The golden bisection number $ g=\frac12\left(\sqrt5-1\right)$ is famous as a mark of beauty in the history of art. It is also famous in mathematics, such as continued fraction and Fibonacci sequence of integers, {\it etc}. We find that in the two-player infinite games a lot of interesting results, where $g$ and some pair of numbers lying near to $g$ play an important role. We show four examples.