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We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above d_P, so that when the degree of the graph that defines the game has a degree d > d_P then there exists a polynomial time algorithm that solves the game with high probability when the number of nodes goes to infinity. We further propose the SWCP (Self-Winning Cycles Propagation) algorithm and show that, when the degree is large enough, SWCP solves the game with higharXiv:2007.08387v1 fatcat:ybur6jrpvjfgrn4z3l6vphucj4