Purpose of last_entry_id for /stream/{sport}/odds ?

I cannot find documentation about what the last_entry_id should do when included as a query param for the /stream/{sport}/odds endpoint, and it's not doing what I expected it to do. Can you tell me what it should do, or when to include it?

Let's say I see events with IDs of 1111-1, 1111-2, 1111-3 being pushed through a stream. If I then start another stream with last_entry_id=1111-1 I would expect to see it start with events 1111-2 & 1111-3, but that's not what happens. So, I'm not sure how I'm supposed to use that query string parameter.

Thanks for your help.