You're pretty much on the money. The only awkwardness to the sentence is the ambiguity (to me anyway) between you looking at some random guy 3 times or looking at three random guys twice each. If you are referring to one random guy I would go so far as to use "triple take".
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Henry74Three times today I did a double take on some random guy in the street taking him at first for a famous chess player.That's fine.
Henry74Also, is "taking him" correct, or should it be "taking them"?Him is correct if you are talking about one man.