Up to how long the judge can give you to leave the country after requesting voluntary departure?

If you request voluntary departure at a master calendar hearing before an Immigration Judge, the judge can grant you up to 120 days to voluntarily depart the United States. While most judges routinely grant the fully 120 days, the length of time is discretionary and set by the judge. You may be asked to pay a $500 voluntary departure bond with ICE within 5 days of the judge's order and provide valid travel documents to your home country.

There is a maximum period of time the judge can give you, but no minimum. The question is what benefit you would get from getting an order of voluntary departure as opposed to simply leaving the U.S.