Asymptotic game chromatic number conjecture for random graphs

Let $G_{n,p}$ be the random graph on $n$ vertices in which each edge is present independently with probability $p$, and let $\chi_g(G_{n,p})$ denote its game chromatic number. For a constant $\eta>0$, assume that $p\leq 1-\eta$ and $np\to\infty$, and write $b=1/(1-p)$. Asymptotic game chromatic number conjecture. With high probability,

$$\chi_g(G_{n,p})=(1+o(1))\frac{n}{\log_b np}.$$

The conjecture proposes the asymptotically sharp value of the game chromatic number in the stated range of $p$, improving the paper's upper and lower bounds, which differ only by a multiplicative constant. Its status is not resolved in the supplied source.