Scarface: The World Is Yours/Cops
As you cause crimes, the border of your map will gradually be filling up white. This represents your Visibility to the police. Depending on what kind of crimes you're causing and how remote they are from the public, your Visibility will rise faster or slower. In fact, you can have massive gang wars without it rising it at all just because no public are around and it's off the road. Taking a machine gun into a bank and plugging a few people at the protective glass however, will get you plenty of attention. In addition to this, the police will be driving around on patrol responding to reports and if you're caught red handed your meter will rise immediately. Once the entire border is full you'll need to escape.
 Lose The Cops
Once you've filled your Visibility meter completely white, the cops will be after you, which means they will be trying to kill you. The aim therefore is to "Lose The Cops" and get out of the red ring that is now surrounding where you just were. Of course if you've got some police cars after you, you've got to lose those as well, which can draw out the chase. Perhaps the most annoying feature of Scarface is the fact that you have a timer to escape the police: you have the time it takes for the white border to deplete to get away from the cops, after which the game rudely tells you you're doomed, and no matter what you do you're going to die and you can't go into any menus. While this is a rather simple matter at first, each time you escape your Cop Heat goes up and it becomes harder to escape the next time.
 Cop Heat
Each time you escape from the police, or cause crimes under the watchful eye of the police or even kill a cop, it'll raise your heat. As your heat increases, the lengths to which the police will go after you increases. While at first you could get away just by going around a block, now you have to leave the whole area while the swat team is after you and tire spikes are set up. In addition to this, police patrols will increase, meaning there will be more police cars just wandering around the streets, which makes it a lot harder to get on with your business. Watch your heat meter though, because if it reaches the top there will be an indictment and the police will claim some, if not all your money to pay off their heat level.
 Dealing with Cop Heat
The main way to lower Cop Heat is to pay off Vice. Press , select Empire, then Heat, select Cop Heat and then press to pay to have your heat lowered. The Higher the heat and your reputation the more you'll have to pay.
There are other ways to lower Cop Heat. One is find a cop and holster your weapon (this will usually keep the cop from chasing you). Fast Talk him by using the meter to decrease your heat, for free, plus you'll get some balls to boot. Fail, however, and the cop will confiscate your weapons, drugs, and dirty money.
One final way to lower Cop Heat is to hire the Assassin. Completing her targeted hit missions will usually lower Cop Heat. However, she isn't available until you reach Reputation Level 5, at which point you may find paying off Vice a simpler solution.