# A Carnival Puzzle Suppose a carnival has games \(A_{1},A_{2}\), and exactly one must be played. Game \(A_{i}\) has: 1. A four-sided die with \(F_{i}\in\{1,2,3,4\}\) good faces. 2. A starter score \(S_{i}\in\{0,1,2,3,4\}\). Playing game \(A_{i}\) requires one to: 1. Roll its die exactly four times. 2. Exit the carnival with score \(\max(S,S_{i})+S_{3-i}\), where \(S\) is the number of rolls that landed on good faces. When should one play either game?