Time traveller story set in Australia where the ending is determined with a roll of the dice

I’m looking for the title and the author of a young adult book set in Australia. I read this in the 1980s or 1990s so it was published before 2000 and took place

I do not remember the overall arc of the plot, but I remember some specific story details:

• The book takes place in Australia in the 1970s, 1980s or 1990s
• The protagonist is filled with dread over the thought of a global nuclear war
• One of the characters is a time traveler who reveals that he or she was actually sent back in time to study Aboriginal culture. In the book time travel was an imprecise technology and
  the character is quite surprised to have arrived while Western civilization is in existence. The character had expected to land somewhere in the 60,000 years of Aboriginal culture rather than the Western post-WWII culture since "your civilization doesn’t last very long" (I recall the character saying something to that effect).
• The protagonist or another main character is constantly rolling dice to make decisions.
• The book has at least 2 endings and the canonical ending is chosen by the reader casting a die.

Any help identifying this novel is greatly appreciated!