This phrase comes from card games, where having better cards means more chance of winning. He was born into a wealthy family, so the odds are stacked in his favor from the start.
Pro Tip 2/3
Advantage Nuance
It implies an unfair advantage, as though the situation was manipulated to benefit someone. Because the principal’s son is leading the project, the cards are stacked in his favor.
Pro Tip 3/3
Common Misuse
Don't use this phrase when someone has earned their advantage through hard work alone. She studied hard for the test; it's not like the odds are stacked in her favor.