BGonline.org Forums

Donkey Variant, ROLLOUTS

Posted By: Nack Ballard
Date: Wednesday, 9 April 2014, at 5:31 a.m.

In Response To: Donkey Variant (Nack Ballard)

		White is Player 2 score: 0 pip: 166 Unlimited Game Jacoby Beaver pip: 144 score: 0 Blue is Player 1
XGID=-a-aB-DaC-B-bBbc--Ab-c--A-:0:0:1:51:0:0:3:0:10
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- -33D-52R-62R-31H-61U-62P-61D-324-42H-41U-41K-1-F-43H-31-51 [K @12 k17 X40 P49 R51] "<=20**5

1.	Rollout1	8/7* 8/3*	eq: +0.444
	Player: Opponent: 58.68% (G:25.98% B:2.01%) 41.32% (G:12.27% B:0.92%) Conf.: ± 0.004 (+0.439...+0.448) - [100.0%] Duration: 7 hours 35 minutes
2.	Rollout1	24/18	eq: +0.432 (-0.012)
	Player: Opponent: 60.41% (G:17.34% B:0.62%) 39.59% (G:8.04% B:0.32%) Conf.: ± 0.004 (+0.428...+0.436) - [0.0%] Duration: 9 hours 54 minutes
3.	Rollout1	8/7* 6/1*	eq: +0.426 (-0.017)
	Player: Opponent: 58.30% (G:24.90% B:1.12%) 41.70% (G:11.75% B:0.72%) Conf.: ± 0.005 (+0.422...+0.431) - [0.0%] Duration: 8 hours 49 minutes
4.	Rollout2	18/13 8/7*	eq: +0.404 (-0.040)
	Player: Opponent: 58.52% (G:21.11% B:1.23%) 41.48% (G:10.38% B:0.49%) Conf.: ± 0.008 (+0.395...+0.412) - [0.0%] Duration: 1 hour 26 minutes
5.	Rollout2	10/5 6/5	eq: +0.395 (-0.049)
	Player: Opponent: 58.78% (G:22.10% B:1.26%) 41.22% (G:10.80% B:0.61%) Conf.: ± 0.008 (+0.386...+0.403) - [0.0%] Duration: 1 hour 23 minutes
6.	Rollout2	24/23 18/13	eq: +0.393 (-0.051)
	Player: Opponent: 59.15% (G:18.53% B:0.86%) 40.85% (G:9.37% B:0.32%) Conf.: ± 0.009 (+0.384...+0.402) - [0.0%] Duration: 1 hour 30 minutes
1 20736 Games rolled with Variance Reduction. Dice Seed: 43733867 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 43733867 Moves: 3-ply, cube decisions: XG Roller

According to the rollout, K (Kill, 8/7 8/3*) is best, @ (anchor, 24/18) is second, and lower-case k (kill, 8/7 6/1*) comes in third, but all three are very close. Six of seven respondents chose one of those top moves (two for K, three for @, and one for k).

Comparing the two double-hitters to each other, the move that breaks a point while keeping a four-stack and leaving an extra blot beats out (by .017) the safer move with the better distribution. This gives us an idea of the elevated importance of attacking on the higher inside point when hitting a second checker. When you're missed (which happens more often when you hit two checkers rather than one), securing the 3pt will be better than securing the 1pt, especially if the opponent immediately anchors on the other point.

Tim (who chose K), said, "There's probably a reason that Nack put a dilly builder on White's 4pt (duplicating White's threes everywhere?) but I'm missing the point of that hint." Indeed, one of my sub-goals was to have 10/5 6/5 (making the 5pt) close enough that someone might vote for it. One respondent did take the bait, but only because he was sharp enough to notice the resulting duplication of 3s and 4s and 6s (not mentioned by anyone else).

I guess it was worth it, but I paid a price. Retrofitting a (well-played) game sequence was tricky with White having ten checkers behind her 8pt (and none on it), a stripped 6pt, a dilly on her 4pt, and three back checker blots laid bare with the other side on roll. Robert understandably asks how such a weird position could have arisen, and in how few moves with reasonable play. [Answer: With all moves being best or within .02, my solution requires 31 plays, with 51 being the 32nd roll.]

Near the end of the game sequence (spelled out beneath the diagram), each player has an opportunity to make an initial double. (In both cases, rollouts conclude that doubling is correct by less than .01, so not doubling is still well within the .02 threshold of "well played"). White's opportunity comes just prior to his second 41K, and Blue's opportunity comes just prior to his rolling the 51 that is on the board.

As the game sequence allows for this flexibility, I have included two additional rollouts below (which can be viewed side-by-side if you widen your window): one with Blue owning the cube, and one with White owning the cube.

Immediately below are the nacbracs summaries (also shown in the captions) for playing 51 with the three different positionings of the cube. I'll let you derive your own conclusions or speculations.

........Cube in center.... [K @12 k17 X40 P49 R51] "<=20**5
........Blue owns cube.. [K k17 @23 P33 X42 R42] "<=10**5
........White owns cube [@ K13 k21 P27 R35 X40] "<=10**5

Key: K = Kill (8/7* 8/3), k = kill 8/7* 6/1*, @ = anchor (24/18), X = hit and split (18/13 8/7*), P = Point (10/5 6/5), R = Run (24/23 18/13).

........Nactation tutorial ....(For larger text, click on the double-arrow to the right of “Bookmarks”)
........Explanation of nacbracs

Nack

		White is Player 2 score: 0 pip: 166 Unlimited Game Jacoby Beaver pip: 144 score: 0 Blue is Player 1
XGID=-a-aB-DaC-B-bBbc--Ab-c--A-:1:1:1:51:0:0:3:0:10
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- -33D-52R-62R-31H-61U-62P-61D-324-42H-41U-C-41K-1-F-43H-31-51 [K k17 @23 P33 X42 R42] "<=10**5

1.	Rollout1	8/7* 8/3*	eq: +0.554
	Player: Opponent: 58.51% (G:26.38% B:1.97%) 41.49% (G:12.51% B:0.99%) Conf.: ± 0.005 (+0.549...+0.559) - [100.0%] Duration: 2 hours 46 minutes
2.	Rollout1	8/7* 6/1*	eq: +0.537 (-0.017)
	Player: Opponent: 58.32% (G:24.90% B:1.13%) 41.68% (G:11.77% B:0.73%) Conf.: ± 0.005 (+0.532...+0.542) - [0.0%] Duration: 2 hours 46 minutes
3.	Rollout1	24/18	eq: +0.531 (-0.023)
	Player: Opponent: 60.39% (G:17.53% B:0.65%) 39.61% (G:8.04% B:0.32%) Conf.: ± 0.005 (+0.527...+0.536) - [0.0%] Duration: 2 hours 58 minutes
4.	Rollout2	10/5 6/5	eq: +0.520 (-0.033)
	Player: Opponent: 58.67% (G:22.29% B:1.31%) 41.33% (G:10.85% B:0.60%) Conf.: ± 0.006 (+0.514...+0.527) - [0.0%] Duration: 1 hour 39 minutes
5.	Rollout2	18/13 8/7*	eq: +0.512 (-0.042)
	Player: Opponent: 58.37% (G:21.21% B:1.28%) 41.63% (G:10.42% B:0.49%) Conf.: ± 0.007 (+0.505...+0.519) - [0.0%] Duration: 1 hour 36 minutes
6.	Rollout2	24/23 18/13	eq: +0.512 (-0.042)
	Player: Opponent: 59.18% (G:18.87% B:0.89%) 40.82% (G:9.45% B:0.35%) Conf.: ± 0.007 (+0.505...+0.519) - [0.0%] Duration: 1 hour 48 minutes
1 10368 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 65904545 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 166 Unlimited Game Jacoby Beaver pip: 144 score: 0 Blue is Player 1
XGID=-a-aB-DaC-B-bBbc--Ab-c--A-:1:-1:1:51:0:0:3:0:10
42P-43S-65R-21P-41K-1-61U-F-52S-41U-43K-31-41L-65S-64H-41U- -33D-52R-62R-31H-61U-62P-61D-324-42H-41U-41K-1-F-43H-31-C-51 [@ K13 k21 P27 R35 X40] "<=10**5

1.	Rollout1	24/18	eq: +0.162
	Player: Opponent: 60.43% (G:17.63% B:0.66%) 39.57% (G:8.02% B:0.32%) Conf.: ± 0.004 (+0.158...+0.166) - [100.0%] Duration: 3 hours 07 minutes
2.	Rollout1	8/7* 8/3*	eq: +0.149 (-0.013)
	Player: Opponent: 58.52% (G:26.42% B:2.01%) 41.48% (G:12.45% B:0.95%) Conf.: ± 0.005 (+0.145...+0.154) - [0.0%] Duration: 3 hours 21 minutes
3.	Rollout1	8/7* 6/1*	eq: +0.141 (-0.021)
	Player: Opponent: 58.44% (G:25.00% B:1.12%) 41.56% (G:11.79% B:0.71%) Conf.: ± 0.004 (+0.137...+0.145) - [0.0%] Duration: 4 hours 11 minutes
4.	Rollout2	10/5 6/5	eq: +0.135 (-0.027)
	Player: Opponent: 58.67% (G:21.90% B:1.23%) 41.33% (G:10.54% B:0.58%) Conf.: ± 0.006 (+0.129...+0.140) - [0.0%] Duration: 2 hours 08 minutes
5.	Rollout2	24/23 18/13	eq: +0.127 (-0.035)
	Player: Opponent: 59.13% (G:19.07% B:0.91%) 40.87% (G:9.32% B:0.33%) Conf.: ± 0.005 (+0.122...+0.132) - [0.0%] Duration: 2 hours 08 minutes
6.	Rollout2	18/13 8/7*	eq: +0.122 (-0.040)
	Player: Opponent: 58.41% (G:21.69% B:1.37%) 41.59% (G:10.44% B:0.47%) Conf.: ± 0.006 (+0.117...+0.128) - [0.0%] Duration: 2 hours 27 minutes
1 10368 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 92861368 Moves: 3-ply, cube decisions: XG Roller

Messages In This Thread

• Donkey Variant
  Nack Ballard -- Sunday, 6 April 2014, at 1:56 p.m.
  • Donkey Variant
    MishyPoo -- Sunday, 6 April 2014, at 2:52 p.m.
  • Donkey Variant
    Christian Munk-Christensen -- Sunday, 6 April 2014, at 3:43 p.m.
  • Donkey Variant
    mandm1951 -- Sunday, 6 April 2014, at 4:51 p.m.
  • Donkey Variant
    Timothy Chow -- Sunday, 6 April 2014, at 5:31 p.m.
  • Donkey Variant
    Robert Chow -- Sunday, 6 April 2014, at 5:58 p.m.
  • Donkey Variant
    Fatboy -- Sunday, 6 April 2014, at 6:04 p.m.
    • Donkey Variant
      Stick -- Sunday, 6 April 2014, at 7:30 p.m.
      • Donkey Variant
        Fatboy -- Monday, 7 April 2014, at 12:05 a.m.
        • Donkey Variant
          Stick -- Monday, 7 April 2014, at 12:58 a.m.
          • Donkey Variant
            Nack Ballard -- Monday, 7 April 2014, at 2:03 a.m.
            • Donkey Variant
              Keene -- Monday, 7 April 2014, at 2:30 a.m.
          • Donkey Variant
            Fatboy -- Monday, 7 April 2014, at 8:13 a.m.
            • Donkey variant
              Timothy Chow -- Monday, 7 April 2014, at 1:56 p.m.
  • Donkey Variant
    Stick -- Sunday, 6 April 2014, at 7:34 p.m.
  • Donkey Variant
    Keene -- Sunday, 6 April 2014, at 11:33 p.m.
  • Donkey Variant
    Robert Chow -- Wednesday, 9 April 2014, at 1:16 a.m.
  • Donkey Variant, ROLLOUTS
    Nack Ballard -- Wednesday, 9 April 2014, at 5:31 a.m.
    • A couple of followup questions
      Timothy Chow -- Wednesday, 9 April 2014, at 3:04 p.m.
      • A couple of followup questions
        Nack Ballard -- Wednesday, 9 April 2014, at 9:06 p.m.
        • A couple of followup questions
          Timothy Chow -- Thursday, 10 April 2014, at 2:20 p.m.
      • Cube rolllouts after 51K
        Nack Ballard -- Thursday, 10 April 2014, at 10:38 p.m.
        • Cube rolllouts after 51K
          Timothy Chow -- Friday, 11 April 2014, at 3:10 p.m.
    • Donkey Variant, ROLLOUTS
      Robert Chow -- Wednesday, 9 April 2014, at 4:10 p.m.
      • Retrograde chess problems
        Nack Ballard -- Wednesday, 9 April 2014, at 9:43 p.m.
        • Retrograde chess problems
          Robert Chow -- Thursday, 10 April 2014, at 2:16 a.m.
          • Retrograde chess problems
            Timothy Chow -- Thursday, 10 April 2014, at 2:29 p.m.
            • Retrograde chess problems
              Robert Chow -- Thursday, 10 April 2014, at 6:10 p.m.