When should the troops come home?

The day Saddam is found, I guess. The trick is, of course, they aren't really looking for him. So, in addition to forcing the soldiers into an hour or two of arabic language training EVERY SINGLE NIGHT, would be to put them on the track of just hunting him. Everyone else should go home as civilian replacements (police) can be found. America doesn't have such police. So we are kinda fucked.