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Suppose that two players take turns coloring the vertices of a given graph Gwith k colors. In each move the current player colors a vertex such thatneighboring vertices get different colors. The first player wins this game ifand only if at the end, all the vertices are colored. The game chromatic number$\chi_g(G)$ is defined as the smallest k for which the first player has awinning strategy.  Recently, Bohman, Frieze and Sudakov [Random Structures and Algorithms 2008]analysed the game chromatic number of random graphs and obtained lower andupper bounds of the same order of magnitude. In this paper we improve existingresults and show that with high probability, the game chromatic number$\chi_g(G_{n,p})$ of dense random graphs is asymptotically twice as large asthe ordinary chromatic number $\chi(G_{n,p})$.

The game chromatic number of dense random graphs