The sentence "I'm gonna cut me a piece of cake" strikes me as something the average redneck might say, and I have no trouble accepting it as a colloquialism. On the other hand, "I'm going to cut myself a piece of cake", which should technically be more correct, doesn't seem to make any sense. In fact, I don't think I would ever use it, and I don't recall ever hearing any such sentence either (outside of the use of "pour" in "I'll pour myself a drink".) Assuming that my brain isn't "malfunctioning" again (please tell me if you think it is), what makes the former sentence more "acceptable" (note the use of quotes) than the latter?

Thanks in advance.
What exactly is it you don't like about "I'm going to cut myself a piece of cake"? There's nothing wrong with this.

I don't think there's anything wrong or unidiomatic with "I'm going to cut myself a piece of cake," except that for a split second you leave your listener wondering whether you are about to engage in self-mutilation. "I'm going to get myself a piece of cake" or "I'm going to serve myself a piece of cake" would eliminate that brief period of suspense. I could certainly imagine someone saying "It's almost New Years, and my diet starts at midnight. In the meantime, I'm going to cut myself another piece of cake!" or just
"I'm going to cut myself a piece of cake -- can I get some for you too?"
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Thanks for confirming my fear. It would appear my brain IS malfunctioning after all. This is precisely what I meant when I said I that I kept losing the ability to tell idiomatic uses from unidiomatic ones. Even though I appreciate literature and read an average of 10-11 books a month, I keep forgetting how to speak - literally! Using language to communicate has never been natural to me, and probably never will be. I guess I'm more of an abstract thinker... Still, I'm sure you can imagine how inconvenient it is.

I'm not sure why "I'm going to cut myself a piece of cake" seemed so odd to me... Maybe because I would more likely say "I'm going to get a piece of cake" or "I'm going to help myself to a piece of cake"... Also, for a moment, I was under the impression that only "pour myself a drink" was correct and that "cut myself" and "slice myself a piece of cake" were not... Go figure! In case you're wondering, I gave up trying to understand how my brain works a long time ago...
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I hear someone say "do you want me to cut you a piece?" And that gives me the shudders. I have been asking to rephrase it but the speaker finds nothing wrong with it. Like you wrote, I think the ordering of the words can mislead the hearer mid-sentence.