Less than 9
Let me think....4 cards for "low balance forgiveness" which I keep in a separate pouch and use once a month together to buy gas (either $0.99 per card or $1.99 per card).
4 cards up for tradelines (some overlap with above for when no tradeline has been sold)
Core cards for rewards, including rotating....that's another 4
Old cards that hold age of credit and churned cards that I simply haven't cancelled (probably 6)
Store cards opened to get big discounts (Dick's comes to mind, having saved several hundred dollars on a kayak and paddles)....
Amazon cards because it seems that I'm always getting a pop up to save $40 by applying for yet another amazon card (5).
On average, 1 card to get spend for sign on bonus.
Lots of sock drawered cards above. I only really actively carry 2 cards at a time. The rotating categories determine what those cards are.