The Best Backgammon Opening Moves, Roll by Roll
What to play for every non-double opening roll, from the universally-agreed best (3-1) to the rolls even strong players still argue about.

There are 15 distinct non-double rolls you can open a game with (doubles are rarer and get their own treatment at the end). Modern computer rollouts have settled most of these — a few are still genuinely debated among strong players. Here's the current consensus, roll by roll.
The rolls that are settled
3-1 — make your 5-point. Play 8/5, 6/5. This is the single best opening roll in the game and essentially every strong player agrees: making your 5-point on move one gives you the best structural point on the board before your opponent has touched anything.
6-5 — run a back checker. Play 24/13, known as the "lover's leap." Rather than splitting or building, you run one back checker all the way to your own midpoint in a single move, leaving no blot exposed anywhere. It's the standard, low-risk play for this roll.
5-3 — make your 3-point. Play 8/3, 6/3. A clear point-making play; the 3-point is less valuable than the 5-point or bar-point, but making any point on the opening roll is still strong and safe.
4-2 — make your 4-point. Play 8/4, 6/4. Same logic as 5-3: a made point early is good, even though the 4-point sits deeper in your home board than the 5-point.
6-1 — make your bar-point. Play 13/7, 8/7. Modern rollouts favor making the bar-point over the older-style split play (running a back checker to your 23-point). The bar-point is a genuinely strong blocking point.
The rolls that are still debated
For the remaining rolls — 2-1, 4-1, 5-1, 3-2, and a few others — strong players and rollout-backed references don't fully agree, and different opening books have shifted their recommendations over the years as computer analysis improved. In general terms, these rolls tend to come down to a choice between splitting a back checker toward your opponent's bar-point area, or building by bringing a midpoint checker down to create future point-making chances — with the "best" choice depending on razor-thin equity differences that even engines sometimes disagree on. Rather than assert a single correct answer here, the honest takeaway is: any of the commonly taught plays for these rolls are reasonable, and the gap between them is small enough that it won't decide your game on its own.
A word on doubles
Double rolls (3-3, 4-4, 5-5, 6-6, and so on) let you make four moves instead of two, which usually makes the best play more obvious rather than less — big doubles like 6-6 (running both back checkers while making your bar-point) and 3-3 (making both your 5-point and 3-point) are among the strongest opening rolls in the game precisely because they let you do two good things in one turn. 1-1 and 2-2 are weaker doubles and are treated more cautiously by strong players, since neither gives you as much structural improvement.
Why this matters less than it seems
Opening theory gets a disproportionate amount of attention because it's the one position every single game shares. In practice, the difference between the "best" and "second-best" opening play is almost always small compared to the decisions you'll face by move five or six, once contact and blots start shaping the position. Memorizing this list is a fine start; learning to count shots and read a position is what actually wins games.