Click fraud is the practice of deceptively clicking on search ads with the intention of either increasing third-party website revenues or exhausting an advertiser's budget. Search advertisers are forced to trust that search engines detect and prevent click fraud even though the engines get paid for every undetected fraudulent click. We find conditions under which it is in a search engine's interest to allow some click fraud. Under full information in a second-price auction, if x% of clicks are fraudulent, advertisers will lower their bids by x%, leaving the auction outcome and search engine revenues unchanged. However, if we allow for uncertainty in the amount of click fraud or change the auction type to include a click-through component, search engine revenues may rise or fall with click fraud. A decrease occurs when the keyword auction is relatively competitive because advertisers lower their budgets to hedge against downside risk. If the keyword auction is less competitive, click fraud may transfer surplus from the winning advertiser to the search engine. Our results suggest that the search advertising industry would benefit from using a neutral third party to audit search engines' click fraud detection algorithms.