Festival of FIVES -- ROLLOUTS at Five Scores

White is Player 2

score: 0
pip: 165

Unlimited Game
Jacoby Beaver

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:0:3:0:10
51S-21U-41X-65R-65H-54Z-41H-32H-52P-41H-54K-42-42R-55
(perfectly played money sequence)..........Nactation tutorial

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

What would you play for Blue with double 5s, at each of the four (classically recognized) main scores? And at c6 (Crawford, -1-6)?

Nobody responded (possibly because I posted during the New York tournament), so I'll just display the rollouts (no analysis).

For best viewing, widen your window to accommodate side-by-side diagrams.

........m (money).... 3-ply/XGR ...and 4-ply

White is Player 2

score: 0
pip: 165

Unlimited Game
Jacoby Beaver

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:0:3:0:10

mP S12 Y40 M62 R62 r69 s85 R93] "<=62*5

Rollout¹

21/11*(2)

eq: +0.071

Player:
Opponent:

51.76% (G:14.10% B:0.73%)
48.24% (G:13.13% B:0.56%)

Conf.: ¡Ó 0.003 (+0.068...+0.074) - [100.0%]
Duration: 1 day 08 hours 07 minutes

Rollout¹

23/18(2) 21/11*

eq: +0.059 (-0.012)

Player:
Opponent:

51.78% (G:11.91% B:0.55%)
48.22% (G:12.58% B:0.46%)

Conf.: ¡Ó 0.002 (+0.057...+0.062) - [0.0%]
Duration: 1 day 07 hours 54 minutes

Rollout²

21/11* 6/1*(2)

eq: +0.031 (-0.040)

Player:
Opponent:

49.48% (G:18.15% B:0.61%)
50.52% (G:13.46% B:0.65%)

Conf.: ¡Ó 0.009 (+0.023...+0.040) - [0.0%]
Duration: 2 hours 42 minutes

Rollout²

21/11* 8/3(2)

eq: +0.009 (-0.062)

Player:
Opponent:

49.70% (G:15.36% B:0.80%)
50.30% (G:13.42% B:0.66%)

Conf.: ¡Ó 0.010 (-0.001...+0.019) - [0.0%]
Duration: 2 hours 53 minutes

Rollout²

23/18(2) 21/16(2)

eq: +0.009 (-0.062)

Player:
Opponent:

50.16% (G:9.46% B:0.35%)
49.84% (G:9.81% B:0.38%)

Conf.: ¡Ó 0.007 (+0.001...+0.016) - [0.0%]
Duration: 2 hours 50 minutes

Rollout²

23/13 21/16(2)

eq: +0.002 (-0.069)

Player:
Opponent:

50.36% (G:9.73% B:0.38%)
49.64% (G:11.55% B:0.41%)

Conf.: ¡Ó 0.008 (-0.006...+0.009) - [0.0%]
Duration: 3 hours 00 minute

Rollout²

23/13 21/11*

eq: -0.014 (-0.085)

Player:
Opponent:

49.73% (G:12.43% B:0.59%)
50.27% (G:13.32% B:0.56%)

Conf.: ¡Ó 0.008 (-0.022...-0.006) - [0.0%]
Duration: 3 hours 18 minutes

Rollout²

23/13(2)

eq: -0.022 (-0.093)

Player:
Opponent:

49.00% (G:9.77% B:0.38%)
51.00% (G:8.58% B:0.32%)

Conf.: ¡Ó 0.007 (-0.029...-0.015) - [0.0%]
Duration: 3 hours 00 minute

¹ 62208 Games rolled with Variance Reduction.
Dice Seed: 22304267
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 22304267
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 165

Unlimited Game
Jacoby Beaver

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:0:3:0:10

m[P S18] "^5

Rollout¹

21/11*(2)

eq: +0.068

Player:
Opponent:

51.65% (G:14.22% B:0.69%)
48.35% (G:13.23% B:0.55%)

Conf.: ¡Ó 0.007 (+0.061...+0.074) - [100.0%]
Duration: 2 days 12 hours 57 minutes

Rollout¹

23/18(2) 21/11*

eq: +0.050 (-0.018)

Player:
Opponent:

51.60% (G:12.14% B:0.56%)
48.40% (G:12.55% B:0.46%)

Conf.: ¡Ó 0.007 (+0.044...+0.057) - [0.0%]
Duration: 2 days 16 hours 57 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 91373876
Moves and cube decisions: 4-ply
Search interval: Large

........d (double match point).... 3-ply/XGR ...and 4-ply

White is Player 2

score: 0
pip: 165

1 point match

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:0:0:1:10

d[S P6 R28 r30 M45 s46 Y46] "<=62*5

Rollout¹

23/18(2) 21/11*

eq: +0.034

Player:
Opponent:

51.70% (G:14.18% B:1.67%)
48.30% (G:13.68% B:1.42%)

Conf.: ¡Ó 0.001 (+0.033...+0.035) - [100.0%]
Duration: 1 day 03 hours 41 minutes

Rollout¹

21/11*(2)

eq: +0.028 (-0.006)

Player:
Opponent:

51.41% (G:17.45% B:2.40%)
48.59% (G:14.45% B:1.76%)

Conf.: ¡Ó 0.001 (+0.027...+0.029) - [0.0%]
Duration: 1 day 03 hours 31 minutes

Rollout²

23/18(2) 21/16(2)

eq: +0.006 (-0.028)

Player:
Opponent:

50.29% (G:10.13% B:0.85%)
49.71% (G:10.98% B:1.13%)

Conf.: ¡Ó 0.003 (+0.003...+0.009) - [0.0%]
Duration: 2 hours 10 minutes

Rollout²

23/13 21/16(2)

eq: +0.004 (-0.030)

Player:
Opponent:

50.19% (G:10.94% B:1.09%)
49.81% (G:11.77% B:1.22%)

Conf.: ¡Ó 0.003 (+0.001...+0.007) - [0.0%]
Duration: 2 hours 08 minutes

Rollout²

21/11* 8/3(2)

eq: -0.011 (-0.045)

Player:
Opponent:

49.47% (G:18.76% B:3.45%)
50.53% (G:14.97% B:2.04%)

Conf.: ¡Ó 0.003 (-0.014...-0.007) - [0.0%]
Duration: 2 hours 41 minutes

Rollout²

23/13 21/11*

eq: -0.011 (-0.045)

Player:
Opponent:

49.43% (G:15.34% B:2.10%)
50.57% (G:15.36% B:1.89%)

Conf.: ¡Ó 0.003 (-0.015...-0.008) - [0.0%]
Duration: 2 hours 51 minutes

Rollout²

21/11* 6/1*(2)

eq: -0.012 (-0.046)

Player:
Opponent:

49.39% (G:21.48% B:1.55%)
50.61% (G:14.47% B:2.19%)

Conf.: ¡Ó 0.003 (-0.015...-0.009) - [0.0%]
Duration: 2 hours 29 minutes

Rollout²

23/18 21/16 21/11*

eq: -0.014 (-0.048)

Player:
Opponent:

49.30% (G:15.51% B:2.36%)
50.70% (G:17.45% B:2.55%)

Conf.: ¡Ó 0.003 (-0.017...-0.011) - [0.0%]
Duration: 5 hours 06 minutes

Rollout²

23/18 21/11* 11/6

eq: -0.019 (-0.053)

Player:
Opponent:

49.03% (G:16.76% B:2.28%)
50.97% (G:15.59% B:2.03%)

Conf.: ¡Ó 0.003 (-0.022...-0.016) - [0.0%]
Duration: 3 hours 54 minutes

10.

Rollout²

23/13(2)

eq: -0.023 (-0.057)

Player:
Opponent:

48.87% (G:11.58% B:1.20%)
51.13% (G:10.65% B:0.89%)

Conf.: ¡Ó 0.003 (-0.025...-0.020) - [0.0%]
Duration: 3 hours 19 minutes

¹ 62208 Games rolled with Variance Reduction.
Dice Seed: 69838067
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 69838067
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 165

1 point match

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:0:0:1:10

d[S P7] "^7

Rollout¹

23/18(2) 21/11*

eq: +0.034

Player:
Opponent:

51.70% (G:14.13% B:1.69%)
48.30% (G:13.74% B:1.63%)

Conf.: ¡Ó 0.002 (+0.032...+0.036) - [100.0%]
Duration: 2 days 16 hours 30 minutes

Rollout¹

21/11*(2)

eq: +0.027 (-0.007)

Player:
Opponent:

51.37% (G:17.52% B:2.46%)
48.63% (G:14.33% B:1.59%)

Conf.: ¡Ó 0.002 (+0.025...+0.029) - [0.0%]
Duration: 2 days 15 hours 28 minutes

¹ 7776 Games rolled with Variance Reduction.
Dice Seed: 79125573
Moves and cube decisions: 4-ply

........s (gammon save).... 3-ply/XGR ...and 4-ply

White is Player 2

score: 0
pip: 165

2 point match
Crawford

pip: 183
score: 1

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:1:0:1:2:10

s[R R7 S37 r42 P54 c56] "<=114*5

Rollout¹

23/13(2)

eq: -0.191

Player:
Opponent:

48.49% (G:12.36% B:1.34%)
51.51% (G:8.06% B:0.66%)

Conf.: ¡Ó 0.001 (-0.192...-0.191) - [100.0%]
Duration: 2 days 06 hours 49 minutes

Rollout¹

23/18(2) 21/16(2)

eq: -0.198 (-0.007)

Player:
Opponent:

50.80% (G:11.52% B:1.20%)
49.20% (G:10.69% B:0.68%)

Conf.: ¡Ó 0.001 (-0.199...-0.197) - [0.0%]
Duration: 2 days 05 hours 55 minutes

Rollout²

23/18(2) 21/11*

eq: -0.229 (-0.038)

Player:
Opponent:

51.80% (G:15.93% B:2.13%)
48.20% (G:13.24% B:0.95%)

Conf.: ¡Ó 0.004 (-0.233...-0.225) - [0.0%]
Duration: 2 hours 46 minutes

Rollout²

23/13 21/16(2)

eq: -0.233 (-0.042)

Player:
Opponent:

50.46% (G:12.03% B:1.18%)
49.54% (G:12.12% B:0.84%)

Conf.: ¡Ó 0.004 (-0.237...-0.229) - [0.0%]
Duration: 2 hours 18 minutes

Rollout²

21/11*(2)

eq: -0.246 (-0.054)

Player:
Opponent:

51.16% (G:18.47% B:2.69%)
48.84% (G:13.45% B:1.33%)

Conf.: ¡Ó 0.004 (-0.250...-0.241) - [0.0%]
Duration: 2 hours 39 minutes

Rollout²

23/18(2) 8/3(2)

eq: -0.247 (-0.056)

Player:
Opponent:

48.99% (G:14.94% B:1.74%)
51.01% (G:11.35% B:0.99%)

Conf.: ¡Ó 0.004 (-0.251...-0.243) - [0.0%]
Duration: 2 hours 11 minutes

¹ 114048 Games rolled with Variance Reduction.
Dice Seed: 18112521
Moves: 3-ply, cube decisions: XG Roller

² 5184 Games rolled with Variance Reduction.
Dice Seed: 18112521
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 165

2 point match
Crawford

pip: 183
score: 1

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:1:0:1:2:10

s[R R9] "^15

Rollout¹

23/13(2)

eq: -0.193

Player:
Opponent:

48.34% (G:12.12% B:1.37%)
51.66% (G:7.98% B:0.64%)

Conf.: ¡Ó 0.002 (-0.194...-0.191) - [100.0%]
Duration: 4 days 08 hours 38 minutes

Rollout¹

23/18(2) 21/16(2)

eq: -0.201 (-0.009)

Player:
Opponent:

51.06% (G:11.87% B:1.23%)
48.94% (G:11.12% B:0.76%)

Conf.: ¡Ó 0.002 (-0.203...-0.200) - [0.0%]
Duration: 4 days 09 hours 21 minutes

¹ 15552 Games rolled with Variance Reduction.
Moves: 4-ply, cube decisions: XG Roller

........g (gammon go) 3-ply/XGR

White is Player 2

score: 1
pip: 165

2 point match
Crawford

pip: 183
score: 0

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:0:1:1:2:10
g[Y P33 M47 A65 S70] "<=5

1. Rollout¹ 21/11* 6/1*(2) eq: +0.337
Player:
Opponent: 50.84% (G:16.01% B:1.48%)
49.16% (G:14.53% B:2.07%) Conf.: ¡Ó 0.004 (+0.333...+0.341) - [100.0%]
Duration: 2 hours 02 minutes
2. Rollout¹ 21/11*(2) eq: +0.304 (-0.033)
Player:
Opponent: 53.24% (G:11.97% B:1.43%)
46.76% (G:13.20% B:1.30%) Conf.: ¡Ó 0.004 (+0.300...+0.308) - [0.0%]
Duration: 2 hours 17 minutes
3. Rollout¹ 21/11* 8/3(2) eq: +0.290 (-0.047)
Player:
Opponent: 50.88% (G:13.61% B:1.75%)
49.12% (G:14.74% B:1.82%) Conf.: ¡Ó 0.004 (+0.285...+0.294) - [0.0%]
Duration: 2 hours 16 minutes
4. Rollout¹ 8/3(2) 6/1*(2) eq: +0.272 (-0.065)
Player:
Opponent: 48.12% (G:15.50% B:0.88%)
51.88% (G:14.38% B:1.64%) Conf.: ¡Ó 0.004 (+0.268...+0.276) - [0.0%]
Duration: 1 hour 49 minutes
5. Rollout¹ 23/18(2) 21/11* eq: +0.267 (-0.070)
Player:
Opponent: 52.62% (G:10.75% B:1.09%)
47.38% (G:13.55% B:1.32%) Conf.: ¡Ó 0.004 (+0.264...+0.271) - [0.0%]
Duration: 2 hours 24 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 18112521
Moves: 3-ply, cube decisions: XG Roller

........c6 (Crawford, ¡V1¡V6).... 3-ply/XGR ...and 4-ply

White is Player 2

score: 0
pip: 165

6 point match
Crawford

pip: 183
score: 5

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:5:0:1:6:10

c6[R R11 S12 r19 P21] "<=20**10

Rollout¹

23/18(2) 21/16(2)

eq: -0.122

Player:
Opponent:

50.33% (G:10.91% B:0.99%)
49.67% (G:10.16% B:0.45%)

Conf.: ¡Ó 0.002 (-0.124...-0.121) - [100.0%]
Duration: 8 hours 37 minutes

Rollout¹

23/13(2)

eq: -0.133 (-0.011)

Player:
Opponent:

48.64% (G:11.79% B:1.23%)
51.36% (G:8.34% B:0.39%)

Conf.: ¡Ó 0.002 (-0.134...-0.131) - [0.0%]
Duration: 8 hours 30 minutes

Rollout¹

23/18(2) 21/11*

eq: -0.134 (-0.012)

Player:
Opponent:

51.61% (G:15.06% B:1.86%)
48.39% (G:13.13% B:0.65%)

Conf.: ¡Ó 0.002 (-0.136...-0.132) - [0.0%]
Duration: 10 hours 02 minutes

Rollout²

23/13 21/16(2)

eq: -0.141 (-0.019)

Player:
Opponent:

50.21% (G:11.14% B:1.15%)
49.79% (G:11.47% B:0.52%)

Conf.: ¡Ó 0.002 (-0.144...-0.139) - [0.0%]
Duration: 3 hours 51 minutes

Rollout²

21/11*(2)

eq: -0.143 (-0.021)

Player:
Opponent:

51.39% (G:18.02% B:2.52%)
48.61% (G:13.46% B:0.84%)

Conf.: ¡Ó 0.003 (-0.146...-0.140) - [0.0%]
Duration: 4 hours 38 minutes

¹ 20736 Games rolled with Variance Reduction.
Dice Seed: 51644510
Moves: 3-ply, cube decisions: XG Roller

² 10368 Games rolled with Variance Reduction.
Dice Seed: 51644510
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 165

6 point match
Crawford

pip: 183
score: 5

Blue is Player 1

XGID=-a---aD-D--acCb--b-e-B-B--:0:0:1:55:5:0:1:6:10

c6[R R10 S11] "^36

Rollout¹

23/18(2) 21/16(2)

eq: -0.124

Player:
Opponent:

50.38% (G:10.81% B:1.10%)
49.62% (G:10.39% B:0.43%)

Conf.: ¡Ó 0.001 (-0.125...-0.123) - [100.0%]
Duration: 11 days 01 hour 44 minutes

Rollout¹

23/13(2)

eq: -0.134 (-0.010)

Player:
Opponent:

48.66% (G:12.09% B:1.26%)
51.34% (G:8.44% B:0.37%)

Conf.: ¡Ó 0.001 (-0.135...-0.133) - [0.0%]
Duration: 10 days 21 hours 55 minutes

Rollout¹

23/18(2) 21/11*

eq: -0.135 (-0.011)

Player:
Opponent:

51.56% (G:15.03% B:1.77%)
48.44% (G:13.13% B:0.60%)

Conf.: ¡Ó 0.001 (-0.136...-0.134) - [0.0%]
Duration: 12 days 13 hours 17 minutes

¹ 36288 Games rolled with Variance Reduction.
Dice Seed: 10472771
Moves and cube decisions: 4-ply

At Crawford, when the opponent needs an even number of points 6 or more, R (Run, 23/18(2) 21/16(2)) is the best play (as exemplified in the above pair of rollouts). This is also true at ¡V2¡Vn, where "n" is an even number of points 8 or more; e.g., ¡V2¡V8 [R S11 R13 P24] "<=15**5 and [R S18 R23 P36] "^5. (For both c and ¡V2, I rolled out all opponent-even scores up to ¡V20.)

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, P is best, then relatively S is ¡V.012, Y is ¡V.040, etc.

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

..... m[P S12 Y40 M62 R62 r69 s85 R93] "<=62*5 ..... m[P S18] "^5
...... d[S P6 R28 r30 M45 s46 Y46] "<=62*5................. d[S P7] "^7
...... s[R R7 S37 r42 P54 c56] "<=114*5......................... s[R R9] "^15
...... g[Y P33 M47 A65 S70] "<=5
.... c6[R R11 S12 r19 P21] "<=20**10......................... c6[R R10 S11] "^36

Nactation Key:..A (Attack) = 8/3(2) 6/1*(2), c (cross) = 23/18(2) 8/3(2), f (field) = 23/18 21/11* 11/6, M (Magnify) = 21/11* 8/3(2), P (Point) = 21/11*(2), R (Run) = 23/18(2) 21/16(2), r = 21/16(2) 23/13, R = 23/13(2), S (Split 3:1) = 23/18(2) 21/16*, s = 23/13 21/16*, Y (Yosemite) = 21/11* 6/1*(2).

Nactation tutorial ? explanation of nacbracs

In the above summary, a quick look down the left column reveals that each of the five scores (m, d, s, g, c6) champions a different best play (P, S, R, Y, R). Moreover, the margins of .012, .006, .007, .033 and .011 (equal or) exceed their respective "tied" error-scale cusps of .010, .0045, .007, .007 and ~.008. As such, this position is the first "R4+1" ever constructed, unless the third diagram (prime-versus-prime position) at the "mainly here" link below also qualifies (close).

The power score (of this double 5s position) is [sqrt 12 + sqrt 6*20/9 + sqrt 37*10/7 + sqrt 33*10/7] = 21.25. For more information on four-score positions, error-scale cusps and power scores, click mainly here, also on these links: 1, 2, 3, and 4. (Eventually, I'll post a consolidated update.)

Nack

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