To play your cards right means to work or negotiate correctly or skilfully.
To do the correct things to achieve a desired result.
If you behave in the right way, you might succeed at something.
1. Damian played his cards right and got a promotion at work.
2. If you play your cards right, you can get whatever you want.
3. Let’s play our cards right so that we can rob the painting for millions!
4. You’d better play your cards right if you want to get your father’s inheritance.
aim, attempt, compete, do one’s utmost, drive, fight, go all out, go the limit, labor, leave no stone unturned, make every effort, push, seek, shoot for, strive, tackle, take on, try hard, work