DursunCan Ask your hosting support about enabling the LSCache module. I just had a similar problem on production site and it turned out that the module was disabled.
Fealist I have installed it.
When you test it, keep in mind that there is a lot going on in this forum and every time someone makes a post it clears the cache for the home page and the discussion that the post appeared in. If you arrive at a page that is not cached, that means you are the first guest visitor to the page since the last cache was cleared. In that case, refresh the page again.
I also plan to add a "Serve Stale" option.