You are playing in a game show, and have won $1,200 so far. Now it's the final round, and you must choose to play double-or-nothing game. The host offers you to play the "Monty Hall" problem with 4 boxes, where only one box contains the "double" prize. You should choose a box, then the host opens two empty boxes and gives you the chance to switch boxes or to stick to your first choice. Assuming you choose the best strategy, what are your chances of doubling your prize? (You should enter a value is in the range 0-1)