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Running Chase Encounters

There’s three ranges a chase can take place at. A close range chase is probably what you think of as soon as the word “chase” is brought up. The pursuer and the quarry are both within sight of one another. The quarry can attempt some daring feat of Athletics or Acrobatics to try and get away, and the pursuer must either match pace or do better. The quarry gets to set their own DC for the check, because they’re choosing what fence to jump or rooftop to leap from or river to dive into. If the quarry fails their check, they stumble and fail and the pursuer catches them automatically. If the quarry succeeds, then the pursuer must either attempt the same stunt at the same DC or else must attempt an even more spectacular stunt with a DC 5 points higher. If the pursuer fails the check, then regardless of what DC they chose the chase moves to long range. If the pursuer passes the check and picked the same DC as the quarry, the chase continues at short range. If the pursuer passes the check and picked the higher DC, they’ve out-stunted the quarry and caught them. Note that this isn’t an opposed check. If the quarry picks a fairly modest DC 15 but then rolls a natural 20 and gets a total result of 27, the pursuer is still picking between a DC 15 stunt to keep up or a DC 20 stunt to catch the quarry immediately.
In a long range chase, the pursuer catches only occasional glimpses of the quarry as they sprint through tangled underbrush or narrow alleyways. At this stage the quarry must attempt to disappear before the pursuer rounds the corner and catches another glimpse. The quarry can roll either Athletics, Acrobatics, or Stealth, in the former two cases to pour on some extra speed and round a corner before their pursuer catches a glimpse, so that the pursuer has no idea which corner they turned or what way they went, and in the latter case the quarry attempts to hide before the pursuer catches up and sees where they’ve gone. Either way, this is an opposed check, with the pursuer rolling their choice of Athletics or Acrobatics against a quarry’s Athletics or Acrobatics and rolling Perception if the quarry rolled Stealth. If the quarry succeeds, they are out of sight and the chase moves to extreme range. If they fail, the pursuer is gaining ground (either because they’re moving faster or because the quarry stopped to hide and was then spotted) and the chase moves to close range.
In an extreme range chase the pursuer can’t see the quarry at all and is instead following tracks. The pursuer first makes a Survival check to find tracks at all, and must beat the navigation DC for whatever terrain the chase is taking place in. If the quarry likes, they can roll their own Survival check to set the DC, but they must accept the results of their Survival check even if it is worse than the navigation DC of the terrain. If the pursuer succeeds on their Survival check, the quarry sets the DC for an Athletics check, and just like at close range, the chase moves to long range if the quarry fails their Athletics check, and if they succeed, the pursuer can either make an Athletics check against the same DC to maintain pace or raise the DC by 5 to move to long range. If they fail either check, the quarry has escaped completely. If they maintain pace, the pursuer must make another Survival check before making the next Athletics check.
In an urban environment, rather than making a Survival check, the pursuer makes an Investigation check. The default DC is 5 for a village, 10 for a town or small city, 15 for a larger city, and 20 for a metropolis. If they like, the quarry can roll either Stealth (to hide altogether) or Deception (to avoid being recognized) to dodge their tail, and just like with the wilderness Survival check, their check replaces the default DC. If the pursuer succeeds, the chase moves to long range immediately, without any Athletics checks.
Description is the soul of a chase encounter. There’s not as much meat on these bones as combat, stealth, or social encounters, and it’s fine if chases just don’t take up as much of the spotlight as some other encounter types, especially since it’s very easy for a chase to blend in with combat when the pursuer catches the quarry or with stealth when the quarry gets away and starts stalking the pursuer and in a dozen other ways tends to end up as a hybrid encounter. To keep the chase parts interesting, however, it’s important to ask for actual specific stunts performed.
Let your players invent some scenery to help them out – they’re going to use Acrobatics to jump up onto a balcony and then dash inside the apartment, or they’re going to use Athletics to leap up and grab the edge of a low wall dividing two quarters of the city and haul themselves up on top of it, or they’re going to dive into the river that cuts through the city and swim through it. If someone suggests something that’s not appropriate for the location, try to avoid just saying “no, they don’t have that kind of thing here” and instead say something more like “well, this is the poor section of town so it’d probably be the wall around a workshop instead of a noble estate, but some basic idea, go ahead and roll.” This helps create a feel for the location the chase is taking place in without making your players feel like they need to guess the appropriate scenery before you’ll let them make their stunt. If you’re having trouble coming up with something, it can’t hurt to ask for help, though: “The river is clear on the other side of town, but there’s probably something you can swim through, any ideas?” might prompt the player to say “maybe someone’s cesspool?” to which the only appropriate response is “hey, man, it’s your brand new leather armor, if you want to drag it through a cesspool, that’s not my problem.”