What does Waverly mean when she describes chess as "a game of secrets in which one must show and never tell"? How can that strategy be used in life ?

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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.

I loved the secrets I found within the sixty-four black and white squares. I carefully drew a handmade chessboard and pinned it to the wall next to my bed, where I would stare for hours at imaginary battles.

Waverly is talking about chess. She loved the game and the studied the game all day. In fact, she says:

I studied each chess piece, trying to absorb the power each contained. I learned about opening moves and why it's important to control the center early on; the shortest distance between two points is straight down the middle...

The reason for this is obvious. She wanted to win. Therefore, she wanted to learn strategies of how to win effectively. Mastery over any field requires this devotion. Waverly had it this passion. 

As for how it can be applied to life, Waverly learned from her mother that any type of strategy could be used for life. In fact, as a little girl her mother taught her the "art of invisible strength," which could be used to win arguments and earn respect. So, from this perspective, she learned these secrets even when she was a child. At the end of the story, she faced her greatest challenge, her mother. This is how the story ends:

Her black men advanced across the plane, slowly marching to each successive level as a single unit. My white pieces screamed as they scurried and fell off the board one by one. As her men drew closer to my edge, I felt myself growing light. I rose up into the air and flew out the window. Higher and higher, above the alley, over the tops of tiled roofs, where I was gathered up by the wind and pushed up toward the night sky until everything below me disappeared and I was alone.

I closed my eyes and pondered my next move.

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