The description for greed mode doesn't really explain anything... is there any specifics on it?
You hit a button to start waves of enemies every 8 seconds. The longer you survive the more money you make. You can hit that button again (1/2 heart damage) to throw in the towel at any time.
Most of your prizes will come from the shop, I believe (?) but there are treasure rooms, so not sure. Maybe you need to buy a key to use them when they repopulate? There's also boss fights, devil rooms, etc.
It seems like maybe enemies don't drop pickups, so all healing has to be done through the shop/items. Risk/reward - stay alive longer, make more money, become more powerful, stay alive longer...