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Bar Point Bewilderment, FOUR SCORE Rollouts

Posted By: Nack Ballard
Date: Saturday, 20 June 2015, at 12:55 a.m.

		White is Player 2 score: 0 pip: 137 Unlimited Game Jacoby Beaver pip: 153 score: 0 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:0:0:3:0:10
54S-44P-33_M-41H-52C-51A-51H-11P-11P-66 (perfectly played money sequence)

In the position diagrammed above (originally posted here), bgonliners were asked:

"What would you play for Blue with double 6s, at each of the four (classically recognized) main scores?"

m (Money)...(as shown)

The best move is F (Field) = 24/18(2) 13/1*, chosen by Sean Garber, and by Igor, who said: "The toughest choice is for money. If not for the QF (four-score position?), I'd probably go with the DMP move. But let's say I want to please Nack by falling into the QF trap and I'll name F as the money move." [Great choice, and well nactated! Tri-areal doublets -- those played into three quadrants -- are explained on page 108 of the Nactation tutorial.]

There seems to be a growing belief (first voiced, I think, by Joe Russell) that my Challenge posts are automatically four-score positions. Fortunately, even if true (though I never said one way or the other), choosing the best move for each score is still a challenge. As Sean implies, Challenge #1 and #2 were NOT four-score positions, though #3, #4 and #5 were. Igor did choose four different best plays for this thread (Challenge #6) but suspects I've been setting a trap and this time perhaps it is not four-score. Well, I admit that is the sort of trap I might set, so if some day I get around to posting a Challenge #7, be forewarned -- who knows!

Below are rollouts, 3-ply and 4-ply:

........m (Money) 3-ply

		White is Player 2 score: 0 pip: 137 Unlimited Game Jacoby Beaver pip: 153 score: 0 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:0:0:3:0:10
m[F B16 S27 P59] "<=31*18 5

1.	Rollout1	24/18(2) 13/1*	eq: +0.430
	Player: Opponent: 56.74% (G:27.44% B:0.56%) 43.26% (G:13.43% B:0.65%) Conf.: ± 0.002 (+0.429...+0.432) - [100.0%] Duration: 8 hours 26 minutes
2.	Rollout1	24/18(2) 13/7(2)	eq: +0.415 (-0.016)
	Player: Opponent: 59.90% (G:20.29% B:0.80%) 40.10% (G:13.63% B:0.58%) Conf.: ± 0.002 (+0.412...+0.417) - [0.0%] Duration: 12 hours 10 minutes
3.	Rollout2	24/18(3) 13/7	eq: +0.403 (-0.027)
	Player: Opponent: 58.47% (G:18.87% B:0.42%) 41.53% (G:10.07% B:0.32%) Conf.: ± 0.004 (+0.400...+0.407) - [0.0%] Duration: 6 hours 40 minutes
4.	Rollout3	13/1*(2)	eq: +0.372 (-0.059)
	Player: Opponent: 52.27% (G:34.72% B:0.40%) 47.73% (G:15.46% B:1.10%) Conf.: ± 0.009 (+0.363...+0.381) - [0.0%] Duration: 1 hour 18 minutes
1 51840 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller 2 20736 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller 3 5184 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller

........m (Money) 4-ply

		White is Player 2 score: 0 pip: 137 Unlimited Game Jacoby Beaver pip: 153 score: 0 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:0:0:3:0:10
m[F B14] "^28

1.	Rollout1	24/18(2) 13/1*	eq: +0.431
	Player: Opponent: 56.75% (G:27.70% B:0.57%) 43.25% (G:13.42% B:0.67%) Conf.: ± 0.002 (+0.429...+0.433) - [100.0%] Duration: 1 day 17 hours 15 minutes
2.	Rollout1	24/18(2) 13/7(2)	eq: +0.417 (-0.014)
	Player: Opponent: 59.94% (G:20.57% B:0.86%) 40.06% (G:13.74% B:0.59%) Conf.: ± 0.003 (+0.415...+0.420) - [0.0%] Duration: 2 days 06 hours 49 minutes
1 28512 Games rolled with Variance Reduction. Dice Seed: 13389739 Moves and cube decisions: 4-ply Search interval: Large

d (DMP)...

The best move is B (Both) = 24/18(2) 13/7(2), selected by two respondents:

Igor: "At DMP priming and running game plans dominate attacking, so my choice is B."

Diversification to four different best plays does not necessarily improve one's overall choices. David Rennie selected B for both money and DMP, but stated that IF this is a four-score position he'd go with B for money and F for DMP (which is reversed). So, while he actually picked three of the four right, with a four-score assumption he would have gotten only two right! (On the other hand, for money Igor chose F instead of B only because of diversification, so he increased from three right to four right.)

Here is the rollout:

........d (DMP) 3-ply

		White is Player 2 score: 0 pip: 137 1 point match pip: 153 score: 0 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:0:0:0:1:10
d[B S21 F53 P159] "<=5

1.	Rollout1	24/18(2) 13/7(2)	eq: +0.201
	Player: Opponent: 60.04% (G:20.51% B:2.43%) 39.96% (G:14.44% B:1.52%) Conf.: ± 0.003 (+0.198...+0.204) - [100.0%] Duration: 1 hour 16 minutes
2.	Rollout1	24/18(3) 13/7	eq: +0.180 (-0.021)
	Player: Opponent: 59.00% (G:16.71% B:1.16%) 41.00% (G:10.03% B:0.75%) Conf.: ± 0.002 (+0.178...+0.182) - [0.0%] Duration: 1 hour 22 minutes
3.	Rollout1	24/18(2) 13/1*	eq: +0.148 (-0.053)
	Player: Opponent: 57.38% (G:27.30% B:1.18%) 42.62% (G:13.68% B:1.61%) Conf.: ± 0.002 (+0.145...+0.150) - [0.0%] Duration: 1 hour 18 minutes
4.	Rollout1	13/1*(2)	eq: +0.042 (-0.159)
	Player: Opponent: 52.09% (G:34.58% B:0.61%) 47.91% (G:15.09% B:2.78%) Conf.: ± 0.003 (+0.039...+0.044) - [0.0%] Duration: 1 hour 00 minute
1 5184 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller

s (Gammon Save)...

The best move is S (Split 3:1) = 24/18(3) 13/7, supported by Sean and David (without comment), and by Igor: "At GS advanced anchors are of high priority, so I'd go with S."

It is a big sacrifice not to make the powerful prime; i.e., failing to cover the offensive bar point. In exchange, however, Blue extricates his third back checker, leaves only one blot (instead of two) and risks 13 shots instead of 30 (all numbers except 63 62 66 22). These are considerations of elevated importance at Gammon Save.

Here is the rollout:

........s (Gammon Save) 3-ply

		White is Player 2 score: 0 pip: 137 2 point match Crawford pip: 153 score: 1 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:1:0:1:2:10
s[S B47 F97 P243] "<=5

1.	Rollout1	24/18(3) 13/7	eq: -0.031
	Player: Opponent: 59.15% (G:18.20% B:1.51%) 40.85% (G:10.69% B:0.61%) Conf.: ± 0.003 (-0.034...-0.027) - [100.0%] Duration: 1 hour 18 minutes
2.	Rollout1	24/18(2) 13/7(2)	eq: -0.077 (-0.047)
	Player: Opponent: 60.08% (G:20.91% B:2.90%) 39.92% (G:13.95% B:1.36%) Conf.: ± 0.004 (-0.081...-0.073) - [0.0%] Duration: 1 hour 13 minutes
3.	Rollout1	24/18(2) 13/1*	eq: -0.128 (-0.097)
	Player: Opponent: 57.58% (G:27.20% B:1.51%) 42.42% (G:13.97% B:1.47%) Conf.: ± 0.004 (-0.131...-0.124) - [0.0%] Duration: 1 hour 12 minutes
4.	Rollout1	13/1*(2)	eq: -0.274 (-0.243)
	Player: Opponent: 52.69% (G:34.97% B:0.77%) 47.31% (G:16.37% B:3.35%) Conf.: ± 0.004 (-0.278...-0.270) - [0.0%] Duration: 55 minutes 33 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 41258338 Moves: 3-ply, cube decisions: XG Roller

g (Gammon Go)...

The best move is P (Point) = 13/1*(2). The three respondents who chose correctly seemed to find this the most easily decided score. Sean and David added no comment, but Igor elaborated slightly: "It looks clear to attack with O." [O (Outer) is the areal description. I chose to use the style description P (Point). Both are correct Nactations.]

Blue's aim, at the risk of his back checkers getting stuck, is to maximize his chance of hitting White's other blot. This is frequently a key theme at Gammon Go.

Here is the rollout:

........g (Gammon Go) 3-ply

		White is Player 2 score: 1 pip: 137 2 point match Crawford pip: 153 score: 0 Blue is Player 1
XGID=-a-BBBC-a---cC---b-ccb--C-:0:0:1:66:0:1:1:2:10
g[P F15 B105 S150] "<=10*5

1.	Rollout1	13/1*(2)	eq: +0.734
	Player: Opponent: 52.16% (G:34.56% B:0.99%) 47.84% (G:15.31% B:3.08%) Conf.: ± 0.003 (+0.731...+0.737) - [100.0%] Duration: 1 hour 56 minutes
2.	Rollout1	24/18(2) 13/1*	eq: +0.719 (-0.015)
	Player: Opponent: 57.04% (G:28.93% B:1.23%) 42.96% (G:14.37% B:1.86%) Conf.: ± 0.003 (+0.717...+0.722) - [0.0%] Duration: 2 hours 23 minutes
3.	Rollout2	24/18(2) 13/7(2)	eq: +0.627 (-0.107)
	Player: Opponent: 59.43% (G:21.94% B:1.45%) 40.57% (G:14.91% B:1.81%) Conf.: ± 0.004 (+0.624...+0.631) - [0.0%] Duration: 1 hour 09 minutes
4.	Rollout2	24/18(3) 13/7	eq: +0.582 (-0.153)
	Player: Opponent: 57.36% (G:21.74% B:1.02%) 42.64% (G:12.50% B:1.11%) Conf.: ± 0.004 (+0.578...+0.585) - [0.0%] Duration: 1 hour 13 minutes
1 10368 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller 2 5184 Games rolled with Variance Reduction. Dice Seed: 50362527 Moves: 3-ply, cube decisions: XG Roller

The nacbracs summary below lists the best play at each score followed by successively weaker plays (with error sizes), according to the rollouts (diagrammed above). For example, for m (Money) 3-ply, F is best, then relatively B is –.016, S is –.027, and P is –.059.

...............3-ply.................................................4-ply

..... m[F B16 S27 P59] "<=31*18 5........... m[F B14] "^28
...... d[B S21 F53 P159] "<=5
...... s[S B47 F97 P243] "<=5
...... g[P F15 B105 S150] "<=10*5

Key: ..B (Both) = 24/18(2) 13/7(2), F (Field) = 24/18(2) 13/1*, P (Point) = 13/1*(2), S (Split 3:1) = 24/18(3) 13/7.

Nactation tutorial • explanation of nacbracs

In the above summary, a quick look down the left column reveals that each of the four scores (m, d, s, g) champions a different best play (F, B, S, P). Moreover, the margins of .016, .021, .047 and .015 exceed their respective "tied" error-scale cusps of .010, .0045, .007 and .007.

The power score (of this double 6s position) is [sqrt 16 + sqrt 21*20/9 + sqrt 47*10/7 + sqrt 15*10/7] = 23.65. For more information on four-score positions, error-scale cusps and power scores, click mainly here, also here, here, and here.

Nack

Messages In This Thread

• Bar Point Bewilderment, FOUR SCORE Rollouts
  Nack Ballard -- Saturday, 20 June 2015, at 12:55 a.m.
  • Slight correction (28 numbers)
    Nack Ballard -- Saturday, 20 June 2015, at 8:39 a.m.