There are basically 3 possible outcomes for any chase in the Dungeon:
1: The player characters escape and reach safety
2: The player characters fail to escape and are caught or combat starts
3: The player characters fail to escape but the chase continues
Resolving a chase:
Each player rolls two d20s, adds their Dexterity modifier and subtracts the Encumbrance penalties:
-2 for Dead Weight and -4 for Overweight.
If you are Morbidly Encumbered you can't run until you drop something.
I'm using the Encumbrance Rules from Last Gasp for the penalties by the way.
Any result equal or greater than 10 is a success. With two successes the character escapes and reaches safety. With only one success the chase continues. With two failures the character is caught.
Characters that succeed decide whether or not they wait for their companions that failed.
The target number (10) can be modified according to the circumstances and the pursuers. One alternative is to use the Dexterity score of the pursuing monster to determine the target number, however thats ill advised for monsters with high scores like 16 or higher.
An additional penalty of -1 can be applied for each additional round of chase, to a maximum of -3.
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