Races and Chases make great action sequences in books, comics, movies, and tv-shows, but sometimes feel flat when it comes to the gaming table. Part of this is that it is hard to get the sensation of speed and danger that comes naturally with a high speed chase - or the direct competition of a race - when you're sitting around a table rolling dice. And part of it is because while RPGs have a lot to say about how you swing a sword or shoot a gun and hit someone, they have less to say about the nuances of movement.
This is forgivable for the most part. Imagine having to determine a character's unique speed, how quick they can turn, and how fast they can accelerate. Quite a lot of systems will just say "a character moves X units." Some get more complex and do it by size - small creatures move slower than medium or larger creatures. Some will derive your speed from other stats, but not much about the rest.
This makes chase scenes and race scenes harder because there is a lot more to a chase than just which vehicle has the fastest top speed. Unless, of course, you're talking about a drag race. Even then the decision point comes down to vehicle and the only real test of character is can they execute on the vehicle while keeping it under control?
A drag race is how a lot of races and chases in RPGs get handled. You have two vehicles (or characters) trying to beat the other person to a certain point. The only thing that really matters here is top speed, right? Well, even then it is more complex than that. Let's take 2 vehicles for this. We'll say Vehicle A has an acceleration of 4 ambigunits and a top speed of 8 ambigunits. vehicle B has an acceleration of 3 ambigunits and a top speed of 10 ambigunits. Who wins the race?
Well, it depends on how long the race goes.
It breaks down like this: assuming both pilots keep control of their vehicles, after turn 1 A has moved 4 units (and has a speed of 4) while B has moved 3 units and has a speed of 3. After turn 2 A has moved 12 units and has a speed of 8, while B has moved 9 units and has a speed of 6. After turn 3 A has moved 20 units and has a speed of 8, while B has moved 18 units and has a Speed of 9. Finally on turn 4 A has moved 28 units and has a speed of 8 while B has moved 28 units and has a speed of 10.
If the race goes to 5 turns then B wins. At 4 turns it is a draw (with the GM having to finagle to figure out if B is passing A at the line, or A is still a bit ahead.) Every turn before 4 though A is the winner off of raw acceleration despite a lower top speed.
Corners & Obstacles
The fact is most vehicles you see in races are capable of going a lot faster than they are seen going for most of the race. However, due to the nature of turns (or obstacles for chases) you can't necessarily be going as fast as you can if you want to stay in the race. You can only go as fast as you can safely slow down from in order to successfully take the next turn. After the turn you accelerate back to whatever speed you can make before the following turn.
Unless there are a lot of open straight aways - or your race is set up like NASCAR where it is more endurance and crowd technique than cornering and acceleration work - how a vehicle handles and accelerates will determine more about speed than anything else.
When it comes to chases this gets even more convoluted, but boils down to a simple line from Burn Notice (heavily paraphrased from memory): often times the person to win in a chase is the first person to do something the other person can't or won't do
Constant Dice Rolling Won't Generate Excitement
The final thing to cover here is that even if we take into consideration the turns, the acceleration, and the speed (all of which help make chases on screen more exciting) there is one last problem: just rolling dice alone can be boring and weird.
Assume you went and made a track or course for the race/chase. You have where the vehicles can go fast, you have where the turns are, you have the obstacles. How this plays out now though is just a sequence of dice rolls. You can try to spice those up with descriptions, but ultimately it feels like a place where maybe one roll should ride and determine the whole thing or like you are rolling to see who fails first to a significant enough degree to cause a crash. If we want our race or chase to be fun and engaging, we need to do more than just call for X dice rolls.
Decisions Make Things Interesting
The trick then is right here: focus on the decisions. The tension in a work of fiction is from the question of whether or not the hero will succeed (to escape, to win, to catch the guy) and/or what the cost of doing so will be along the way. The focus for the tension and drama is on the character, which is heightened and brought to the fore by the action sequence we see. That means you need stakes. But it also means we need decision points.
Combat brings this about naturally. It is why some people can have enjoyment from a D&D combat purely from the mechanics. Every turn is a group tactics contest with decisions galore to be made: where do I move? How do I move? Can those monsters attack me if I do? Is it better to attack monster A or B? Less tactical/crunchy RPGs don't have this which is where other things need to come into play.
For a race or chase it is no different. You need to give the PCs decisions to make that have meaningful impact. Do they take the dangerous shortcut? It is a harder roll, with a greater chance for big damage on their vehicle - but if they pull it off they will get a significant gain on their opponent. Do they take the safe play on the corner or risk it by going for the pass by threading the needle through a crowd? Do they plow through the road block, try to go around, or divert to another path?
The decisions, and the consequences of those decisions, is what drives the scene and keeps things interesting and engaging. Good and bad things can come from them. The dice rolls then add spice to those rolls. But the meat, the engagement, and the excitement comes in the decisions because they stage the dice roll. The player makes a choice, they roll to see if they can pull that off. It's a lot more interesting than just "I go faster so I catch the guy/win."