What's the best way to escape the police in a high-speed car chase?

The following strategies may improve your odds:

• Try to elude the police in a district with a strict pursuit policy. Because of the danger of high-speed pursuits, many districts will call off high-speed chases almost instantly
• Going near the airport or going into tunnels may require helicopters chasing you to give up pursuit
• Cut across a field / go off-road -- cops may try to continue on the road and meet you on the other side. You may be able to escape before they make it around
• Pull ahead of the cops then turn off the road. Repeat with multiple turns and eventually stop and kill your lights.

Simple: Elude law enforcement in a jurisdiction with a strict pursuit policy. In my department, unless a suspect vehicle was an obvious DWI (swerving white line to white line, erratic speed changes) or had committed a violent felony, vehicle pursuits got cancelled by a commander almost instantly. There is so much liability at play in a pursuit situation that many departments are getting very conservative in their response protocols to situations like this.

As far as maneuvering tactics when they're actually pursuing you, there's really no sense diving in - you've got too many things going against you:

• Communication. Every involved officer, as well as their supervisors and their supervisors' supervisors, have radios, both in-car and portable on their person. Can you dial your cell phone and drive with one hand at 120 mph while you coordinate with accomplices miles down the road? Probably not.
• Collaboration. If a pursuit has been sanctioned, the longer it goes on the more officers are going to be in on the hunt. And if you stray toward the boundary of a jurisdiction (city limit, county border, and so on), you're going to get mutual aid response from other agencies, who may be even less restricted than your original pursuers. Have fun with that.
• Convergence. You can go in one direction at a time, but law enforcement response to your location will be omnidirectional. You're going to have LEOs swarming your vehicle from 360 degrees and, if a helicopter gets tossed in the mix, three dimensions. You simply cannot go fast enough to counter this. Even if you were trying to elude the North Dakota Highway Patrol on I-94 in an Italian supercar, you've still got a lot of variables to buck regarding interagency cooperation.
• Contraptions. Hope you've got solid rubber tires, because if the agency gets a lock on your direction of flight, you're getting spiked - and if you hit spikes, you're hosed. You'll drive for a while, because spike strips are designed to puncture tires so they slowly deflate as opposed to blowing out. But once they're flat, driving on them will make them disintegrate; then you're driving on rims. Now you're limited to fifteen to twenty miles per hour, and you're in danger of your vehicle catching fire from the spraying sparks. Meanwhile, the agency is moving the K-9 unit to point position so when you shoulder your smoldering jalopy and make a run for it, Cujo's got less ground to cover before he eats your forearm. Did you think to wear chain mail?
• Concentration. How often do you drive in this manner? Unless you're running because you're on parole, this is likely your first dance. Sure, you've driven fast before - for a while. Then, for whatever reason, you got uncomfortable and backed off. Maybe your car made a sound you got concerned about, maybe you caught a glint you thought might be a trooper's windshield, maybe you thought you heard the faintest pulses of a siren. Whatever it was, it weakened your resolve and you slowed down. You have no such luxury here. And while this is fresh for you, this is, to many of the people pursuing you, another day another dollar. They've trained for this in training scenarios and have been involved in pursuits in the field. They run code multiple times a week. Even if one of your pursuers was a rookie who got eaten up by the stress, there will be a dozen vets to take his place.
• Cognizance. Unless you've lived around and driven on your path of flight for decades, I can almost guarantee you do not know it as well as your pursuers. I drove a hundred miles a night, four nights a week, on the same few dozen streets in my beat. I knew every pothole and curbstone, every back alley and shortcut. Plus, supplementing my knowledge was dispatch, who had a real time, God's eye view of the situation, and who could foreshadow upcoming turns based on officers' GPS and current road conditions.
• Conveyances. Your chosen city of flight may have the rattiest squad cars in the country, but they have the distinct benefit of redundancy. Your escape vehicle is precious, because there is only one. Nuke a tire from hitting spikes or a pothole, and you're roasted. If a patrol car has a blowout, that unit will fall out and be replaced by another. If you think your car can outrun and outlast what will effectively be an infinite number of responding unit vehicles (when you account for interagency involvement), have at it; otherwise, you may need to rethink your day.
• Control. What is your flight plan - are you going to rely on top end speed on the open highway? Or are you going to try to lose responding officers in an intricate series of turns? You've got a tall order ahead either way.

1. First, if you've got something in your hands that can outperform Crown Victoria and Charger interceptors on the interstate, you're going to be relatively easy to spot - you won't be doing this in a stock Toyota. Second, you've got Little Brother to worry about - if you wax someone's doors at double the speed limit, they're probably going to call the police. Instant update to last known location and direction of travel, which allows retriangulation if you managed to create space. You probably haven't, though, because even with vehicles capable of impressive top end speed, there comes a point where the vehicle is so functionally light you can no longer safely operate it in real world driving conditions. My top speed running code in a Crown Vic was 134 mph, which was frankly stupid - the suspension was floating so badly that driving over a heads-up penny probably would have sent me into a terminal fishtail. This all means that, while you may maintain some semblance of distance between yourself and the point car, you're very unlikely to be completely leaving them in your sonic wake.
2. Alternately, if you're banking on turns (you got me, pun intended), you're going to have to keep your head about you. Stress has a tendency to get the better of your attempts at rational thought. Was that three lefts or four? This looks familiar, I'd better go the other way...was that a school crossing sign or a dead end sign? Is Main Street continuous this far south? Which side of the tracks am I on? Ah, now we're cooking with - what? Since when is there a cul-de-sac here? Game over - whether that consists of walking backward at gunpoint or feeling Cujo getting his nom nom nom on.