The matching system on LuckyCrush works by using a unique algorithm to pair users based on their interests, likes, dislikes, and overall compatibility. This algorithm is designed to match people who have similar personalities and interests, while also taking into account factors like age and location. The system also allows users to customize their search by selecting certain criteria such as age range and sex preferences. Once a match is found, users are able to start chatting with one another in an anonymous environment. Reviews of the site have praised the matching system for its accuracy in finding potential matches that meet the user's needs.