Senat - so how'd they figure out the rules - from tomb paintings?

I recently got a version of “Senat,” the ancient Egyptian game that’s similar to backgammon. It’s fun (especially since I’m on a winning streak versus the Beloved - woo-hoo!), but I’m wondering - how do we know what the rules are? They’re fairly complicated, and the game wasn’t played for a couple of millenia.

Where Egyptologists able to figure the rules out just from illustrations in tomb paintings? did they find the board and counters in King Tut’s tomb? was there an ancient papyrus: “The Rules of Senat accoring to Thoth-Hoyle?” Or, did they just sit down and say “dunno how Tut did it - here’s how we’ll play.”

The best I could find was this:

shareware versions of senet are availible for download many places on the web, such as
http://ourworld.compuserve.com/homepages/PSNeeley/senet.htm
http://www.newton.cam.ac.uk/egypt/ad/senet.html