BGonline.org Forums

22 to play -- VARIANT (1 pip different) -- Rollouts and explanation

Posted By: Nack Ballard
Date: Thursday, 15 November 2018, at 12:34 a.m.

In Response To: Help: 22 to play -- VARIANT (1 pip different) (David Levy)

		White is Player 2 score: 0 pip: 82 7 point match Crawford pip: 117 score: 6 Blue is Player 1
XGID=-BBB--BaBABa-------bbdbcB-:0:0:1:22:6:0:1:7:10
Original position

1.	Rollout1	9/7* 7/5 6/4(2)	eq: -0.471
	Player: Opponent: 28.81% (G:3.27% B:0.03%) 71.19% (G:27.47% B:1.44%) Conf.: ± 0.002 (-0.473...-0.469) - [100.0%] Duration: 10 minutes 30 seconds
2.	Rollout1	10/6 9/7* 7/5	eq: -0.483 (-0.011)
	Player: Opponent: 28.93% (G:3.30% B:0.04%) 71.07% (G:32.05% B:2.10%) Conf.: ± 0.002 (-0.485...-0.481) - [0.0%] Duration: 11 minutes 17 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 34574574 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 81 7 point match Crawford pip: 117 score: 6 Blue is Player 1
XGID=-BBB--BaBAB-a------bbdbcB-:0:0:1:22:6:0:1:7:10
Variant (White's 14pt blot is moved to her 13pt)

1.	Rollout1	10/6 9/7* 7/5	eq: -0.461
	Player: Opponent: 29.78% (G:4.22% B:0.05%) 70.22% (G:30.67% B:1.87%) Conf.: ± 0.002 (-0.463...-0.459) - [100.0%] Duration: 12 minutes 43 seconds
2.	Rollout1	9/7* 7/5 6/4(2)	eq: -0.469 (-0.008)
	Player: Opponent: 28.94% (G:3.62% B:0.04%) 71.06% (G:26.83% B:1.46%) Conf.: ± 0.002 (-0.470...-0.467) - [0.0%] Duration: 11 minutes 36 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 58946702 Moves: 3-ply, cube decisions: XG Roller

The original position is first (on the left if your window is sufficiently wide). The variant position is second (on the right). The only difference is White's 1 pip in the outfield. Why does that cause 9/7*/5 6/4(2) to go from +.011 to –.008? For the answer, read on.

When Blue plays 10/6 9/7*/5 and White rolls 44 (from the bar):

In the first (original) position, White can play 14/2 in the first position, maintaining her five-prime. In the second (variant) position, White must play 13/5 6/2, breaking her 6pt.

We can check the approximate impact of the double 4s by plugging the after-positions into XGR++. White's equity is .370 in the first case, compared to –.284 in the second case. The difference x 1/36 (chances of rolling double 4s) = .018. This accounts for almost all of (.011 + .008) = .019 difference that is rolled out.

White's 1-pip (14/13) difference is almost immaterial when Blue plays 9/7*/5 6/4(2) because White's 44 will fan either way.

[The difference on double 6s (using the same methodology) is 20/36 of .001, and actually if you go out an extra decimal place with all numbers the sum including 66 lands almost exactly on the (.0112 + .0075) = .0187 rollout swing, but that's partly luck because with these mere-5k rollouts there is still variance of +/- .0038 (accounting for +/- .0019 for each play in each position).]

Nice problem.

Nack

Messages In This Thread

• 22 to play in poor ace-point game
  David Levy -- Saturday, 10 November 2018, at 4:56 p.m.
  • A interesting problem, yes, but certainly not a poor ace-point game at DMP
    Jim Stutz -- Saturday, 10 November 2018, at 10:58 p.m.
    • A interesting problem, yes, but certainly not a poor ace-point game at DMP
      neilkaz -- Sunday, 11 November 2018, at 12:28 a.m.
    • A poor ace-point game?
      David Levy -- Sunday, 11 November 2018, at 7:59 p.m.
  • 22 to play in poor ace-point game
    ah_clem -- Sunday, 11 November 2018, at 3:07 p.m.
  • 22 to play in poor ace-point game
    ah_clem -- Sunday, 11 November 2018, at 3:14 p.m.
  • 22 to play -- VARIANT (1 pip different)
    Nack Ballard -- Tuesday, 13 November 2018, at 5:50 p.m.
    • 22 to play -- VARIANT (1 pip different)
      ah_clem -- Tuesday, 13 November 2018, at 7:02 p.m.
    • 22 to play -- VARIANT (1 pip different)
      David Levy -- Tuesday, 13 November 2018, at 7:44 p.m.
      • 22 to play -- VARIANT (1 pip different)
        Nack Ballard -- Tuesday, 13 November 2018, at 8:01 p.m.
        • Help: 22 to play -- VARIANT (1 pip different)
          David Levy -- Wednesday, 14 November 2018, at 10:01 p.m.
          • 22 to play -- VARIANT (1 pip different) -- Rollouts and explanation
            Nack Ballard -- Thursday, 15 November 2018, at 12:34 a.m.
  • This rollout still leaves me with questions
    David Levy -- Tuesday, 13 November 2018, at 7:41 p.m.
    • This rollout still leaves me with questions
      Nack Ballard -- Tuesday, 13 November 2018, at 8:53 p.m.
    • Full disclosure, which will come as no surprise
      Jim Stutz -- Wednesday, 14 November 2018, at 7:47 a.m.
      • Full disclosure, which will come as no surprise
        ah_clem -- Wednesday, 14 November 2018, at 2:50 p.m.
      • Full disclosure, which will come as no surprise
        Albert Steg -- Wednesday, 14 November 2018, at 5:20 p.m.
      • Full disclosure, which will come as no surprise
        Fatboy -- Wednesday, 14 November 2018, at 5:38 p.m.