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I refer to the old fable that if you set enough monkeys at enough keyboards for a long enough period of time, they will (through random typing), reproduce the "Complete Works of Shakespeare," or any other tome.

Is it likely that someone will "copy" someone else's "five consecutive words" through a random process? Or is that a high enough bar that it takes some "doing" to copy it?

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Re the "million monkeys at a million keyboards will eventually reproduce Shakespeare": as it happens, the existence of the Internet has proven that theory wrong. –  Lauren Ipsum Apr 5 '13 at 0:01
@Lauren: Some argue "Just give them some more time." –  SF. Apr 10 '13 at 12:01
@SF. But given Moore's Law, that time continually speeds up. We've had like fifty years of Internet time in the last decade. –  Lauren Ipsum Apr 10 '13 at 13:21
@Lauren: Typing speed is not regulated by Moore's law. –  SF. Apr 10 '13 at 13:27
@Lauren RE "million monkeys at a million keyboards" As it happens, elementary probability theory as proven that wrong. –  Jay Apr 18 '13 at 15:01

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I'm completely sure picks like "as he walked up to", "he screwed his eyebrows and" or "as far as I know" will happen notoriously but they don't constitute plagiarism because they are very common expressions.

Don't count conjunctions, pronouns, particles and prepositions in the "five word" count - you'll start getting correct matches, and they will be exceptionally rare. Include these "generic words" and you'll get a ton of false positives.

(my experience is with writing variations of "dissociated press" program: find a sequence of words repeating within the same text and cut the text there, continuing from the found match, so that it reads smoothly as a sentence but makes for nonsensical text, a run-on story pieced together from random pieces of a different story in a grammatically correct manner. Finding a repeating sequence of three words within a 130k words document was nearly impossible.)

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If we're genuinely talking just five consecutive words: yes, that could happen by chance.

But plagiarism is not just about five words in the middle of a 120-page thesis. It's lifting ideas, plots, characters, paragraphs, pages. See the Opal Mehta mess for an example of what's really plagiarism.

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Indeed, if someone was really "prosecuting" by a 5-consecutive-word rule, I think a would-be plagiarist could beat that by going through the text and substituting some pronouns and prepositions, rearranging word order here and there, etc, while still retaining the sense of the original. He'd have to be meticulous to make sure that he made at least one such change every five words, but in principle it would work. But I'd think by any reasonable definition it would still be plagiarism.

To take a trivial example: Winston Churchill famously said, "I have nothing to offer but blood, toil, tears, and sweat." I could write, "I have nothing to give but blood, toil, sweat, and tears." If I actually claimed that sentence to be original, I would surely be guilty of plagiarism. But it has no five consecutive words in common.

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