Amex Blue Cash - keep a balance?

Has anybody worked out whether it is better to carry a balance on your Amex Blue Cash credit card? You get an extra 2 percent bonus on "everyday" purchases, and half a percent on others, if you carry a balance.

Does it benefit you to leave a small balance one month (even a dollar or so), and then keep paying it down whenever you can through the month (to keep the average daily balance down). Apparently you can make an online payment every 24 hours, and can pay even though the internet interface says you have a zero balance (I just tested it). You would incur some interest charge, but wouldn't the extra reward percentage more than make up for it?

I don't have much experience with carrying a balance on a card - I generally pay them off every month, so I'd appreciate it if anyone had any calculation or experience on this.

 

Hate to admit this, but we actually spend about $3000 a month. We put everything we can on there - utility bills, business expenses, etc. Probably only about $600 to $800 a month would be the "everyday purchase" stuff subject to the extra 2 percent bonus - the rest would only be the .5 percent stuff.

I think I'm going to try it next month. I'm wondering if I'd be permitted to pay the card down even more than I owe on it, in which case through most of the month I'd have no average daily balance at all.