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42 to play -- ROLLOUT and VARIANTS

Posted By: Nack Ballard
Date: Sunday, 6 January 2019, at 9:46 p.m.

In Response To: 42 to play - Answer (benf)

		White is Player 2 score: 0 pip: 119 Unlimited Game Jacoby Beaver pip: 131 score: 0 Blue is Player 1
XGID=-----BDCBa-AbB-aabbbb-bA--:0:0:1:24:0:0:3:0:10
Original position

1.	Rollout1	13/9* 11/9	eq: -0.066
	Player: Opponent: 47.71% (G:14.96% B:0.74%) 52.29% (G:14.12% B:0.69%) Conf.: � 0.015 (-0.081...-0.051) - [100.0%] Duration: 4 minutes 19 seconds
2.	Rollout2	11/9* 9/5	eq: -0.175 (-0.110)
	Player: Opponent: 44.19% (G:14.50% B:0.55%) 55.81% (G:13.21% B:0.57%) Conf.: � 0.013 (-0.188...-0.162) - [0.0%] Duration: 4 minutes 11 seconds
3.	Rollout2	13/11 13/9*	eq: -0.206 (-0.140)
	Player: Opponent: 43.23% (G:12.96% B:0.53%) 56.77% (G:13.89% B:0.60%) Conf.: � 0.015 (-0.221...-0.191) - [0.0%] Duration: 4 minutes 38 seconds
4.	Rollout3	23/21 13/9*	eq: -0.241 (-0.176)
	Player: Opponent: 43.20% (G:13.51% B:0.95%) 56.80% (G:24.06% B:1.84%) Conf.: � 0.014 (-0.256...-0.227) - [0.0%] Duration: 3 minutes 08 seconds
5.	4-ply	13/9* 7/5	eq: -0.307 (-0.241)
	Player: Opponent: 41.10% (G:12.35% B:0.62%) 58.90% (G:19.32% B:1.42%)
1 1297 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller 2 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller 3 1298 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller

Ben's rollout of his original position is shown above. Pay special attention to the comparison of the best play of P (13/9* 11/9) with the fourth best play of X (hit-and-split, 23/21 13/9*), a "whopper with cheese." If for nothing else but thematic reasons, these two plays were addressed by all three respondents, with no other candidate play mentioned.

The margin between these two plays is cut in half when (Blue's blot and) White's entire offensive structure is moved out one pip. Compare Variant 1 below.

		White is Player 2 score: 0 pip: 131 Unlimited Game Jacoby Beaver pip: 130 score: 0 Blue is Player 1
XGID=-----BDCBa-AbBaabbbb-bA---:0:0:1:42:0:0:3:0:10
Variant 1 (Blue's back checker and White's offensive formation moved out)

1.	Rollout1	13/9* 11/9	eq: +0.016
	Player: Opponent: 48.00% (G:19.25% B:0.87%) 52.00% (G:10.67% B:0.50%) Conf.: ± 0.019 (-0.003...+0.034) - [99.5%] Duration: 9 minutes 42 seconds
2.	Rollout1	11/9* 9/5	eq: -0.023 (-0.038)
	Player: Opponent: 46.63% (G:19.29% B:0.65%) 53.37% (G:9.55% B:0.47%) Conf.: ± 0.023 (-0.046...+0.000) - [0.5%] Duration: 9 minutes 45 seconds
3.	Rollout1	22/20 13/9*	eq: -0.075 (-0.091)
	Player: Opponent: 46.49% (G:16.63% B:1.02%) 53.51% (G:14.95% B:1.01%) Conf.: ± 0.015 (-0.090...-0.060) - [0.0%] Duration: 7 minutes 58 seconds
1 1296 Games rolled with Variance Reduction. Dice Seed: 30960182 Moves: 3-ply, cube decisions: XG Roller

The margin between the two featured plays shrunk from .176 to .091.

The margin is relatively affected even more by an additional change. In Variant 2 below, I've moved one of White's blots / return-hitters to her midpoint. Now, hit-and-split leaps "bigly" into first place:

		White is Player 2 score: 0 pip: 134 Unlimited Game Jacoby Beaver pip: 130 score: 0 Blue is Player 1
XGID=-----BDCBa-AcBa-bbbb-bA---:0:0:1:42:0:0:3:0:10
Variant 2 (White's 10pt blot is moved to her midpoint)

1.	Rollout1	22/20 13/9*	eq: +0.039
	Player: Opponent: 49.96% (G:16.14% B:0.68%) 50.04% (G:12.62% B:0.79%) Conf.: ± 0.008 (+0.031...+0.047) - [100.0%] Duration: 12 minutes 24 seconds
2.	Rollout1	13/9* 11/9	eq: -0.011 (-0.050)
	Player: Opponent: 47.90% (G:17.96% B:0.62%) 52.10% (G:10.56% B:0.51%) Conf.: ± 0.011 (-0.022...+0.000) - [0.0%] Duration: 14 minutes 34 seconds
3.	Rollout1	11/9* 9/5	eq: -0.035 (-0.074)
	Player: Opponent: 46.65% (G:18.50% B:0.48%) 53.35% (G:9.41% B:0.42%) Conf.: ± 0.010 (-0.045...-0.025) - [0.0%] Duration: 14 minutes 17 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 73431211 Moves: 3-ply, cube decisions: XG Roller

[If instead, it is the 11pt blot (instead of the 10pt blot) that is moved to the midpoint, the X/P margin is similar: .044 in favor of hit-and-split -- 5k rollout not shown.]

Down a different rabbit hole, you may find it interesting to reconcile the contrast of the two positions below (displayed side by side, if your window is wide). In both cases (from benf's original position), White's 8pt has been uncovered and one of the blots behind it (either 9pt or 10pt) is covered instead. At first glance, the conceptual difference might appear negligible. Nevertheless, Blue should definitely make different plays.

		White is Player 2 score: 0 pip: 120 Unlimited Game Jacoby Beaver pip: 131 score: 0 Blue is Player 1
XGID=-----BDCBa-AbB-ababbb-bA--:0:0:1:42:0:0:3:0:10
Variant 3: ..White owns her 9pt

1.	Rollout1	13/9* 11/9	eq: +0.142
	Player: Opponent: 53.15% (G:16.49% B:0.85%) 46.85% (G:12.71% B:0.55%) Conf.: ± 0.008 (+0.134...+0.150) - [100.0%] Duration: 33 minutes 22 seconds
2.	Rollout1	23/17*	eq: +0.115 (-0.026)
	Player: Opponent: 54.26% (G:13.45% B:0.80%) 45.74% (G:13.96% B:0.60%) Conf.: ± 0.007 (+0.108...+0.123) - [0.0%] Duration: 30 minutes 38 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 73431211 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 121 Unlimited Game Jacoby Beaver pip: 131 score: 0 Blue is Player 1
XGID=-----BDCBa-AbB-baabbb-bA--:0:0:1:42:0:0:3:0:10
Variant 4: ..White owns her 10pt

1.	Rollout1	23/17*	eq: +0.154
	Player: Opponent: 55.17% (G:13.66% B:0.71%) 44.83% (G:13.33% B:0.58%) Conf.: ± 0.007 (+0.147...+0.161) - [99.9%] Duration: 31 minutes 04 seconds
2.	Rollout1	13/9* 11/9	eq: +0.138 (-0.016)
	Player: Opponent: 52.73% (G:17.32% B:0.90%) 47.27% (G:12.72% B:0.56%) Conf.: ± 0.008 (+0.130...+0.146) - [0.1%] Duration: 34 minutes 54 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 73431211 Moves: 3-ply, cube decisions: XG Roller

See the reason?

Nack

Messages In This Thread

• 42 to play
  benf -- Thursday, 3 January 2019, at 10:37 p.m.
  • 42 to play
    Ian Terry -- Friday, 4 January 2019, at 8:01 a.m.
  • 42 to play
    Casper Van der Tak -- Friday, 4 January 2019, at 8:19 a.m.
    • 42 to play
      neilkaz -- Saturday, 5 January 2019, at 5:57 p.m.
  • 42 to play - Answer
    benf -- Sunday, 6 January 2019, at 8:00 p.m.
    • 42 to play -- ROLLOUT and VARIANTS
      Nack Ballard -- Sunday, 6 January 2019, at 9:46 p.m.
      • 42 to play -- ROLLOUT and VARIANTS
        Casper Van der Tak -- Tuesday, 8 January 2019, at 11:02 a.m.
        • 42 to play -- ROLLOUT and VARIANTS
          Nack Ballard -- Wednesday, 9 January 2019, at 1:31 a.m.
          • 42 to play -- ROLLOUT and VARIANTS
            Casper Van der Tak -- Friday, 11 January 2019, at 8:24 a.m.
            • 42 to play -- ROLLOUT and VARIANTS
              Nack Ballard -- Saturday, 12 January 2019, at 5:45 a.m.
              • 42 to play -- ROLLOUT and VARIANTS
                Casper Van der Tak -- Saturday, 12 January 2019, at 7:40 a.m.
                • 42 to play -- EXPLANATION
                  Nack Ballard -- Saturday, 12 January 2019, at 5:42 p.m.