HTML games run in a web browser and are commonly built with Twine (often the SugarCube format) or custom JavaScript. You extract the download and open the HTML file, which works on Windows, Mac and Linux, and often on Android too.
Saves are kept in browser storage, so clearing site data or switching browsers can wipe your progress. Use the game's export or save-to-disk option when available. Many HTML games load images or videos from separate folders, so keep the directory structure intact. LustFever keeps each listing on the latest version and links to the developer.
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