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Looking for an English equivalent of the Chinese noun 心眼 if there is any, or the best way to describe it.
If someones has 心眼, then you can say they are sly.

But, what do they have if they are sly?

To try and describe the word's meaning, it is a noun that means something like figurative 'brains', 'sneaky' or 'trickery'. If someone is said to have bad 心眼, it means they can think up trickery and be evil to deliberately sabotage someone, or at least to work a situation to their advantage/avoid being disadvantaged. 心眼 on it's own doesn't necessarily have to be evil, it can also be to protect oneself. For example:

• Say you are going to a party out of necessity but you don't really want to go. In Chinese, if you had 'a little 心眼'(多一点心眼), you can say you still have things to do, and leave early.




• An example of bad 心眼 could be where a person deliberately runs late when they need to give another person a ride, or fixing a deck of cards before a game so that when it is dealt, specific cards to to a specific person.




• If a person has no 心眼, it means they are too naive and easy to take advantage of. In English, you can say they have no brains.

What I want to do is, rather than having to say "A person is sly" in the nominative case, I want to say "A person has no ___" in the accusative case (I believe they are in the right cases, please correct if this is wrong).

To me it sounds you're describing guile:

clever but sometimes dishonest behaviour that you use to deceive someone:
The president will need to use all her political guile to stay in power.

He is a simple man, totally lacking in guile.
-- Cambridge Dictionary

Guile is the quality of being good at deceiving people in a clever way.
His cunning and guile were not attributes I would ever underestimate.

I love children's innocence and lack of guile.
-- Collins English Dictionary

The word you are looking for may be cunning. A person with cunning can be sly, clever, sneaky or scrappy. It's considered neither inherently positive or negative, much like the Chinese phrase, and it captures that idea of someone who finds an unexpected way to turn a situation to their advantage.

However, it's usually not correct to say that a person has no cunning. In the case you describe, where someone is too easily tricked or taken advantage of, they are described as being gullible.

That noun is most likely smarts. It can be used both in positive and negative sense.

ODO:

smart
NOUN
2 (smarts) North American informal

Intelligence; acumen.

‘Nikki was intelligent while Jack had a different type of smarts.’

‘He has great vision and tremendous smarts in terms of knowing when to
fair catch a ball and when to let it bounce.’

I was first going to go with adroitness or savoir-faire, but I think simple "cleverness" might be better.

clever

1.c. Crafty; cunning

2.a. Exhibiting ingenuity or imagination; creative or artful.
b. Witty; amusing: an evening of clever repartee.
c. Characterized by
cunning or shrewdness: clever manipulation of public opinion.
American Heritage Dictionary

1.b : mentally quick and resourceful
a clever young lawyer
2 : marked by wit or ingenuity
Merriam-Webster Dictionary

Finding an appropriate word like this is a bit tricky, because many have a negative tone, as if it's a quality usually used for deceit. Words like artfulness and craftiness both have these. However I think cleverness is pretty neutral.