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If you want to win there are few moves you must do which the computer knows already so if you go second you cannot win. Since the maximum time change is 60 minutes so if you can get it to be the computers move 75 minutes before 12 then no matter what the computer does you will always be able to reach 12 since since if they do 15 mins then you can do 60 mins and you can always win if you go first.

To get to 75 mins before twelve (10.45) you must first get to 9.30 (75 mins before 10.45) and before 8.15 then 7.00 and so on.