AbstractWe present a purely combinatorial proof of Alon and Tarsi’s Theorem aboutlist colorings and orientations of graphs. More precisely, we describe a winningstrategy for Mrs. Correct in the corresponding coloring game of Mr. Paint and Mrs.Correct. This strategy produces correct vertex colorings, even if the colors are takenfrom lists that are not completely fixed before the coloration process starts. Theresulting strengthening of Alon and Tarsi’s Theorem leads also to strengthening ofits numerous repercussions. For example we study upper bounds for list chromaticnumbers of bipartite graphs and list chromatic indices of complete graphs. Asreal life application, we examine a chess tournament time scheduling problem withunreliable participants...