Optional House Rules for D&D 5e

[Check out this newer post on this subject: D&D 5E – Quick Reference – Chase Rules.]
A couple of years ago I published chase rules for D&D v3.5. You can download them here.
With the release of the fifth edition of Dungeons and Dragons, those rules seem rather heavy. You can still use them if your campaign will have a lot of chases. However, in keeping with the slimmed down rules of 5e, I am proposing a simple house rule for chases. The description below is in terms of a PC character chasing a fleeing foe. Keep in mind that the same rules apply when the PC is the one fleeing.
What if your opponent tries to run away?
Most of the time the standard rules for combat work just fine. A chase may occur when one or more opponent turns and runs away. In game terms, he uses the Dash action to spend his entire turn moving away from combat as quickly as possible. If he starts his turn within 5 feet of you, or passes within 5 feet of you, you can use your Reaction to make an opportunity attack.
What if you want to chase him?
It all depends on how far away you are from him at the beginning of your turn. Compare this distance to your characters speed. There are three possible results.
1) You can use your Move to get within 5 feet of him.
- You can attack him and combat continues.
2) You can catch up to him by using your Dash action.
[If you have enough speed to pass him you may do that, but if you come within 5 feet of him as you pass, he gets to use his Reaction to make an opportunity attack against you, so you will typically want to stop when you get within 5 feet.]
- You stop within 5 feet of him.
- If he continues to run away you can use your Reaction to attack him. [If you speed is the same or greater than his, this can repeat each round. This is not a good strategy for your opponent, unless he can reach shelter or he is leading you into an ambush.]
- Or he may choose to turn and fight on his turn.
3) You cannot get to within 5 feet of him using your Dash action.
- If your speed is greater than his, you should catch up with him in a few rounds.
- If your speed is less than his, and you have no way to increase your speed, he will get farther away each round. You may as well attempt to shoot him with ranged weapons until he is out of range.
- If your speed is the same as his, he will stay the same distance away from you forever. You move closer on your turn, he moves away on his. This is where a house rule is needed.
House Rule #1
A chase is not a race. There are multiple factors that could enable a creature to catch up to another one that has the same speed. Even a lucky slower creature should have a chance. Here is my house rule:
At the end of a turn where you have used a Dash action to advance toward an opponent that is fleeing, you may call for a Strength (Athletics) contest between the two characters. If you win the contest, you move an additional 5 feet toward your opponent. If you lose the contest, you move back 5 feet.
House Rule #2
Characters can’t continue running at top speed forever. For extended chases:
After 5 rounds of continuous running, a character must make a [DC 15] Constitution save or suffer one level of exhaustion. Each additional round of continuous running requires another save at an additional +2 to the DC.
The DM may rule that certain creatures are immune to this exhaustion effect, or that they can run for longer periods before requiring this check.