The bottom line
At the market, ask for a small-end (or first-cut) three-bone rib roast. If that doesn't ring a bell with the meat person, ask for the roast to be cut from the loin end. The grade—Prime or Choice—is up to you, and your wallet.
How to carve a beef rib roast
1. Using a long, sharp slicing knife or chef’s knife, cut the meat from the rib bones in one piece, following the contour of the bones.
2. Slice the meat across the grain into whatever thickness you prefer. If you like, cut between the bones to make individual ribs for gnawing on in the privacy of your kitchen.