If this is inside a node view template, you should set the cache_ttl to 0 (or a few seconds). see http://ez.no/doc/ez_publish/technical_manual/4_x/reference/template_functions/variables/set_block
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The random article is shown on the front page, in a section set for news. The other elements may be cached, but not the news box - since a new article should be loaded foreach page reload.
So if I put a second cach block around my news container, and inside this I put the cache_ttl, then I should be turning off caching for just that part?
No it turns of cache for the whole view*, cache_ttl only affects view cache as you have on content/view, it will not affect cach-blocks in the view or in your pagelayout. This is why setting it to for instance 30 or 60 seconds might be enough for you, as in do you really need a new item on every single page reload? If you do, consider preloading something like ten random items at a time and use javascript to select one of them on every single load, or load the whole block with ajax or something.
*view: the content ($module_result.content) on your page that is relevant to the url your on, excluding dynamic headers, menues, footer and anything else from your pagelayout. Only content/view/.. ur's are cached with view cache, hence the full name of the cache "Content view cache".