Jellyfish is a ruthless backgammon program I discovered last month when reading Stephen Glenn's Geeklist about his ten favorite games. I used to think I was good at backgammon until I downloaded this program.
It asks you to register but the author has since made public a username/registration code combo to make the game free.
The die rolls are absolutely fair - I have no doubt of that. And I have many times accepted the computer's double offer and won. Usually the computer won't offer unless odds are heavily stacked in its favor, but there are conditions when its assessments are wrong. And if you have built a big lead the computer will double immediately to catch up - clearly you cannot refuse those.