There are two ways to conduct short-range chases: a simple way, and a more detailed way. Choose whichever seems like the most fun at the time!
The Simple Way
Just have each PC roll against a target number equal to [(2xBasic Speed) +3 – Peril]. (i.e. if your basic speed is 5, and Peril is 1, then you roll against 12, which is 2×5+3-1. ) Anyone who succeeds manages to catch up with the quarry (or manages to escape, if you are the quarry). Anyone who fails, fails.
The Detailed Way
If you want more detail, use the Chase rules in GURPS Action 2: Exploits, pp. 31-53. Begin by rolling 1d for starting range. (Need a die roller?)
1- Close, 2 – Short, 3-4 – Medium, 5 – Long, 6 – Extreme.
Each chase round, roll to determine which chase maneuver the quarry attempts – unless they are forced to take an “Emergency Action,” or similar, in which case, they will attempt that. Simply re-roll any result if everyone agrees it is quite inappropriate. The PCs, who are in pursuit, can choose any maneuver they wish – but if they attempt to perform a maneuver that requires “suitable scenery,” see below.
|Quarry Chase Maneuvers
Roll 1d, 1d. (Need a die roller?)
The quarry is always considered to have access to “suitable scenery” for any chase maneuver they attempt. The PCs have no such luck! To perform a maneuver that requires “suitable scenery,” the players must first make a relevant skill roll (e.g, Acrobatics, Riding etc) at a penalty of (Peril+5). This significantly increases the chance of failure and critical failure, but it does allow the player to exercise some GM-like control over their PC’s environment. The situation may seem unfair – the NPC quarry doesn’t need to do this – but on the other hand, the quarry’s maneuvers are decided at random, so we can call it even.