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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: 137Unlimited Game
Jacoby Beaverpip: 153
score: 0
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:0:0:3:0:10 54S44P33_M41H52C51A51H11P11P66
(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 (fourscore 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! Triareal 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 fourscore 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 fourscore 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 fourscore. 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, 3ply and 4ply:
........m (Money) 3ply
White is Player 2
score: 0
pip: 137Unlimited Game
Jacoby Beaverpip: 153
score: 0
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:0:0:3:0:10 m[F B16 S27 P59] "<=31*18 5
1. Rollout^{1} 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 minutes2. Rollout^{1} 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 minutes3. Rollout^{2} 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 minutes4. Rollout^{3} 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: 3ply, cube decisions: XG Roller
^{2} 20736 Games rolled with Variance Reduction.
Dice Seed: 50362527
Moves: 3ply, cube decisions: XG Roller
^{3} 5184 Games rolled with Variance Reduction.
Dice Seed: 50362527
Moves: 3ply, cube decisions: XG Roller........m (Money) 4ply
White is Player 2
score: 0
pip: 137Unlimited Game
Jacoby Beaverpip: 153
score: 0
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:0:0:3:0:10 m[F B14] "^28
1. Rollout^{1} 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 minutes2. Rollout^{1} 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: 4ply
Search interval: Larged (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 fourscore 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 fourscore 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) 3ply
White is Player 2
score: 0
pip: 1371 point match pip: 153
score: 0
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:0:0:0:1:10 d[B S21 F53 P159] "<=5
1. Rollout^{1} 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 minutes2. Rollout^{1} 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 minutes3. Rollout^{1} 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 minutes4. Rollout^{1} 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: 3ply, cube decisions: XG Rollers (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) 3ply
White is Player 2
score: 0
pip: 1372 point match
Crawfordpip: 153
score: 1
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:1:0:1:2:10 s[S B47 F97 P243] "<=5
1. Rollout^{1} 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 minutes2. Rollout^{1} 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 minutes3. Rollout^{1} 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 minutes4. Rollout^{1} 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: 3ply, cube decisions: XG Rollerg (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) 3ply
White is Player 2
score: 1
pip: 1372 point match
Crawfordpip: 153
score: 0
Blue is Player 1XGID=aBBBCacCbccbC:0:0:1:66:0:1:1:2:10 g[P F15 B105 S150] "<=10*5
1. Rollout^{1} 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 minutes2. Rollout^{1} 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 minutes3. Rollout^{2} 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 minutes4. Rollout^{2} 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: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction.
Dice Seed: 50362527
Moves: 3ply, 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) 3ply, F is best, then relatively B is –.016, S is –.027, and P is –.059................3ply.................................................4ply
..... 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*5Key: ..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" errorscale 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 fourscore positions, errorscale cusps and power scores, click mainly here, also here, here, and here.
Nack

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