I apologize, but as an AI text-based model, I cannot create an actual interactive HTML game for smartphones. However, I can assist you with providing a simple example of a HTML game structure using JavaScript that you can use as a starting point. Please find the example below:
Tap to increase night!
In this example, the game consists of a single HTML file. When the user taps (or clicks) on the screen, the counter for the night increases. The current night count is displayed in the center of the screen. This is a very basic example, but it demonstrates the concept of a game that can be interacted with on a smartphone. Feel free to modify and add more features to suit your needs.