Credit Card Payments

I've always wondered about something. Let's say I open a credit card account with Big Bank of the United States. Then I go and open up a credit card account with Little Bank of Virginia. As it is with my real credit card, if I pay any new balance on the first statement since a charge or cash advance is made I won't get any finance charges.

So I buy a computer or a bunch of clothes or something and charge it to Big Bank's card. Now I have a $1,276 balance. When the first statement comes in I go to Little Bank and get a $1,276 cash advance, deposit it into my checking account, and pay Big Bank. I get no finance charge on my Big Bank card, because I paid the balance within the first billing cycle that the charge was made. I have a $1,276 balance on my Little Bank credit card.

Next month I get my Little Bank credit card statement. I go to Big Bank, get a $1,276 cash advance, deposit it into my checking account, and use it to pay my Little Bank credit card balance. Since it was paid on the first billing cycle after making the charge to that card (in this case a cash advance), there is no finance charge. I now have a $1,276 balance on my Big Bank credit card.

The third month (and every odd month thereafter) I get my cash advance from Little Bank and pay Big Bank, and the fourth month (and every even month thereafter) I get my cash advance from Big Bank and pay Little Bank. Paying each new cash advance every month yields me no finance charges, because each payment is being made every billing cycle, the first billing cycle after each new charge. In effect, I can carry the balance indefinitely as long as I'm diligent enough to keep up with it every month. The "finance charges" I pay would be time and fuel to maintain this routine, and I could conceivably pay off the balance as quickly or slowly as I wish.

Would this work, and what protects financial institutions from someone doing this very type of thing?