Why 13/10 13/9
13/10 13/9 brings two builders down for your 5-point, 4-point and bar point. 24/20 13/10 and 24/21 13/9 each combine one builder with a split of the back checkers.
The top five plays, rolled out
| # | Play | Equity | Behind the best | Wins | Gammons won · lost | 3-ply (rank) |
|---|---|---|---|---|---|---|
| 1 | 13/10 13/9 | +0.015 ±0.015 | — | 49.9% | 16.2% · 14.7% | +0.012 (#1) |
| 2 | 24/20 13/10 | +0.014 ±0.013 | 0.000 ≈ | 50.1% | 14.4% · 13.8% | +0.001 (#3) |
| 3 | 24/21 13/9 | +0.004 ±0.014 | 0.010 ≈ | 50.0% | 14.8% · 14.2% | +0.006 (#2) |
| 4 | 24/21 24/20 | −0.020 ±0.012 | 0.035 | 50.1% | 13.1% · 13.7% | −0.006 (#4) |
| 5 | 13/9 8/5 | −0.088 ±0.015 | 0.103 | 48.1% | 15.0% · 16.1% | −0.064 (#5) |
Equity is the average result in points per game for the player on roll, with the cube in play: each play rolled out 1,296 times, ± one standard error. Gammons include backgammons. ≈ marks a play behind the best by less than twice the larger standard error, inside the margin of error.
The alternatives
GNU Backgammon cannot separate the three: the rollouts put them within 0.010 of each other. Splitting both back checkers with 24/21 24/20 is a small step back, and 13/9 8/5, which slots the 5-point, costs 0.103.
All 17 legal plays, ranked at 3-ply
- 13/10 13/9 +0.012
- 24/21 13/9 +0.006
- 24/20 13/10 +0.001
- 24/21 24/20 −0.006
- 13/9 8/5 −0.064
- 13/6 −0.071
- 13/9 6/3 −0.084
- 13/10 8/4 −0.089
- 24/20 8/5 −0.097
- 24/20 6/3 −0.105
- 24/21 6/2 −0.111
- 24/21 8/4 −0.117
- 13/10 6/2 −0.131
- 8/4 6/3 −0.194
- 8/5 6/2 −0.206
- 6/3 6/2 −0.254
- 8/5 8/4 −0.270
Questions about the 4-3 opening
What is the best opening move for 4-3 in backgammon?
13/10 13/9 and 24/20 13/10 are effectively tied. In GNU Backgammon rollouts of the top five plays, 13/10 13/9 scores +0.015 and 24/20 13/10 +0.014, a gap inside the margin of error.
Is 24/20 13/10 a mistake with an opening 4-3?
No. It finishes level with 13/10 13/9 in GNU Backgammon’s rollouts, so the two plays are effectively equal.
How was this 4-3 analysis made?
GNU Backgammon 1.07.001 ranked all 17 legal plays at 3-ply, then rolled out the best five, 1,296 games each, with the cube in play (money game, Jacoby off). GNU Backgammon 1.06.002, the version Boardgammon’s servers run, ranks the same five plays in the same order at 3-ply.
How these numbers were made
GNU Backgammon 1.07.001 ranked every legal play at 3-ply with the cube in play (money game, Jacoby off, no beavers), then rolled out the best five: 1,296 games each, with variance reduction and quasi-random dice. GNU Backgammon 1.06.002, the version Boardgammon’s servers run, ranks the same five plays in the same order at 3-ply. Evaluated on 2026-10-20. The same engine analyses every finished online game on Boardgammon: see how that compares. New to the numbers? Read what equity and a rollout are.
Terms on this page: Builder, Diversification, Anchor, Slot. Next in the strategy guides: cube theory.