As a parent also, I think it simply varies from child to child. There is a point in time between vision developing and object permanence being learned where peek-a-boo is absolutely magic.
Peek-a-boo is a ton of fun with infants but I don't buy the explanation that it has to do with object permanence. At the same stage where peek-a-boo is hilarious my kids have also each been perfectly capable of watching me hide something and then going looking for it.
