Choosing a correct algorithm design is not an easy task in designing solutions to solve realife problems. In this report we discuss recursive backtrack algorithm used to solve single player game problems called peg solitaire. We discuss the design, implementation, theoretical analysis and empirical analysis of the algorithm. We discovered that it is not easy to compare theoritical analysis with empirical analysis when using backtracking analysis in this given problem[2, 13]. At the theoritical analysis part we discuss other aspects that help us understand the algorithm better, they are best case, average case and worst case. We then try to prove that our theoritical analysis is true with use of empirical analysis. In the conclusion section we discuss that recursive backtrack is optimal for some cases but not for all(it is not a perfect design).