100 traders, 100 boxes

A math/probability problem I think is awesome and counterintuitive, and may be instructive about financial markets:

A hedge fund manager puts 100 traders in a room and instructs them:

"On the trading desk, there are 100 boxes. Each box has one of your names. You can go onto the trading desk and open any 50 boxes you choose, to try to find your name. If every one of the 100 traders in this room finds his or her name, you will each get a $1,000,000 bonus. If anyone fails, I will crush all your $100,000 BMWs to create my modern art masterpiece. You can devise a strategy before anyone leaves the room, but once a trader has opened the boxes, they must leave the trading desk exactly as it was before you entered and cannot communicate with anyone else."

Questions: Should they take the bet? Is there a correct strategy? What is the probability all 100 will each find their name?

A hint, if you want one, by copy and pasting the lines below.