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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.
I remember the phrase "it's all in the wrist" from a Rock'em sock'em robots commercial probably 50 years ago. They also said, you knocked my block off
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So I just heard a quote from the TV show In the Dark where one woman says - “Bring a lesbian sounds exhausting”. And the other woman responds with - “You know, it certainly is on the wrist”.

I tried to look up what “on the wrist” meant exactly but I can’t find anything online… It’s not the same as “in the wrist” most likely though but I’d like to know what both these expressions mean! Does anyone know? Thanks!

apple piano 823I tried to look up what “on the wrist” meant exactly but I can’t find anything online

And no wonder. What she said was short for "It certainly is exhausting on the wrist", which is not very good English. Things are not exhausting on things. She confused the expressions "to be hard on something" and "to be exhausting for something". She was making a quip, joking that there are behaviors that lesbians engage in that require a lot of wrist action. What she was referring to I don't know, and please don't tell me.

apple piano 823It’s not the same as “in the wrist” most likely though but I’d like to know what both these expressions mean!

"On the wrist" is not an expression. "In the wrist" only occurs in "It's all in the wrist", which has already been explained. That involves a specific definition of "in" that will not appear in every dictionary. In fact, it is not in MW or the AHD online. It is the "in" you see in "the proof of the pudding is in the tasting", meaning that it is only by means of tasting the pudding that you can judge it.