Stop the Clock

This is a game for two players. You can use the interactivity below, or you could print off a page of blank clock faces in Word or as a pdf.

Set the time on the clock to 6 o'clock to start the game.
Decide who will go first (player 1) and who will go second (player 2).
Take it in turns to choose to move the hands of the clock on by $\frac{1}{2}$ hour or by 1 hour. For example, player 1 could choose $\frac{1}{2}$ hour, so the clock hands move to 6.30, then player 2 might choose 1 hour, moving the clock hands to 7.30... etc.
The winner is the player who moves the hands exactly onto 12 o'clock.

Can you work out a winning strategy so that you can always beat your opponent?