Many technical approaches for detecting and preventing cybercrime utilise big data and machine learning, drawing upon knowledge about the behaviour of legitimate customers and indicators of cybercrime. These include fraud detection systems, behavioural analysis, spam detection, intrusion detection systems, anti-virus software, and denial of service attack protection. However, criminals have adapted their methods in response to big data systems. We present case studies for a number of different cybercrime types to highlight the methods used for cheating such systems. We argue that big data solutions are not a silver bullet approach to disrupting cybercrime, but rather represent a Red Queen’s race, requiring constant running to stay in one spot.