How is a "gray" IP address converted to a "white" one?

Question

Computer networks

Greetings. I am engaged in studying of networks, in passing moonlighting as the small administrator. Faced with such situations. The user needed to set up a game server for friends at home. The user via DHCP came to the WAN port "gray" IP - 10.1.0.7, which was NATized by the provider to white 109.167. (etc). It was decided not to bother with VPN, Hamachi and other similar services and connect the "external" IP service. Usually, after that, an external IP immediately comes to the WAN port, but, to my surprise, the "gray" IP remained, but 2ip.ru now shows a different IP address (different from the original 109.167 ..). And everything works well, on the router port forwarding is done on the "gray" IP 10.1.0.7, and from the Internet the server is available via external IP. Actually the question how and why does the provider do it? What is the advantage of this method instead of the traditional issuance of a "white" IP on the WAN port?

Answer 1

It's just how the provider's network is organized. It has white ip addresses on the border device (border), and NAT 1: 1 is made in your direction for the purchased white ip