# The Artifact Rolling 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?