I would do one of several things.
1. Implement a relatively simple form of detection, but don't check it until late in the game. Then, in the middle of an epic climax, disallow a crucial move that makes pirates unable to beat the game.
2. Don't use any DRM for single-player, but add things like pre-planned DLC and multiplayer for those who authenticate.
3. In a pure effort to curb the day-one piracy method, use some convoluted and new restrictive system that disables internal game features and divides its efforts across the code, requiring internet access on launch...but then include a contractual obligation on the game's website that all that DRM WILL be removed, no net connection required, exactly two months after release.