wat? In what world do you live in where Facebook has a huge advantage, let alone any advantage, over Google who has been tackling the problem of click fraud for 10+ years. FB doesn't even do a very good job of detecting fake accounts (I have a few active ones of my own).
The problem of detecting fake accounts is different from that of detecting fraud. Let say you have a probabilistic model that assigns a score to an account based upon how likely it is to be fake, what do you do with this information ?
To detect fake accounts you'd set a threshold which if you drop below a certain score you'd start to suspend accounts Lets say you're right 99% of the time, that still means you're going to suspend hundreds of thousands of legitimate users. Suspending a real account is far worse than letting a hundred fake accounts continue to exist, so Facebook errs on the side of letting fake accounts continue to exist (but they do for example delete likes from what they suspect to be fake accounts as that has a much smaller false-positive downnside).
However to detect click-fraud you can look at the scores across the range of accounts that are clicking on an ad. If you detect a high amount of activity from a group of users who are at your threshold level for being "fake users" you can apply a lot more sophistication to your click fraud model.