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This example doesn't really answer your question, but it makes me think that "I Feel Lucky" doesn't account for that many searches.
This was a 2 word search that only brings a few hundred referrals a month, so I don't know how applicale it is to the more popular searches. But it was the only on that I could think of that even remotely applied to the question.
Surprisingly, spot #10 (if 10 per page) gets more than position #4. Something to do with being the last link before the next button, and the way humans read pages.
There is a whole science behind this that I suspect the PPC people have pretty good numbers for.
IE5 seems to send "http://www.google.com/" when I click the lucky button, so for a good test we need to include only browsers that send the redirecting URL.
I have only 3 matching hits from the last fortnight (I don't know if they always send the redirecting 'referer'):
MSIE 5.0 on Mac_PowerPC
MSIE 5.14 on Mac_PowerPC
"NCBrowser/2.35; ANTFresco/2.17" on RISC OS-NC 5.13