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In this paper, we analyze Birds of a Feather (BoaF), a perfectinformation one-player card game that is the subject of the 2019 EAAI Undergraduate Research Challenge. We prove that the generalized N × N BoaF game is NP-complete, and then explore the one million deals in the 4×4 BoaF testbed. We present several graph-theoretic algorithms to prove that 1880 of these million deals are unsolvable, and conclude the paper with two search algorithms that efficiently show that all of the remaining 998,120 deals are in fact solvable.