There's been a lot of interest over in the OSR Discord channel about my chase rules. I originally posted them here, but they've since gone through a few updates and slight revisions, so I thought I'd post an updated and clarified version for anyone who'd like to use them.
Each round, each group of pursuers and fugitives rolls 2d6. If the fugitives are slower than the pursuers (for example, because of encumbrance), they roll an extra 1d6. If the fugitives narrate some clever maneuvering or other interference with the pursuit, the pursuers only roll 1d6.
If all of the fugitives' dice match one another (i.e. they roll doubles or triples) then they get away and the chase ends. If the pursuers roll doubles, they corner the fugitives and the chase ends. Ties go to the fugitives.
If any of the results on the fugitives' dice match the pursuers, then they can each exchange a round of missile fire with one another. e.g. if the fugitives roll 2d6 and get a 4 and a 6, and the pursuers roll a 4 and a 5, then the 4s match one another and each side can shoot the other. You can't reload or do anything other than take a snap shot.
If either side's roll totals to 7, then they can take a round of melee attacks against, or other actions affecting, the other side. Only the side that rolls the 7 gets to make the attacks. Actions can include reloading your ranged weapon, or casting a spell.
If either the pursuers or fugitives have more than one member on their side, they can choose to split off at any time and roll separately, but they're only affected by their own dice rolls.
The chase continues until the fugitives get away, are cornered, or either side is dead.