In reference to <a href="http://utlt.keenspace.com/d/20050419.html">this strip</a>, there seem to be two kinds of toy cranes: Fair and unfair. The difference is that the unfair ones do not have the strength to hold a toy all the way out.
Assuming:
1. Ben runs a fair game.
2. The machine is loaded past the point where toys are attainable (from the pictures, it is).
3. guest isn't stupidly trying to get a covered toy over and over again.
...the guest should be able to a stuffed animal out of the machine over the course of a night. Maybe not the one she wants, but an animal.
(Good joke nonetheless, don't get me wrong. Bad luck <em>could</em> be a factor even with a fair, loaded machine, it would just have to be really bad luck.)
My brother has hundreds of these stuffed animals and is something of an expert on the subject of toy cranes.