With Citi it depends on many factors and is not always cut and dried. I received a 6k SL on both my AAdvantage and Double Cash to start.
After having my Double Cash for about 9 or 10 months, Citi increased the limit to $7,400 with a SP. That's a fine limit for many people.
Citi also decreased my initial 18.9% APR on AAdvantage down to 13% over a period of just five weeks and several requests. I followed ihcole's example in doing that - and got the rate down to 13% on a five-week old card!
I think another factor is that here on myfico, we have a different outlook and perspective on credit than most. Most regular consumers do not expect a 15k starting limit on a card, nor are they asking for 3x CLI's on cards. So it's important to realize and understand the perspective and viewpoint we operate from. 
If you read the threads on our board, many Citi SP CLi's tend to be in the range of $1,400- $1,900. That would be a fine CLI for many consumers, but from our perspective, we can get used to seeing larger numbers, so some of us are unhappy with those amounts.
Citi indeed does not like too many new accounts - and they consider new accounts as far as the last 12 months in some situations. I do think that many people who wait 10-12 months with no new accounts will see some CLI or new card progress from Citi (as long as they didn't add 20 new accounts just prior to that period!).
Other factors including income and AAoA also come into play. Remember that others on the board with higher Citi limits may have a higher income, or a 20 year AAoA.
I receive continual balance transfer offers on both of my Citi cards for 18 month BT's with really good fee rates - just got one for 1% fee. My AAdvantage is only 4 months old, so I was pretty surprised.
I'd like my Citi cards to be higher and have 12k-15k limits on each card eventually. I just know with Citi that it will take some time.
Very true Hum!
In my limited experience with them I've learned if you really want a substantial cli. You have to be willing to take a HP. Not written in stone of course, but most have gotten decent CLI's once they have some history with Citi.
The Citi DC went from being my least used card to the household's most used with a REAL limit increase.
Definitely one of my favorites!
I've looked at the other offerings. For me nothing stands out for my lifestyle.
I'll leave well enough alone with a single card, while badgering them for another major limit increase in 4 months, till I hit that magic number.
I say no. Dividend opened in '14, around $4k, opened+closed+opened many more cards behind it, yet it grows.... Magic Citi beans growing? All auto..
