Delivery room is private. Recovery room may be shared depending on the demand of the hospital itself. But, I would say it's even rare to share a recovery room. Ask at your next appointment, they might even be able to schedule you for a tour of L&D.
I googled this is what I found: "as far as mt. sinai goes, it's an older hospital, so that means less rooms, which also means that standard rooms have 2 beds. by day 2 i couldn't take my roommate anymore, and i paid for a private room...priced like i was staying at the ritz (lol) but worth it".
What does your insurance cover? Mine always covered a "semi-private" room. With DS it was no biggie because they only had private rooms. With DD, there were 2 beds, but no one else in the hospital at the time, so I had it to myself. We had an early release.
For my labor & delivery, I always was in a private room. Semi-private was for recovery.
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