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This question remarks that the SE way of counting the number of days in private beta is (or was) non-human.
But where is this statistic anyway? I can't find it anywhere on the (currently private beta) Politics.SE. Area 51 states it has been in private beta for 5 days. Does that mean it's going to be so for 2 more days? Or more?
A site is generally in Private Beta for 7 days. However, some sites have remained in Private Beta for a little longer in order to allow the committers enough time to actually build up enough good content to move to Public Beta.
This isn't something that happens automatically, so you won't see a statistic that says "5 more days of private beta" because the decision to move forward is at the sole discretion of the Stack Exchange Community Team.
If Stack Exchange feels that the site doesn't have enough great content to make a good impression, then they'll keep it in Private Beta and work with that fledgling community to help it build up the good content that it needs to be a viable Stack Exchange Q&A site.
As an update, the May 2016 "standard length" for private beta seems to be more along the lines of three weeks.
Retrocomputing went into public beta on their 20th day.
Language Learning was in private beta for 21 days.
Latin Language followed suit with a 21 day private beta.
Some sites seem to qualify slightly earlier (probably due to extremely high user-interest).
Etherium moved from private to public in a brisk 12 days (Jan 20 - Feb 2).
But even that was nearly double the 7-day count mentioned in the other answers.
It's going to be at least 2 more days.
Every site starts with a 7-days-long private beta. Most sites then move on to public beta after 7 days, but some sites stay in private beta longer depending on how they start out.
We review each site on a case-by-case basis, and we haven't discussed Politics yet, so right now I don't know which way that one's going to go.
(Come to think of it, I'm not sure if that number is updated if we decide to extend the private beta beyond the initial minimum of 7 days. One way to find out!)
