), while others are opposed rolls, where the DC varies (such as attacking and defending in combat). For all checks, the roll must meet or exceed the DC to succeed.
With a certain amount of skill, some tasks are so easy that characters have almost no chance of failure. Some tasks are similarly easy, but become dangerous if threatening circumstances present themselves. To attempt an automatic success, a character chooses one of the following three actions, which take the place of the d20 roll. Skill and circumstance may limit the actions a character may attempt to automatically succeed at. In the interests of speedy gameplay, characters may take 0 on the same action as often as they choose. Characters may take 10 or roll on a single action up to three times before frustration sets in. If that doesnt succeed, the character must take 20 to try to succeed. Some actions (like attack and defense rolls) can only be made once, because the results are applied immediately after the roll, as opposed to, say, picking a lock, which can be attempted and re-attempted fairly easily.
A character may always choose to 'Take 0' on a d20 roll. He simply takes his skill (plus situational modifiers) and compares it to the DC. If the skill total is enough, then the action is a sucess. A character may always take 0 on any action, even in threatening situations (like combat). Taking 0 takes no longer than taking the same action with a d20 roll.
A character may choose to take 10 if the environment is free of major distractions, but the action being attempted poses singificant danger if failed. If a character is performing an action that only allows taking 10 in a distraction-free environment, the character may no longer take 10 on the action (but may take 0). Example: Climbing a cliff on a balmy afternoon (dangerous, but distraction-free) : may take 10. Halfway up the cliff, realizing that the 'cliff' is actually a sleeping Tarrasque (very dangerous, major distraction) : may not take 10 anymore. Taking 10 takes no longer than taking the same action with a d20 roll.
If the character has sufficient skill, patience, is free from distraction, and the action has no penalty for failure, then the character may attempt to take the action over and over untill he rolls a twenty, at which point he will determine if he is capable of performing the action. To speed up gameplay, the character simply assumes a twenty was rolled, and adds it to his skill to see if he succeeds. Spending the effort required to do something perfectly is time consuming, so it is not always in the character's best interest. Taking 20 takes twenty times longer than taking the same action with a d20 roll.
Time & Space
The world is divided into hexes. Each hex is 3 ft across. Time is divided into rounds. Each round is 10 seconds long.
In all cases, numbers are rounded down. Any decimal part of a number is ignored, and only the integer part is used. 10, 10.2, 10.5, and 10.9999 are all equal to 10 in AoE.