Run

Run is a statistic that represents a character's skill in both chasing creatures and fleeing from pursuing creatures. Your Run bonus is equal to your Strength modifier plus your Dexterity modifier plus 1 for every 5 feet of movement speed you possess.

For example, a character with a Strength of 8, a Dexterity of 16, and a movement speed of 30 feet would have a Run bonus of +8.

Participating in a Chase
In a chase, one or more creatures attempt to catch up to one or more creatures who are attempting to flee. Once a chase has begun, all participants, both pursuers and runners, make Run checks. If a pursuer exceeds a runner's check, then that pursuer will eventually catch up to the runner. If it is necessary to determine precisely when a pursuer catches up to a runner take the starting distance in feet from the pursuer and runner (with the default assumption being the runner's movement speed) divided by the difference between the pursuer and runner's Run checks, rounded down to find the amount of time, in rounds, it takes the pursuer to reach the runner.

For example, a pursuer has a run check of 26 and a runner has a run check of 19. They were 30 feet away from each other when the chase began. The difference between their run checks is 7. 30 divided by 7 is 4.28, rounded down is 4, so it takes the pursuer 4 rounds to reach the runner.

Once a pursuer has caught up to a runner they both roll a initiative check, beginning a new battle with the pursuer starting at any distance they wish from the runner.