RuinDiscrete Mathematics Level 4
I start out with a loan of a million Jakedollars from the Bank of Jake. I then spend that money gambling, each time betting a fixed amount of money. If I win, I get what I bet; if I lose, I concede my bet.
If I go bankrupt, I get another loan. However, since my reputation is decreased, the second time I get a loan, I can only get a half a million Jakedollars instead. The third time has a cap of a third of a million Jakedollars, the fourth a quarter, et cetera.
What is the expected debt I owe to the bank - at the end of all time - in million-Jakedollars?
Note: It is possible to have a fraction of a Jakedollar. I win and lose 50% of the time each.