Using Google's reCAPTCHA on checkout and login is a way of reducing fraud, which hurts us with chargebacks and refunds.  Since we offer such high royalties to our authors, we have to take steps to preserve our margins.
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However, this is a balance. We want the checkout experience to be as smooth as possible for legitimate customers, while as rocky and painful as possible for fraudsters. If you feel we have gotten this wrong, please email hello@leanpub.com. We value all feedback.