Amy Tan has written a remarkable story about a young girl who must contend with two opposing cultures-- American individualism vs. Chinese emphasis on the group.
Invisible strength is the ability to restrain one's emotions and not cave to instant gratification.
Memei and her family change the rules and sacrifice a great deal since an individual's success is deemed as the family's success.
As the eNotes summary suggests, if Memei wants to express her individuality, she must isolate herself from her family.
Controlling one's emotions and showing discipline and resolve are the elements of invisible strength since they are not easily seen by others on the outside.
Knowing one's "enemies" and how they will react is more about observing behavior and developing a strategy which may help explain the conflict between Memei and her mother.
Meimei's mother feels that her daughter is ashamed of her, her family, and her race so she ignores her daughter which forces Meimei to choose between individuality and family.
The characters' actions are dictated by how they view the world and the strategies they employ to get their point across.
eNotes summary also discusses the themes in "rules of the Game."