Case studies
At the beginning of this chapter, we introduced three problems faced by Tom and Fang. These problems involve randomized algorithms and probabilistic reasoning and can be solved using the optimal stopping theory. Essentially, these problems focus on determining when to stop searching rather than what to search for. As case studies, we will analyze and solve these problems in detail, applying the concepts we have learned in this chapter.
Optimal selection in an online dating app
A new online dating app, Matcher, has been designed to help users find their best possible partners. The app operates similarly to a game, where users are presented with one potential match at a time, selected randomly from a pool of 
potential matches (the total number of matches is unknown to the users). Tom, our user, has a maximum of 
likes available (where
). His goal is to maximize his chances of finding the best possible matches using his limited likes.
When Tom opens the Matcher app...
