I play online backgammon on msn, but when I'm playing in person with someone we usually play "acee deucee" (not sure if I spelled it right).
This is not a 100% perfect design - you may have to trim an area slightly to fit your needs. I didn't trim anything. It's still a super game room decoration idea.
For my first decoration I painted the backgammon game with acrylic paint, which is the reason for some of the warping on my design. I sealed the game with glossy Mod Podge. The dice have rhinestuds and glued on numbers (you'll have to create your own numbers by using the font you like).
The second backgammon game decoration is just plain 65 lb cardstock, not heavy weight. I used hotfix rhinestones on the dice and glued on the numbers.
I didn't create the digital file for the game to be able to close, but I bet you can make hinges on your own and make it work for you.
First design using .022 chipboard.
2nd decoration made using 65 lb cardstock
Ok, chat with ya later.