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The expression "It's all in the wrist" or some variations thereof seem to mean something like "it all depends on how you move your wrist, i.e., how you play your hand".
First, please confirm if I got the meaning right.

Secondly, is this expression commonly used among native speakers?
If so, how come I'm unable to look it up in a dictionary?
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JungKimThe expression "It's all in the wrist" or some variations thereof seem to mean something like "it all depends on how you move your wrist
That's correct. It would be used literally for any action that requires manual skill, specifically the movement of the wrist.
I don't believe it's something I hear every day, or even every month. I can't even remember the last time I heard it -- probably years ago.

CJ
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Actually the origin of the word was introduced at stony creek brewery in branford ct as .... "It's all in the wreest!

The specific phrase is not in the dictionary; but the OED, for instance, cites phrases such as "wrist-play" and quotes someone about cricket, saying, "There is no real batting without wrist play." This is from the late 19th Century.

So there may have been something in the past about increasing skill by controlling the wrist, but no longer. It is now said only as a joke, usually after someone achieves something difficult by accident. For instance, in PeeWee's Big Adventure, PeeWee Herman falls off his bike, does a roll, and comes out unharmed and looking good. He then says, "I meant to do that." "It's all in the wrist" is a phrase like that, now used to cover accidentally succeeding.

It is also used for what is now called "humble bragging". The last time I specifically heard it used this way is in Tron. Jeff Bridges's character is playing the video game central to the plot of the movie, and he wins easily. He turns to the people gathered to watch him play and says, "It's all in the wrist." In fact, he is the author of the game, which is why he plays so well—but the game has been stolen from him, so for legal reasons, he can't reveal the game actually belongs to him.

humble brag
  1. an ostensibly modest or self-deprecating statement whose actual purpose is to draw attention to something of which one is proud.