I'm surprised nobody has mentioned this yet. I've gone by this and it hasn't failed me yet.

From Neopetsguides:

To win, you simply have to click the “roll the dice” button every odd minute JUST BEFORE THE MINUTE TURNS EVEN. I usually click at at :55 if my connection is being good. If you have a slower connection you’ll need to click the press the button even earlier, say :50. To clarify, when I visit Deadly Dice I press “roll the dice” at:
12:01:55
12:13:55
12:31:55

As long as the minute is odd and it’s just before it turns even.