(Tired. Sleepy. I'll finish this example later.)
In the light of the next day, I'm not as keen on this idea. Last night, I had the idea, not fully worked out, and started writing. Many times that how I work out ideas. Writing it out exposes flaws.
The basic idea is sound, but I want to go even more simple. What I'd really like is a system that can be used both as a Chase System for both Tactical Combat Chases and Non-Tactical Descriptive Story Type Chases. I'd switch as needed, possibly in the same chase. The above rules do accomplish that, but I also want to just roll Opposed Rolls and have the winner move a bit further than the loser. Something like a standard 5 feet would be great. That way, chases are fairly lengthly (I can adjust if I want shorter chases to bigger units) and action oriented.
But, I don't want to break existing rules. If I do that simple 5 foot thing, then a character would move his Speed except when in a chase, when he would move something more or something less, on average, depending on who is in the chase.
The Speed rating should represent an average movement any time the character moves, in a chase or no.
I'll keep thinking.
I agree with Belzbet - a chase consisting of nothing but opposed checks is going to get very old, very fast - it's no more exciting than a combat where the two sides just stand toe-to-toe and trade full attacks every round. You really need something more - choices for the PCs to make, an evolving tactical situation.
There are plenty of choices to be made. I was going to show that in the example that I didn't finish. The Tactical version of the Chase Rules would be as exciting as combat. Or, rather, the rules would actually be combat with varied movement instead of each character with the same Speed rating moving exactly the same distance each combat round.
Think of it as regular combat spiced up with more emphasis on the movement (Throws for obstacles and options that do not normally happen in a combat).
Plus, normal combats happen in one location where as the Tactical Chase would cover a lot of ground--usually so much that, even if the chase starts on a grid (like the example chase, it moves off the grid after one round), the chase would move into a more descriptive, non-grid based descriptive format usually very quickly.
Decision points for players?
Sometimes Skill checks will present options (as with a Knowledge-Local check that will let the player know that he can cut off his chase-prey by taking a quick right down an alley or a Spot check that will inform the player that a stack of boxes and a Climb check will put the character on the roof tops, giving the character second chase path option).
If a character has CON 8-, he has to make a decision on whether to run or not, because once he runs, he's got to start making Fort based Fatigue checks.
Characters with CON 9+ have to decide when and where to Run, because they can only run 10 times before they have to start making the Fort based Fatigue Checks. This character could run for 10 straight rounds, starting the checks on round 11, or the character could mix and match Run and Hustle moves (sacrificing distance, of course, but gaining a longer time before getting tired) so that the character runs 3 rounds, hustles a round, runs 3 more rounds, then hustles for 3 rounds, then runs for 4 rounds, starting the fatigue checks on round 14.
Plus, there will be decisons involving obstacles: The prey runs through the market, between two stalls. The chasing character can simply follow the prey's path or crash through the merchant's cart, spreading his goods all over the ground. This requires a Jump check that, if successful, will put the character 20 feet closer to his prey (gaining ground). But, if the Jump check fails, the risk is that the charcter goes down and loses two rounds of distance on his prey (the distance between the character is increased by whatever ground the prey covers in two rounds).
So, you see, there will be lots of exciting player decisions during the chases that I'm envisioning.