Apparently there's a subset of American-English speakers that would pronounce "caught" as "kaat". I've always heard it like a longer/smoother "cot" though.
I'd say a good first guess is the "a" in "about" instead.
Yes, in my dialect of American English (raised in Southern California by parents from the midwest), "cot" and "caught" are pronounced almost identically.
I was also raised in Southern California, and both my sisters and I—all born in the 1950s—have had complete cot/caught merger since childhood. The local friends our age whom I surveyed informally about the distinction in 1975 or so, after I learned about it in a linguistics class in college, also had the merger.
Our parents, who were born in the 1920s, both made the cot/caught distinction. Our mother was from the midwest, but our father grew up in the same Southern California city as we did. This suggested to me that, with respect to at least this one phonemic distinction, our language acquisition was influenced more by our peers than by our parents.
I should note that my sisters and I were initially flabbergasted that anyone pronounced those words differently and had trouble hearing the difference, while our parents were upset to learn that we pronounced them the same.
That's also how it rhymes in northern Illinois (Chicago/Rockford/Quad Cities). I've never pronounced "cot" and "caught" alike. Using different pronunciations is a pretty good indicator that someone came from the Chicago area.