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Backgammon to Nackgammon

Posted By: Nack Ballard
Date: Saturday, 17 June 2017, at 1:58 a.m.

In Response To: Question to Nack (Casper Van der Tak)

To get from (the opening position of) backgammon to (the opening position of) Nackgammon, I doubt there is a sequence shorter than the one demonstrated herein. On the short list of 14-roll possibilities is:

...54S-43H-54K-41-64H-64K-42-62H-54K-52-51H-65K-21-61z
...Nactation

This sequence is illustrated with diagrams below. Close plays have been rolled out.

		White is Player 2 score: 0 pip: 158 Unlimited Game Jacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-a---aE-C---dE---d-e----B-:0:0:1:43:0:0:3:0:10
54S-43..Nactation

White opened with 54S and Blue rolls 43. All the rollouts I know support H (Hit, 13/9 8/5*), including David Rockwell's [H X11 K40] "<62*15, which I think is the one currently on the XG opening book site.

In the above diagram, Blue plays H (Hit, 13/9 8/5*). Next, White rolls 54 and hits twice with K (Kill, bar/20*/16* -- much better than anchoring), and Blue enters both checkers with 41. Then, Blue rolls 64 and plays H (Hit, 16/10 8/4*), as the rollout supports below.

		White is Player 2 score: 0 pip: 154 Unlimited Game Jacoby Beaver pip: 191 score: 0 Blue is Player 1
XGID=-a----E-Ba--dD---d-e-A--C-:0:0:-1:64:0:0:3:0:10
54S-43H-54K-41-64..Nactation

1.	Rollout1	16/10 8/4*	eq: +0.408
	Player: Opponent: 58.29% (G:21.39% B:1.81%) 41.71% (G:10.18% B:0.46%) Conf.: ± 0.010 (+0.398...+0.418) - [100.0%] Duration: 1 hour 48 minutes
2.	Rollout1	8/2 6/2	eq: +0.386 (-0.022)
	Player: Opponent: 56.65% (G:23.12% B:2.30%) 43.35% (G:10.17% B:0.43%) Conf.: ± 0.008 (+0.377...+0.394) - [0.0%] Duration: 1 hour 39 minutes
1 6480 Games rolled with Variance Reduction. Dice Seed: 295083 Moves: 3-ply, cube decisions: XG Roller

Above, White plays H (Hit, 16/10 8/4*). Next, Blue rolls his own 64 and hits twice with K (Kill, bar/21*/15*), and White enters both checkers with 42. Then, Blue rolls 62 and plays H (Hit, 15/9 6/4*), as the rollout supports below.

		White is Player 2 score: 0 pip: 174 Unlimited Game Jacoby Beaver pip: 185 score: 0 Blue is Player 1
XGID=-aa-a-E-B---dD-A-c-e----C-:0:0:1:62:0:0:3:0:10
54S-43H-54K-41-64H-64K-42-62..Nactation

1.	Rollout1	15/9 6/4*	eq: -0.192
	Player: Opponent: 46.51% (G:12.53% B:0.61%) 53.49% (G:18.63% B:1.48%) Conf.: ± 0.008 (-0.200...-0.183) - [100.0%] Duration: 2 hours 23 minutes
2.	Rollout1	24/18 15/13	eq: -0.213 (-0.021)
	Player: Opponent: 45.67% (G:10.89% B:0.45%) 54.33% (G:16.89% B:0.91%) Conf.: ± 0.007 (-0.220...-0.205) - [0.0%] Duration: 2 hours 01 minute
1 7776 Games rolled with Variance Reduction. Dice Seed: 16219344 Moves: 3-ply, cube decisions: XG Roller

Above, Blue plays H (Hit, 15/9 6/4*). Next, White rolls 54 and hits twice with K (Kill, bar/21*/16*), Blue enters both checkers with 52, and White rolls 51 in the diagram below.

		White is Player 2 score: 0 pip: 169 Unlimited Game Jacoby Beaver pip: 207 score: 0 Blue is Player 1
XGID=-aa---D-Ba--dD---c-eA--AC-:0:0:-1:51:0:0:3:0:10
54S-43H-54K-41-64H-64K-42-62H-54K-52-51..Nactation

Above, White naturally plays H (Hit, 15/11 6/5*). Next, Blue rolls 65 and hits twice with K (Kill, bar/20*14*), and White enters both checkers with 21, as depicted below.

		White is Player 2 score: 0 pip: 194 Unlimited Game Jacoby Beaver pip: 201 score: 0 Blue is Player 1
XGID=-bb---D-B---dDA--c-d---AC-:0:0:1:61:0:0:3:0:10
54S-43H-54K-41-64H-64K-42-62H-54K-52-51H-65K-21-61 Nactation

1.	Rollout1	24/23 14/8	eq: -0.085
	Player: Opponent: 48.13% (G:12.82% B:0.62%) 51.87% (G:14.79% B:0.77%) Conf.: ± 0.004 (-0.090...-0.081) - [93.9%] Duration: 4 hours 46 minutes
2.	Rollout1	24/18 14/13	eq: -0.090 (-0.005)
	Player: Opponent: 48.34% (G:12.22% B:0.58%) 51.66% (G:15.34% B:0.78%) Conf.: ± 0.004 (-0.094...-0.086) - [6.1%] Duration: 4 hours 59 minutes
3.	Rollout2	23/22 14/8	eq: -0.117 (-0.031)
	Player: Opponent: 47.63% (G:12.87% B:0.64%) 52.37% (G:15.36% B:0.97%) Conf.: ± 0.016 (-0.133...-0.101) - [0.0%] Duration: 15 minutes 57 seconds
1 25920 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller 2 1944 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller

Blue has the final say with 61z, which edges out R, according to the rollout above (I'll eventually extend and confirm to 100% confidence). When Blue completes his move, the opening position of Nackgammon is reached.

The other direction, Nackgammon to backgammon, might be covered in a later post.

Nack

Messages In This Thread

• Question to Nack
  Casper Van der Tak -- Friday, 16 June 2017, at 8:41 a.m.
  • Backgammon to Nackgammon
    Nack Ballard -- Saturday, 17 June 2017, at 1:58 a.m.
    • Backgammon to Nackgammon
      Casper Van der Tak -- Saturday, 17 June 2017, at 9:15 a.m.
      • Backgammon to Nackgammon
        Nack Ballard -- Sunday, 18 June 2017, at 1:30 a.m.
        • Backgammon to Nackgammon
          Casper Van der Tak -- Sunday, 18 June 2017, at 3:29 a.m.
    • My Takeaway From This
      Paul Weaver -- Saturday, 17 June 2017, at 12:39 p.m.
      • Nackgammon: Opening doublets
        Nack Ballard -- Saturday, 17 June 2017, at 8:10 p.m.
      • Nackgammon: Opening moves (SQZR@)
        Nack Ballard -- Saturday, 17 June 2017, at 9:54 p.m.
        • Minor correction
          Nack Ballard -- Saturday, 17 June 2017, at 10:24 p.m.
        • Bug on eXtreme Gammon website
          Timothy Chow -- Sunday, 18 June 2017, at 5:05 p.m.
          • Bug on eXtreme Gammon website
            eXtreme Gammon -- Tuesday, 20 June 2017, at 5:29 p.m.