Walter: Good questions. I think some jolly discussion could be had about how the dice distribution should work. :-)

Backgammon Galore assumes a literal domino set and assigns the 21 dominos in a fixed pattern. Each player plays only their own dominos. When the dominos are exhausted the players swap sets to ensure fairness.

Pythagoras envisages 36 dominos to correspond with the 36 dice rolls and each player picks one from what's left in the set. Whether that's one set per player or a single set between them isn't perfectly clear, though I think he's saying one set each.

This program that I've just played gives each player twelve completely random dominoes. Eg, the computer's selection for the current game includes two 4-4s and four 6-3s, while my set has two 6-3s of its own.

With the 36 domino set per player, one round of dominos would be sufficient for quite a few matches and I imagine that games between good and experienced players would become quite predictable. The program's small random set of dominos makes for more variety of games.