Backgammon Opening Moves & Advanced Replies

The opening of a backgammon game is the most thoroughly analysed phase of the game. Every dice combination that can be rolled on the first turn — 15 distinct non-double rolls, plus 6 doubles in non-tournament rules — has been rolled out to convergence by every major neural-network engine since the late 1990s. The results have refined, and in several cases overturned, the strategic recommendations of pre-engine theory.

This page catalogues all 15 opening rolls with their canonical plays, their recognised nicknames, the statistical rollout edges of the standard play over leading alternatives, and a structural treatment of opening replies — the second-turn position landscape that arises when the second player rolls into the 30 most-played first-turn positions.

For the strategic principles behind the catalogue, see the strategy hub. For the math of the dice distribution, see the mathematics hub.

1. The Dice Distribution

A pair of dice produces 21 distinct rolls (6 doubles + 15 non-doubles) over 36 ordered outcomes. Doubles occur on $6 / 36 = 16.\overline{6}\%$ of all rolls. Non-doubles each occur on $2 / 36 = 5.\overline{5}\%$ of all rolls — the two dice may be ordered either way.

In tournament rules, the opening roll of a game is made by each player rolling one die, with the higher die rolling first and the combination of the two dice played as that player's opening move. This convention means doubles cannot occur on the opening roll in tournament play (a tie reroll is required). Money play often uses a different convention (both players roll both dice and doubles are kept and even auto-double the cube).

The 15 non-double opening rolls below are therefore the complete set of tournament-play opening rolls.

2. The 15 Opening Rolls

The table below gives the canonical play for each roll, its recognised nickname (where one exists), the principal alternative play, and the approximate rollout edge of the canonical play over the alternative, in money-game equity. Edges are measured against XG2 4-ply rollouts; values from GNU Backgammon and Wildbg agree to within ±0.005 equity.

A few of these rolls have stable canonical plays that have not changed since Magriel's Backgammon (1976) — the make-the-point rolls (3-1, 4-2, 5-3, 6-1) in particular. Others have been refined by engine rollout analysis and modern competitive opinion has shifted within the last twenty years: notably the 4-1 and 5-1 openings, where the 1970s pure-style preference for slotting the 5-point has been overturned by neural-network analysis in favour of the split. The 2-1 remains genuinely contested at the rollout level — the slot and split plays are close enough that either is defensible.

Note on edge values. Exact rollout equities depend on the engine, the number of trials, the truncation depth, the seed, and the variance-reduction technique applied. The framings above describe the direction of the modern engine consensus rather than committing to specific edge numbers. For published cubeless equities cell by cell, consult the eXtreme Gammon 2 or GNU Backgammon rollout database.

3. The Five Strongest Opening Rolls

Five opening rolls produce a structurally decisive position on the first turn:

• 3-1 (make the 5-point / Golden Point) — the single strongest opening roll. The 5-point is the highest-priority point in the game. See Golden Point Strategy for the full treatment.
• 4-2 (make the 4-point) — second-strongest. The 4-point combines with the 6- and 8-points to form a 3-prime.
• 6-1 (make the bar-point) — third-strongest. The bar-point (7-point) is the link in any 4- or 5-prime extending from the 6-point.
• 5-3 (make the 3-point) — fourth-strongest. The 3-point is less ranked than the 4- or 5-point but is still a valuable home-board attack and trap point.
• 6-5 (Lover's Leap) — fifth-strongest. Not a point-making roll, but the optimal use of two large dice — running a back checker all the way to the midpoint.

These five rolls account for approximately $5 \times 2 / 36 = 27.8\%$ of all opening rolls. The 1-in-3.6 probability of one of these rolls is one of the principal sources of opening-game variance: the player who rolls one of these on the first turn has a measurable equity advantage of 0.04–0.08 over the player who does not, before any cube action.

4. The Two Weakest Opening Rolls

The two structurally weakest opening rolls are 2-1 and 5-1. Neither makes a point. The 2-1 is a near-tie between the split-builder and the slot of the 5-point — modern rollouts can favour either by a marginal amount depending on the engine and the rollout settings. The 5-1 has settled more firmly: the modern canonical play is the split (24/23, 13/8), and the older slotting alternative (13/8, 6/5) is meaningfully inferior in current XG2 and Wildbg analysis.

The opening principle for these weak rolls is that a small split with an outfield builder is generally preferred to either a pure split or a pure builder play — keeping the back checkers flexible while planting an outfield checker that can be covered next turn.

5. Opening Roll Probability Reference

The 21-roll dice probability table — the foundation for every rollout calculation:

In tournament opening rules, the doubles rows are excluded (reroll required), and the non-double probabilities re-normalise:

$P(\text{roll}) = \frac{1}{15} = 6.\overline{6}\% \text{ for each non-double opening roll.}$

6. Doubles — Best Plays in Response Position

Doubles cannot occur on the opening roll itself, because the standard opening protocol requires each player to roll a single die with non-matching values determining initiative. The table below therefore describes the best play for each doubles roll when it appears as the second player's response (or on any later turn, where the position resembles the standard opening setup closely enough that the canonical play remains the same).

In casual money play with automatic-double conventions, doubles may also appear on the first move as a stake-doubling event without a recorded play; the canonical plays below apply if the doubles roll is then played out normally.

1-1, 3-3, and 4-4 are the three "best ever" opening doubles — each makes two key points in the first turn. 5-5 is the most controversial; the canonical 13/3, 13/3 play makes the 3-point but exposes back checkers, and modern engines have variant recommendations depending on the rollout configuration.

In tournament play, opening doubles are rerolled — so the 1-1 case (the strongest opening roll in the game) cannot be the first roll. It can, of course, occur on any later turn.

7. Opening Replies and the 630 Positional Combinations

After the first player makes their opening play, the second player rolls — and now any of the 21 possible dice combinations is available, including doubles. Combined with the approximately two acceptable plays per first-turn roll for the first player (averaging across the 15 rolls produces ~30 distinct positions reached at the end of turn 1), the second player's universe of possible positions is:

$30 \times 21 = 630 \text{ distinct second-turn positions}$

This is the opening reply problem. Modern engine analysis has rolled out the full grid; the standard reference is the "second-turn equity table" maintained in the GNU Backgammon and eXtreme Gammon rollout databases. The full table is impractical to memorise, but the structural patterns are not.

7.1 The Three Reply Archetypes

Across the 630 second-turn positions, three structural archetypes account for the bulk of the strategic content:

1. First player has made the 5-point, 4-point, or bar-point. The second player's reply is dominated by the question of whether to make a parallel point of their own. The canonical response is to make a point if possible (e.g., second player rolls 3-1 in response → make own 5-point) and otherwise to anchor or split with a deep builder (e.g., second player rolls 4-2 → 8/4 6/4, even though their opponent has already made a home-board point).

2. First player has run with 6-5 or 6-4 (Lover's Leap / Run). The second player's reply hinges on whether to chase with a parallel run or to commit to a building game. Generally, make a point if possible, split otherwise. Running with the second player rarely matches the equity of point-making.

3. First player has played a builder-split (e.g., 4-1 split, 2-1 split). The second player has a fresh tempo opportunity. Hit any blot the first player has left if a hit is available; otherwise play structurally.

7.2 The Hitting Window

Several first-turn plays leave blots within direct-shot range of the second player's back checkers. The most-cited cases:

• First player slots the 5-point (4-1 slot, or 13/8 6/5 alternative on 5-1): second player hits with combinations that produce a 5 from the 24-point (5-1, 5-2, 5-3, 5-4, 5-5, 4-1, 3-2 — 14 rolls of 36, $\approx 38.9\%$ hit probability).
• First player slots the bar-point (any direct-7 slot): second player hits with combinations that produce a 7 from the 24-point (4-3, 5-2, 6-1, 4-4 — 11 rolls of 36, $\approx 30.6\%$ hit probability).

The slot-vs-hit math is foundational. When the first player slots the 5-point on a 4-1 roll, the second player hits roughly 39% of the time and is structurally favoured after a hit. The 61% no-hit case leaves the first player with a covered 5-point and a significant positional edge. The expected-value calculation across the two outcomes is what produces the 4-1 slot's slim +0.005 edge over the split in XG2 rollouts.

8. Where Opening Theory Is Still Open

A small number of opening rolls remain meaningfully contested at the engine level:

• 2-1: the split-builder and the slot of the 5-point are within roughly a millipoint of each other in modern rollouts; the consensus shifts with engine version and rollout settings.
• Rolls where the second-best alternative is within a small equity gap (a few millipoints) — typically the split-vs-builder choices on 3-2 and 5-4 — where over-the-board choice can reasonably go either way.

The rolls that used to be contested — particularly 4-1 and 5-1 — have settled in the modern engine consensus toward the split-builder play and away from the older 1970s pure-style slot. Tournament-level players choose between the remaining genuinely-tied plays based on opponent-modelling (against a holding-game-prone opponent, the split plays gain value; against a positional opponent, the slot plays gain value), score context (match-equity gammon prices shift the calculation), and personal style. Engine rollouts at deeper plies are the only formal authority for the contested cases.

See Also

• Strategy hub
• Golden Point Strategy — the 3-1 opening and the 5-point's structural primacy.
• Prime Building — the structural objective of opening point-making.
• Mathematics — the equity and rollout foundations.
• Glossary — formal definitions for Lover's Leap, Golden Point, slot, split, builder.

Footnotes