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Playing 31 -- ROLLOUTS of Both Positions

Posted By: Nack Ballard
Date: Sunday, 12 June 2016, at 6:01 a.m.

In Response To: Playing 31 (Nack Ballard)

Thanks to Stick, sebalotek, Phil, Keene, Casper, ah_clem, Fatboy, Kevin, Mike M., Steven, garyo and Seth, for their responses and quotes, and to Mike Mannon for supplying and/or extending rollouts.

		White is Player 2 score: 0 pip: 145 Unlimited Game Jacoby Beaver pip: 138 score: 0 Blue is Player 1
XGID=-b-BB-C-C--AcB---c-cbAb-A-:0:0:1:31:0:0:3:0:10
52S-22N-31P-32S-53P-44P-51Z-31

1.	Rollout1	8/5 6/5	eq: +0.402
	Player: Opponent: 59.97% (G:23.15% B:1.66%) 40.03% (G:14.42% B:0.76%) Conf.: ¡Ó 0.004 (+0.399...+0.406) - [100.0%] Duration: 2 hours 14 minutes
2.	Rollout1	24/21 11/10	eq: +0.386 (-0.016)
	Player: Opponent: 58.46% (G:18.86% B:0.58%) 41.54% (G:8.55% B:0.36%) Conf.: ¡Ó 0.003 (+0.384...+0.389) - [0.0%] Duration: 2 hours 37 minutes
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1 31104 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 145 Unlimited Game Jacoby Beaver pip: 137 score: 0 Blue is Player 1
XGID=-b-BB-C-C-A-cB---c-cbAb-A-:0:0:1:31:0:0:3:0:10
32S-32H-61$-55P-51N-32E-53P-31

1.	Rollout1	24/21 10/9	eq: +0.409
	Player: Opponent: 59.17% (G:18.39% B:0.57%) 40.83% (G:8.28% B:0.34%) Conf.: ¡Ó 0.003 (+0.406...+0.412) - [100.0%] Duration: 2 hours 42 minutes
2.	Rollout1	8/5 6/5	eq: +0.393 (-0.016)
	Player: Opponent: 59.45% (G:23.87% B:1.66%) 40.55% (G:14.55% B:0.77%) Conf.: ¡Ó 0.003 (+0.390...+0.397) - [0.0%] Duration: 2 hours 15 minutes
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1 31104 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

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Above, you can see rollouts of the two positions (side by side, if you sufficiently widen your window). In the first position, making the 5pt is better than anchoring by .016. Exactly the opposite is true in the second position.

The basic idea is that it is inefficient to end up with a builder on the 10pt. If Blue anchors in the first position (moving his builder to the 10pt), his offensive 31 and 63 will be duplicated for the next turn (assuming he is not hit). Conversely, if Blue makes the 5pt in the second position (leaving his builder on the 10pt), his 63 will be duplicated (anchor or 7pt).

You can see a more complete accounting of Blue's follow-up numbers in Mike's post.

Here is a good way to drive the point home: In the first diagrammed position, what would you prefer to roll as Blue: 21, 31 or 32? Rank the three rolls.

The answer is that (of the three) 21 is best, 32 is second best, and 31 is worst.

---------------------------------------------------------------------
.....Roll...Equity...Anchoring play

.....21.....+.434.....(builder on 11pt)
.....32.....+.409.....(builder on 9pt)
.....31.....+.386.....(builder on 10pt) or +.402 (make 5pt)
---------------------------------------------------------------------

I did a single-play 5k rollout for 21 (anchoring with 24/21), generating the +.434 equity listed. The other equities have been extracted from the two rollouts above. Blue would rather anchor if his builder ends up on the 11pt or 9pt. If his choice is for the builder to end up on the 10pt, he should settle for making his 5pt, though that is still worse than both anchor+11pt and anchor+9pt.

It is a similar story at DMP, as you can glean from the side-by-side rollout results below. (Multiply the margins by 2.2 to compare their significance to the money margins from the rollouts above.)

		White is Player 2 score: 0 pip: 145 1 point match pip: 138 score: 0 Blue is Player 1
XGID=-b-BB-C-C--AcB---c-cbAb-A-:0:0:1:31:0:0:0:1:10
52S-22N-31P-32S-53P-44P-51Z-31

1.	Rollout1	8/5 6/5	eq: +0.191
	Player: Opponent: 59.54% (G:26.38% B:6.26%) 40.46% (G:15.27% B:2.14%) Conf.: ¡Ó 0.003 (+0.188...+0.194) - [100.0%] Duration: 19 minutes 28 seconds
2.	Rollout1	24/21 11/10	eq: +0.172 (-0.019)
	Player: Opponent: 58.58% (G:20.31% B:1.75%) 41.42% (G:9.56% B:0.74%) Conf.: ¡Ó 0.002 (+0.169...+0.174) - [0.0%] Duration: 19 minutes 12 seconds
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1 5184 Games rolled with Variance Reduction. Dice Seed: 48040528 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 145 1 point match pip: 137 score: 0 Blue is Player 1
XGID=-b-BB-C-C-A-cB---c-cbAb-A-:0:0:1:31:0:0:0:1:10
32S-32H-61$-55P-51N-32E-53P-31

1.	Rollout1	24/21 10/9	eq: +0.186
	Player: Opponent: 59.28% (G:19.76% B:1.93%) 40.72% (G:9.52% B:0.73%) Conf.: ¡Ó 0.001 (+0.184...+0.187) - [100.0%] Duration: 57 minutes 55 seconds
2.	Rollout1	8/5 6/5	eq: +0.177 (-0.009)
	Player: Opponent: 58.83% (G:26.32% B:6.82%) 41.17% (G:15.31% B:2.19%) Conf.: ¡Ó 0.002 (+0.175...+0.178) - [0.0%] Duration: 59 minutes 00 second
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1 15552 Games rolled with Variance Reduction. Dice Seed: 48040528 Moves: 3-ply, cube decisions: XG Roller

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[As you might expect, it is clearly best to make the 5pt at gammon go, or anchor at gammon save, in both positions. To see the effect in both positions when Blue leads ¡V6¡V7 and ¡V5¡V7, we can look forward to viewing the rollouts Steven Carey mentioned here.]

Finally, what would you do in each of the two positions diagrammed below? For answers and analysis, see Backgammon Openings, pages 62¡V63.

		White is Player 2 score: 0 pip: 163 Unlimited Game Jacoby Beaver pip: 162 score: 0 Blue is Player 1
XGID=-b----E-C--AeD---b-dbA--A-:0:0:1:31:0:0:3:0:10
32S-31P-31

		White is Player 2 score: 0 pip: 155 Unlimited Game Jacoby Beaver pip: 162 score: 0 Blue is Player 1
XGID=----b-E-C--AcD-b-c-e-A--A-:0:0:1:31:0:0:3:0:10
32S-33B-31

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Nack

Messages In This Thread

• Playing 31
  Nack Ballard -- Tuesday, 31 May 2016, at 2:55 a.m.
  • Playing 31
    Stick -- Tuesday, 31 May 2016, at 3:31 a.m.
  • Playing 31
    sebalotek -- Tuesday, 31 May 2016, at 7:28 a.m.
  • Playing 31--quotes, as requested
    Phil Simborg -- Tuesday, 31 May 2016, at 1:31 p.m.
  • Playing 31
    Keene -- Tuesday, 31 May 2016, at 3:48 p.m.
  • Playing 31
    Casper Van der Tak -- Tuesday, 31 May 2016, at 4:53 p.m.
  • Playing 31
    ah_clem -- Tuesday, 31 May 2016, at 8:02 p.m.
  • Playing 31
    Fatboy -- Wednesday, 1 June 2016, at 2:10 a.m.
    • Playing 31
      Kevin McDonough -- Wednesday, 1 June 2016, at 2:39 a.m.
      • [Spoiler Alert] – Kevin's post includes rollout data. *NM*
        Taper_Mike -- Wednesday, 1 June 2016, at 4:10 a.m.
        • [Spoiler Alert] – Kevin's post includes rollout data.
          Fatboy -- Wednesday, 1 June 2016, at 6:02 p.m.
  • Playing 31
    Taper_Mike -- Wednesday, 1 June 2016, at 4:08 a.m.
  • Playing 31 -- VARIANT and Original Rollout
    Nack Ballard -- Saturday, 4 June 2016, at 6:46 p.m.
    • Comparing the Original Position and Variant
      Taper_Mike -- Monday, 6 June 2016, at 7:12 a.m.
  • Playing 31
    Steven E. Carey -- Tuesday, 7 June 2016, at 2:00 p.m.
    • Playing 31
      Keene -- Tuesday, 7 June 2016, at 4:51 p.m.
  • quote
    garyo -- Tuesday, 7 June 2016, at 8:40 p.m.
    • quote
      Seth -- Tuesday, 7 June 2016, at 9:15 p.m.
    • quote--Joe Sylvester
      Phil Simborg -- Wednesday, 8 June 2016, at 8:11 a.m.
      • quote--Joe Sylvester
        Seth -- Wednesday, 8 June 2016, at 11:25 a.m.
  • Playing 31 -- ROLLOUTS of Both Positions
    Nack Ballard -- Sunday, 12 June 2016, at 6:01 a.m.
    • Playing 31 -- ROLLOUTS of Both Positions
      Martin -- Sunday, 12 June 2016, at 10:21 a.m.
      • Corrected Text
        Nack Ballard -- Sunday, 12 June 2016, at 11:32 p.m.
    • Playing 31 -- ROLLOUTS of Both Positions
      Steven E. Carey -- Saturday, 18 June 2016, at 10:43 p.m.
      • Playing 31 -- ROLLOUTS of Both Positions
        sebalotek -- Monday, 20 June 2016, at 3:13 a.m.
    • Playing 31 -- ROLLOUTS of Both Positions
      Steven E. Carey -- Tuesday, 21 June 2016, at 6:27 a.m.