  In combinatorial game theory, the lower and upper bounds of the number of
games born by day $4$ have been recognized as $3.0 \cdot 10^{12}$ and
$10^{434}$, respectively. In this study, we improve the lower bound to
$10^{28.2}$ and the upper bound to $4.0 \cdot 10^{184}$, respectively.
