The posts you want to read are Graduation, site closure, and a clearer outlook on the health of SE sites and Feedback Requested: Design-Independent Graduation.
The main criterion is the number of questions per day reaching 10. When this happens, the Community Team reviews the state of the site, trying to determine whether there are enough active and reputation-empowered users for the site to hold a moderator election. If they approve graduation, then (from a post linked above):
- the beta label is removed
- elections are held
- migration paths are set up
- community ads are run
- a link to the site is added to the footer
...Then, as it becomes available
- the site gets their custom design.
- privilege thresholds are increased to graduated site levels
"beta" label is removed, and election is held. The site does not get its custom design at the same time; that takes several additional months (sometimes over a year).
Poker is nearing its 5th birthday, and is averaging 0.9 questions per day. I would not expect graduation within the next couple of years (or ever), unless something changes in the online habits of many poker players. But, as the post I linked affirms, the lack of graduated status is not a "black spot" -- the site still has a home on the Stack Exchange network.