If you bid on 'widget' (with no negative keywords) you should appear for everything widget related, yet if I search for 'widget 10 years' (it seems to be a 3 word and a number thing) then the widget ad doesn't show at all.
It seems if the search term is 3+ words, or if it contains a number at all, then the one word widget isn't showing (at least my categories widget).
Yet for two word broad match phrases, like 'widget info' if I search for 'crazy widget more words info with more words' then the ad shows.
The broadmatch options seem to be built for 2 phrases, and I'm finding that one word terms, which should be a no-no to advertise on as they just aren't targeted at all, if you include a very good negative KW list, seem to be a viable option right now (of course this could change with the next update...)
In this case, I felt the 1-word was important,
because it was not incredibly broad (not that many
scientists in the world), and I needed to
reach people who probably weren't coming to
Google to specifically look for this obscure
product.
I finally managed to combine the 1-word with some
other things that pulled the overall CTR up above
minimums.
Also, I was yesterday starting to experiment in a
new area, and decided to just see how bad the obvious
1-word ad would be. To my surprise, at least in a short
test, the CTR was well above minimums, and the actual
search terms (gathered from web logs) were all relevant.
I'll probably combine that keyword with a list of negatives
and keep using it.
Maybe all my areas of interest are obscure enough that
1-word ads are fine :-).