Intrusive DRM is the least effective method one can do, and we learn that lesson time and time again.
The first and foremost, biggest way to combat piracy, and I may get some hate for saying this, is basic, consumer friendly within reason DRM. Disc Checks, one time online authentication, Steam and the like. Something that means that if you want a pirated copy, you have to get it from unsavory places that may be less then 100% reliable. Once you reach this point, however, you might as well stop, because your game will be hacked. That't a fact of life. All you can do is prevent yourself from losing so much as a significant number of would be buyers.
The second most important step is customer relations. Foster a healthy community that respects you by making long term decisions over short term ones. Pirates tend to be tech savvy and very good at justifying there actions behind some bogus idealism. They will appreciate a company that behaves in an upright manner, and are more likely to either buy a game after trying a pirated copy, or not download a pirated copy to begin with. Yes, there are some exceptions, particularly with some Indie games, but these indie games usually have 0 protection in place.
Thirdly, make demos. Its not as universal as pirates like you to think, but a lot of pirates do pirate a game in lieu of a demo. Also, if a pirated game is the replacement for a demo, then theres a good chance that these skilled justifiers will come up with a reason why they can keep playing the game despite it not being worth paying for.
Fourth, Incentives. Provide a service that makes buying new better then pirating. Even a tiny bit better will discourage piracy HUGELY. If it inconveniences the paying customers though, your moving one step forward, 2 steps back. The company that discovers a cost effective incentive system will be the company that takes the biggest chunk out of piracy. It won't be the company with the most airtight DRM (And by airtight, I mean a colander instead of a rope tied around a puddle.)
Fifth, outside the box solutions. You can't rely on these but they may help. Rocksteady did this by releasing an unplayable version of Arkham Asylum. Convenience of Digital Distribution might make people forget about downloading. Other social tools, when handled in compelling ways, give a reason to not pirate. The Free 2 Play model just doesn't allow Piracy really. You can't use these things in every game, but they can help in the right circumstance.
Sixth, and this is more a do not thing, don't just rely on Multiplayer to discourage pirates. Some games don't need multiplayer, and tacking crappy multiplayer on at the last second is...well, see point 2.
And lastly, figure out a better measure for piracy. Common Sense dictates that every download is NOT a lost sale, since it makes no sense that every person who will get the game for free would pay 60 dollars for it. We have been looking at this problem for ages, and publishers keep pulling numbers out of their asses. Come up with a realistic way to measure profit loss, since profit is your concern, and all the bad ways of dealing with the problem will fall apart.