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64 opening for money / XGR++ analysis

Posted By: Steven E. Carey
Date: Monday, 4 June 2018, at 4:53 p.m.

I think the opening 64 is the most intriguing opening roll. For money and most match scores any of the three plays are valid. It takes an very lopsided match score to eliminate even one of the plays. Only a few scores have only one valid play according to XG (within .020 equity); Gammon Go, -5 -2, -4 -2 most prominently. Of course, that play is making the 2 point. (Is there anyone out there who refuses to make the 2 point?)

I undertook these rollouts to try to prove a theoretical point: what is the difference between XGR+ and XGR++ rollouts. At least for this move it seems to be not very much.

		White is Player 2 score: 0 pip: 167 Unlimited Game Jacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-b----E-C---eE---c-e----B-:0:0:1:64:0:0:3:0:10
Blue to play 64

1.	Rollout1	8/2 6/2	eq: +0.0149
	Player: Opponent: 49.67% (G:16.09% B:0.93%) 50.33% (G:14.26% B:0.66%) Conf.: ±0.0020 (+0.0129...+0.0168) - [95.2%] Duration: 17 days 22 hours 44 minutes
2.	Rollout1	24/18 13/9	eq: +0.0124 (-0.0024)
	Player: Opponent: 50.31% (G:13.73% B:0.68%) 49.69% (G:13.72% B:0.59%) Conf.: ±0.0020 (+0.0104...+0.0145) - [4.8%] Duration: 26 days 08 hours 59 minutes
3.	Rollout1	24/14	eq: +0.0086 (-0.0062)
	Player: Opponent: 50.53% (G:12.22% B:0.59%) 49.47% (G:13.25% B:0.49%) Conf.: ±0.0020 (+0.0067...+0.0106) - [0.0%] Duration: 27 days 05 hours 08 minutes
4.	Book2	24/20 13/7	eq: -0.0589 (-0.0738)
	Player: Opponent: 48.49% (G:13.89% B:0.65%) 51.51% (G:14.29% B:0.65%) Conf.: ±0.0074 (-0.0663...-0.0515) - [0.0%]
5.	Book3	24/20 24/18	eq: -0.0760 (-0.0908)
	Player: Opponent: 48.71% (G:11.29% B:0.48%) 51.29% (G:14.59% B:0.51%)
6.	Book3	13/9 13/7	eq: -0.0812 (-0.0961)
	Player: Opponent: 47.89% (G:14.01% B:0.71%) 52.11% (G:15.13% B:0.95%)
7.	3-ply	13/3	eq: -0.0882 (-0.1030)
	Player: Opponent: 47.52% (G:13.20% B:0.60%) 52.48% (G:14.40% B:0.76%)
1 46656 Games rolled with Variance Reduction. Dice Seed: 58918962 Moves and cube decisions: XG Roller++ 2 Generated by GameSite 2000, Ltd on 2/26/2011 using eXtreme Gammon 2.00 10368 Games rolled with Variance Reduction. Dice Seed: 38613390 Moves: 2-ply, cube decisions: 3-ply Red 3 Generated by GameSite 2000, Ltd on 5/21/2011 using eXtreme Gammon 2.00 Analyzed in XG Roller++

eXtreme Gammon Version: 2.10

Sorry 2 point haters, but making the 2 point is the top play albeit not by very much. Note that the equities have changed very little. The point play gained .0039, the split gained .0003 and the run play gained .0001 in equity. I admit that I was expecting something more dramatic. One thing that I take from this and other first and second move rollouts is that computers can never solve the human element in the game. These are three utterly different moves, pushing the game in very different directions and yet all are equal at a broad range of scores. The right answer, of course, is you. What is your style and how you think your skill interacts with your opponent.

Another interesting aspect is the amount of time for each play. The run play took the longest at 3 weeks 6 days 5 hours 8 minutes, the split play a little shorter at 3 weeks 5 days 8 hours 59 minutes, and the point play 2 weeks 3 days 22 hours 59 minutes. That's over a week less. I assume that is just cube action. The total run time was 10 weeks 1 day 12 hours 51 minutes on a 10 core running a little about 15.2 million positions per second. I ran these one unit of rollouts (1296) at a time, taking a little under 2 days then restart because of memory issues and continue.

And for comparison here is XGR+ analysis by Neil Kazaross.

		White is Player 2 score: 0 pip: 167 Unlimited Game Jacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-b----E-C---eE---c-e----B-:0:0:1:64:0:0:3:0:10
Blue to play 64

1.	Book1	24/18 13/9	eq: +0.0127
	Player: Opponent: 50.38% (G:13.61% B:0.64%) 49.62% (G:13.55% B:0.58%) Conf.: ±0.0022 (+0.0105...+0.0149) - [87.0%]
2.	Book1	8/2 6/2	eq: +0.0110 (-0.0017)
	Player: Opponent: 49.76% (G:15.86% B:0.87%) 50.24% (G:14.29% B:0.65%) Conf.: ±0.0020 (+0.0090...+0.0129) - [12.9%]
3.	Book1	24/14	eq: +0.0085 (-0.0042)
	Player: Opponent: 50.60% (G:11.94% B:0.57%) 49.40% (G:13.10% B:0.47%) Conf.: ±0.0020 (+0.0064...+0.0105) - [0.1%]
4.	Book2	24/20 13/7	eq: -0.0589 (-0.0716)
	Player: Opponent: 48.49% (G:13.89% B:0.65%) 51.51% (G:14.29% B:0.65%) Conf.: ±0.0074 (-0.0663...-0.0515) - [0.0%]
5.	Book3	24/20 24/18	eq: -0.0760 (-0.0886)
	Player: Opponent: 48.71% (G:11.29% B:0.48%) 51.29% (G:14.59% B:0.51%)
6.	Book3	13/9 13/7	eq: -0.0812 (-0.0939)
	Player: Opponent: 47.89% (G:14.01% B:0.71%) 52.11% (G:15.13% B:0.95%)
7.	3-ply	13/3	eq: -0.0882 (-0.1008)
	Player: Opponent: 47.52% (G:13.20% B:0.60%) 52.48% (G:14.40% B:0.76%)
8.	3-ply	24/18 6/2	eq: -0.1232 (-0.1359)
	Player: Opponent: 47.36% (G:11.18% B:0.53%) 52.64% (G:15.26% B:0.68%)
1 Generated by Neil Kazaross on 12/17/2010 using eXtreme Gammon 2.00 46656 Games rolled with Variance Reduction. Dice Seed: 41387960 Moves and cube decisions: XG Roller+ 2 Generated by GameSite 2000, Ltd on 2/26/2011 using eXtreme Gammon 2.00 10368 Games rolled with Variance Reduction. Dice Seed: 38613390 Moves: 2-ply, cube decisions: 3-ply Red 3 Generated by GameSite 2000, Ltd on 5/21/2011 using eXtreme Gammon 2.00 Analyzed in XG Roller++

eXtreme Gammon Version: 2.10

Messages In This Thread

• 64 opening for money / XGR++ analysis
  Steven E. Carey -- Monday, 4 June 2018, at 4:53 p.m.
  • 64 opening for money / XGR++ analysis
    neilkaz -- Monday, 4 June 2018, at 7:10 p.m.
    • 64 opening for money / XGR++ analysis
      Jack Edelson -- Tuesday, 5 June 2018, at 6:02 p.m.
      • 64 opening for money / XGR++ analysis
        Stick -- Tuesday, 5 June 2018, at 6:07 p.m.
    • 64 opening for money / XGR++ analysis
      eXtreme Gammon -- Wednesday, 6 June 2018, at 1:42 a.m.
      • 64 opening for money / XGR++ analysis
        Steven E. Carey -- Wednesday, 6 June 2018, at 5:43 p.m.
        • 64 opening for money / XGR++ analysis
          neilkaz -- Wednesday, 6 June 2018, at 5:56 p.m.
          • 64 opening for money / XGR++ analysis
            Steven E. Carey -- Wednesday, 6 June 2018, at 6:40 p.m.
  • 64 opening for money / XGR++ analysis
    Florin Popa -- Tuesday, 5 June 2018, at 7:51 p.m.
    • 64 opening for money / XGR++ analysis
      Steven E. Carey -- Tuesday, 5 June 2018, at 8:33 p.m.
      • 64 opening for money / XGR++ analysis
        neilkaz -- Tuesday, 5 June 2018, at 10:11 p.m.
        • 64 opening for money / XGR++ analysis
          Steven E. Carey -- Tuesday, 5 June 2018, at 10:50 p.m.
  • Thank you for this
    Fatboy -- Wednesday, 6 June 2018, at 1:55 a.m.