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The chase rules in Introducing Late Night Fighting kinda suck! But they’re just the best that I’ve found when you’re playing voice-only, when you don’t have movable markers, playing pieces, or minis in 2d space. Most of the other parts of the ruleset felt like I pretty much nailed it early on, but chases took a lot of work to get to where they are now, which is at least usable. Informed by, but very vaguely related to Stars Without Number and Unknown Armies, and tries to remain compatible with the 5e DMG.
Ultimately, what ends a chase is getting caught or getting away.
You’re caught when you have no hit points left. So this is probably one of the least intuitive parts of this. To catch someone, make attacks on them.
You get away when they can no longer find you. So there’s a contest between the quarry’s dexterity (“stealth”) ability check vs the pursuer’s wisdom (“perception”) ability check each round. This contest doesn’t cost any actions.
Between each pair of pursuer&quarry there’s escape points. So if Alice and Bob are chasing Carol, Ted, and a skeleton, there are six sets of escape points. Alice vs Carol, Alice vs Ted, Alice vs the skeleton, and similarly for Bob.
The quarry gains one escape point on rounds when they have a higher speed than that pursuer, and loses one escape point on rounds when they have lower speed. When both have the same speed, there’s no change in escape points. Gaining and losing escape points this way doesn’t cost actions, but there are actions (like dashing or using special abilities) that change your speed.
To get that free dex-vs-wis contest to get away, you need at least one escape point.
In dungeons, there’s a round before you can get into the fray for shooting, or preparing your weapons or casting buffing spells.
Outdoors, it’s a random amount of rounds depending on the terrain you’re traveling in.
Terrain Turns Arctic, desert, farmland, or grassland 6d6/6 Forest, swamp, or woodland 2d8/6 Hills, or wasteland 2d10/6 Jungle 2d6/6 Mountains 4d10/6 Dungeon always 1
The rounds tick down as long as at least one of the sides wants to close in and there’s not like a ravine or something in between.
Ranged attacks reach when there are two or fewer escape points, or on the last two volley rounds.
Two-handed ranged weapons, like bows, work with up to ten escape points or volley rounds, but with disadvantage if there are more than two.
For ranged spells, they work the same as one-handed ranged attacks with a few exceptions like Eldritch Spear that are explicitly long-ranged. (The conversion formula from 5e’s spell list is that if spell has more than 300 feet range, divide their range by sixty and round up. Tough titties if you have a 299 feet spell. The reason for this 300 feet threshold is so that most spells will work the same so I don’t have memorize ranges for thousands of spells.) Unlike two-handed ranged weapons, you can’t take disadvantage to reach longer.