“have a deep pocket”is "a person who is very rich"??
i ever once leant a slang"have a deep pocket" from the new concept english. and the teacher said that mean"a person who is very rich",but an american netpal doesnt know what it is at all. so if that one is really a authentic english slang???

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Not necessarily very rich. But he has a lot of money to spend.

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'Deep pocket' is an American slang term for someone who has extensive financial resources or great wealth (very rich!). It is most often used in the plural 'deep pockets' and with reference to big companies or organizations. 'The American tobacco companies have deep pockets.'
Although it can be used in reference to individuals for example Bill Gates, Donald Trump etc
 'Of course he can afford a yacht, he has deep pockets.'

We also say that someone has 'short arms' and 'deep pockets' to describe someone who is rich but miserly/ mean with money.

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Yes, but I know the phrase as "to have deep pockets".

Not everyone knows or uses the same slang. ;)