Don't give a jack

Hi I am new to this site and I'm not really comp lit!
Does any one know the meaning of the saying "I don't give a jack"?

Is it possible that the phrase was "I don't give jack"? That would mean, I don't care anything, I don't care at all. Perhaps the phrase was written by someone not entirely at home with it. Normally, "jack" in a phrase like this is not a commodity measured in units, like "a jack." I don't myself use or hear used the word in this meaning, but I would much more expect to see, "I don't care jack."
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The whole phrase is: I don't give jack sh*t. But I don't know why "jack."