This is follow up question to How much money can we make?
My five friends and I used to loan each other money all the time. But over the past several years we have moved apart. We don't trust PayPal, banks, or the postal service so transferring money over such great distances is extremely difficult.
Fortunately, we have discovered a set of 6 magical fax machines! While ordinary fax machines are unable to fax money, these magical fax machines can*. And like any fax machine, it is possible to retrieve the documents you put into it (including money) even while the receiving fax machine produces a copy.
But these fax machines are not perfect. Each machine can only send one fax to each other machine (so 5 faxes per machine, for 30 faxes total). These faxes can be for any amount of money, but once a fax is started it cannot be interrupted.
For example, if I have \$30 and my friend has \$40, then I can fax my money to my friend and then I will have \$30 and my friend will have \$70. If my friend fax me back, then I will have \$100 and he will have \$70, and neither of us can fax any money to each other any more.
Our years of traveling have left my 5 friends and I broke. Each of us has exactly $1 and one special fax machine.
Working together, what is the maximum amount of money that the six of us can create?
*and there won't be any problems with the fact that all your bills are copies of each other. It's magic
This time you are trying to maximize your money instead of maximizing sum of the money and your friends are of course trying to help you.
How much can you make at most?
Note: You may need to use computer programming or you may not.