the issue is create by caching the page. And as PHP is used to create the random text, a caching plugin is not able to reload it.
It would be nice, if you could find a way, how to deal with it.
So long, i will bypass the issue by:
1 .outsourcing the “what can i draw”-generator to a unique page.
2. set a link from the post to the new page
3. leave the cache on the post
4. deactivate the cache on the generator page