Sure, here's a simple example of a game generator written in a single HTML file using JavaScript. The game generated will be a basic guessing game where the player has to guess a randomly generated number between 1 and 10.
To play the game, simply open this HTML file on a smartphone and it will prompt you to guess the number between 1 and 10. You will have 3 attempts to guess the correct number. After each guess, the game will inform you whether the guess was correct or not, and how many attempts you have left.
Please note that this is a very basic example of a game generator, and you can implement more complex game logic and a wider variety of games by expanding on this foundation.