So long as you've got X dollars in your account you can write checks for X dollars.
"Well, DUH." you say.
Perhaps I haven't been clear.

You open accounts at Banks A and B. You put some arbitrary amount of money in one of the accounts: $1000 in Bank A. You then write a check from Bank A to Account B for $1000 and go deposit it in Bank B. Bank B queries Bank A, confirms you have $1000 in your account, and credits Account B $1000.
"Great, you just transferred $1000 from A to B. So what?" you say.
Actually, no, you haven't.

Until the check from Bank A to Account B clears you still have $1000 in Account A. So, after you deposit the check, but before it clears, you have $1000 at Bank A and $1000 at Bank B. So, you write a check from B to A for $1000 dollars and go deposit it in A. A queries B, confirms there are sufficient funds, and credits A. You now have $2000 in A. You then write a check for $2000 to B and deposit it, giving you $3000 in B. And so on and so forth with a geometric bounty of phantom gains.

Check kiting in and of itself isn't illegal in many places. The crime is committed when you try to use that inflated account balance, I.E. you bounce your account balance up to 70K and then go buy a BMW and skip town. If you leave the inflated balances alone eventually all the checks will clear and you'll be back to your original $1000.

To say it isn't necessarily a crime doesn't mean it won't get you into trouble, of course. Transactions above a given amount are flagged and accounts with too many flags are tracked. Soon enough you'll be invited in to discuss your account activity.

Why bother?
Account balance and throughput plays a fairly large role in credit ratings. So while you can't use that imaginary $70,000 to buy a BMW, you could use it and the half million dollar throughput to get a better rate on financing the lease for a BMW.
Interest. Whether this will work for you depends on how your bank calculates your account balance during a given cycle. Inflate your balance at the right times and you recieve the interest on the inflated balance and all the books balance properly.

There is a question of fairness, of course.
Getting easy credit and then defaulting on it will be its own punishment, of course. If you meet all your obligations, then there should be no complaints.
In the second case the bank gets to make money off your inflated balance as well. Say you get 2% on your account... The Bank is allowed to loan out some portion of your account and charge interest on that loan. What portion and how much interest is controled by the FED. Let's say 7/10 and 6%, respectively. So, of your $1000 the bank can loan out $700. they get 6% of 700 and have to pay you 2% of 1000... giving them a net of $22. If, OTOH, they use the 70K figure they can loan out 49K and so get 6% on that then have to pay you 2% on 70K and still net $1540.

There is of course no necessary reason Accounts A and B need to be owned by the same person, or even that there only be two accounts. With sufficient logistics and trust a network of accounts could perform a complex, variable closed loop of transactions in which no one account or individual does anything to attract attention.
Keep in mind that check kiting type behaviour happens every time a check is deposited. Until it clears, the money is present in both accounts. For a given account it is only randomly that this phantom cash is present when interest is calculated, but at any given time there are hundreds of millions in phantom cash in the system.

Participate in your own manipulation for fun and profit.

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