Here are my simple house rules for pursuit. These rules have been designed for urban pursuit scenarios but could work in dungeon and wilderness settings with some tweaking.
The rules are loosely based on those found in the 4th edition of Warhammer Fantasy Roleplay; personally I'm ok to magpie good stuff from other systems, but I appreciate it might be a step to far for D&D purists.
Simple Pursuit Rules
Step 1
Check movement rates. If the same move rate then follow steps 2-8. If different then apply a +1 to +3 modifier to the movement roll (Step 6) of the faster party.
Step 2
Establish the quarry head start as a numerical value. This could be DM defined or roll 2D6
Step 3
Roll initiative.
Step 4
DM rolls on the event table (below) to determine what actions may be taken.
Step 5
Actions are taken. Some actions may require a modifier. Example actions may be to create or overcome an obstacle, climb, hide, shoot, throw, tackle
Step 6
Move. Both pursuer and quarry roll 1D6. If the pursuer wins, the difference is subtracted from the quarry's head start. If the quarry wins the roll the difference is added to head start. If the Head Start falls to 0, then the quarry has been caught. If the Headstart reaches 12, the quarry has escaped.
Step 7
Every 6 rounds, both the Quarry and Pursuer must make a Constitution check. A failed roll will apply a -1 to their move rolls for the remainder of the pursuit. Penalties for further failed Constitution checks are cumulative.
Repeat steps 3 to 7 until the pursuit is resolved.
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