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Rollout Results

Posted By: Paul Weaver
Date: Sunday, 9 February 2014, at 8:56 a.m.

In Response To: Two Tough Plays (Paul Weaver)

I applaud Mishy Poo for being the only one courageous enough to post answers.

The position after the best play, 6/3* 6/1, is shown on the right. I admit I did not consider this bizarre-looking play over the board.

How can it possibly be right to give up the 6pt and leave a blot in your board when White has a strong four-point board? This play has a few things going for it: (1) It leaves the fewest shots. (2) It is the only one of the three plays that hits; consequently, it is the only play that will results in White's fanning. How often does White fan? Mathematically and theoretically, White fans exactly 25% of the time on an upside-down 1-2-5 three-point board. Empirically, however (and this is a little-known fact), White fans far more often than 25% on this 1-2-5 board. (3) In many variations, White will come in without hitting and Blue will be able to run and eventually safety his back checker, hoping to win the race.

But wait a minute, doesn't this play lose a lot of Gs for Blue? Absolutely, but take a look at the probability distribution. Blue wins enough extra games and Gs to compensate for his gammon losses.

If the universe continues to exist for long enough while mankind continues to waste time playing backgammon, then this parlay will eventually occur zillions and Brazilians of times: (1) the position diagramed below left will occur in a chouette with Blue to play 53, (2) the weakest player will be the only one to suggest the best play of breaking the 6pt and (3) everyone else will shout him down, dismiss his play as "absurd" and ridicule him.

White is NevzatDogan score: 0 pip: 123 Unlimited Game Jacoby Beaver pip: 121 score: 0 Blue is peever XGID=-ABa-BBbB-C-aB---b-bbbAc--:1:-1:1:53:0:0:3:0:10 Blue to play 53 1. Rollout1 6/1 6/3* eq: -0.341 Player: Opponent: 45.48% (G:16.41% B:0.40%) 54.52% (G:23.20% B:0.70%) Conf.: ± 0.009 (-0.349...-0.332) - [100.0%] Duration: 2 minutes 08 seconds 2. Rollout1 13/10 13/8 eq: -0.436 (-0.095) Player: Opponent: 41.87% (G:11.03% B:0.47%) 58.13% (G:16.13% B:0.21%) Conf.: ± 0.007 (-0.443...-0.428) - [0.0%] Duration: 1 minute 56 seconds 3. Rollout1 10/2 eq: -0.440 (-0.099) Player: Opponent: 43.24% (G:11.97% B:0.41%) 56.76% (G:21.27% B:0.58%) Conf.: ± 0.009 (-0.449...-0.431) - [0.0%] Duration: 2 minutes 03 seconds 4. 2-ply 8/5 8/3* eq: -0.471 (-0.130) Player: Opponent: 42.23% (G:15.45% B:0.44%) 57.77% (G:27.43% B:0.92%) 1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller eXtreme Gammon Version: 2.10

White is NevzatDogan score: 0 pip: 126 Unlimited Game Jacoby Beaver pip: 113 score: 0 Blue is peever XGID=aBBA-B-bB-C-aB---b-bbbAc--:1:-1:-1:00:0:0:3:0:10 White on roll, cube action? Analyzed in XG Roller++ No redouble Redouble/Take Player Winning Chances: 54.32% (G:22.15% B:0.61%) 54.30% (G:22.89% B:0.60%) Opponent Winning Chances: 45.68% (G:16.45% B:0.48%) 45.70% (G:16.26% B:0.48%) Cubeless Equities +0.145 +0.307 Cubeful Equities No redouble: +0.326 Redouble/Beaver: -0.001 (-0.327) Redouble/Pass: +1.000 (+0.674) Best Cube action: No redouble / Beaver Percentage of wrong pass needed to make the double decision right: 24.6% eXtreme Gammon Version: 2.10

If the two positions below came up in back-to-back games (which will eventually happen zillions and Brazilians of times), how many of us would get both of these right?

White is NevzatDogan score: 0 pip: 111 Unlimited Game Jacoby Beaver pip: 137 score: 0 Blue is peever XGID=--a-BBCB---AbD--b--cbc-bA-:0:0:1:62:0:0:3:0:10 Blue to play 62 1. Rollout1 24/18 13/11 eq: -0.400 Player: Opponent: 40.84% (G:6.35% B:0.30%) 59.16% (G:24.95% B:0.24%) Conf.: ± 0.016 (-0.417...-0.384) - [100.0%] Duration: 2 minutes 42 seconds 2. Rollout1 13/11 13/7 eq: -0.442 (-0.042) Player: Opponent: 40.54% (G:9.55% B:0.53%) 59.46% (G:24.69% B:0.33%) Conf.: ± 0.012 (-0.454...-0.431) - [0.0%] Duration: 1 minute 47 seconds 3. Rollout1 13/5 eq: -0.549 (-0.149) Player: Opponent: 38.07% (G:10.15% B:0.53%) 61.93% (G:28.54% B:0.39%) Conf.: ± 0.017 (-0.566...-0.533) - [0.0%] Duration: 2 minutes 13 seconds 1 1296 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller eXtreme Gammon Version: 2.10

White is NevzatDogan score: 0 pip: 111 Unlimited Game Jacoby Beaver pip: 137 score: 0 Blue is peever XGID=--a-BBCB---AbD--b--cbc-bA-:1:1:1:62:0:0:3:0:10 Blue to play 62 1. Rollout1 13/11 13/7 eq: -0.194 Player: Opponent: 40.13% (G:9.98% B:0.50%) 59.87% (G:25.24% B:0.35%) Conf.: ± 0.003 (-0.197...-0.191) - [100.0%] Duration: 27 minutes 36 seconds 2. Rollout1 24/18 13/11 eq: -0.202 (-0.009) Player: Opponent: 40.80% (G:6.46% B:0.30%) 59.20% (G:24.89% B:0.25%) Conf.: ± 0.003 (-0.205...-0.200) - [0.0%] Duration: 31 minutes 31 seconds 3. Rollout2 13/5 eq: -0.273 (-0.079) Player: Opponent: 37.85% (G:9.98% B:0.43%) 62.15% (G:27.52% B:0.39%) Conf.: ± 0.029 (-0.302...-0.244) - [0.0%] Duration: 5.8 seconds 1 10368 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller 2 45 Games rolled with Variance Reduction. Moves: 3-ply, cube decisions: XG Roller eXtreme Gammon Version: 2.10

Messages In This Thread

• Two Tough Plays
  Paul Weaver -- Saturday, 8 February 2014, at 6:16 p.m.
  • Two Tough Plays
    MishyPoo -- Saturday, 8 February 2014, at 7:17 p.m.
  • Rollout Results
    Paul Weaver -- Sunday, 9 February 2014, at 8:56 a.m.
    • Rollout Results
      Mr Majestyk -- Sunday, 9 February 2014, at 12:39 p.m.