The Chase is a television game show (2009-present in UK; from 2013-2015; 2021-present in US) that consists of three rounds and three contestants. This presentation explores the probability of a contestant "being caught" by the chaser in the second round of the game. A solution will first come through the use of Markov chains. This result will be improved upon by a method that reveals a connection to a generalized version of Bertrand's Ballot Problem.