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CSP
Freedom
Ink Cash
CSP
QS
Venture
I like hypotheticals like this, because it's an interesting frame for why you like particular products or why you find them valuable. Of my cards, these are what I'd keep and why:
3. Sam's Club MC: Since gas and dining are among my biggest monthly categories, having 5% and 3% cash back, respectively is good. While Sync isn't great at making a good looking website (and no app) and the card looks aren't eye-catching, it counts where it's important. Also, MC has good acceptance everywhere, whereas Discover and AMEX can be problematic.
2. Discover It: It's a de facto 2% card for the first year, and the rotating categories are a great perk. I've found the customer service to be excellent. I'm also quite pleased with my initial CL. I love their site and app; very well organized and informational.
1. AMEX BCE: It is my highest CL and lowest non-promo APR of the three CCs listed here. Their website and app are well organized (although I prefer Discover's) and customer service meets my needs. The AMEX Offers have resulted in lots of saving opportunities. Also, my 1998 backdate makes it my oldest CC.
Combine all Chase cards into a single 50K line.
Combine the Cap One cards into one card if available, otherwise use 15k Venture.
Combine BoA cards, if I cant do that then ill take my Discover as third.
I only have 3 so that answers your question....LOL.
But so I can play I'll say what I'd like to be approved for and keep...
Quicksilver
Sallie Mae
Amex BCP
Amex BCP
Double Cash
Barclay Ring (for if I ever need to carry a balance)