  Let $G$ be a graph with $n$ vertices. The {\em hat guessing number} of $G$ is
defined in terms of the following game: There are $n$ players and one opponent.
The opponent will wear one of the $q$ hats of different colors on the player's
head. At this time, the player can only see the player's hat color at the
adjacent vertex, and communication between players is not allowed. Once players
are assigned hats, each player must guess the color of his hat at the same
time. If at least one player guesses right, then they will win collectively.
Given a graph $G$, its hat guessing number $HG(G)$ is the largest integer $q$
such that there exists a guessing strategy guaranteeing at least one correct
guess for any hat assignment of $q$ different colors.
  Let $\mathcal{G}(n,p)$ denote the Erd\H{o}s-R\'{e}nyi random graphs with $n$
vertices and edge-chosen probability $ p\in(0,1)$. Alon-Chizewer and
Bosek-Dudek-Farnik-Grytczuk-Mazur investigated the lower and upper bound for
$HG(G)$ when $G\in \mathcal{G}(n,1/2)$, respectively. In this paper, we extends
their results by showing that for any constant number $p$, we have $n^{1 -
o(1)}\le HG(G) \le (1-o(1))n$ with high probability when $G\in
\mathcal{G}(n,p)$.
