Why is Waverly so eager to learn to play that she is willing to give away all her Life Savers?

Waverly begins the story "The Rules of the Game," an excerpt from Amy Tan's The Joy Luck Club, by saying that she learned "the art of invisible strength" from her mother. Later in the story, Waverly and her brother get a couple of charity gifts from a local church: her brother gets a chess board (missing two pieces) and Waverly gets some Life Savers. Once she and her brother begin playing chess, Waverly is drawn to the complex rules and the "secrets" she thinks are held by the game.
As Waverly begins to research the "rules of the game," she explains her fascination with chess: 

I also found out why I should never reveal "why" to others. A little knowledge withheld is a great advantage one should store for future use. That is the power of chess. It is a game of secrets in which one must show and never tell.

Again, it is the secret knowledge and power of the game that attracts and keeps Waverly's interest. There seems to be a connection between this and her opening comment about "invisible strength." Chess is a quiet game, but Waverly feels very powerful when she is playing because she feels her knowledge gives her an advantage. Waverly eventually abandons all other hobbies and pursuits to study and perfect her chess strategies.
However, Waverly's mother becomes very interested in her daughter's chess skills, and she stands over her and makes Waverly feel like she cannot concentrate. In public, her mother embarrasses Waverly to the point that Waverly tells her she should just learn to play chess herself instead of bragging about her daughter. Waverly doesn't understand how proud her mother is and only sees her mother trying to benefit from Waverly's own skill. At the end of the story, Waverly imagines her relationship with her mother as a chess match and thinks of strategies to overcome her. 
Waverly's relationship with chess allows her to feel more self-assured and gives her an identity separate from her family. Therefore, she certainly feels her trade of the chess board for the Life Savers was the right move.