BGonline.org Forums

Prime-versus-Prime, challenge #1, ROLLOUTS

Posted By: Nack Ballard
Date: Monday, 1 September 2014, at 4:26 p.m.

In Response To: Prime-versus-Prime, challenge #1 (Nack Ballard)

m (money, center cube)

		White is Player 2 score: 0 pip: 99 Unlimited Game Jacoby Beaver pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:0:0:1:52:0:0:3:0:10
32S-43H-22E-22E-54@-44S-41U-51r-52R-11B-31P-32N-31D-65S- -F-66D-63H-F-11D-426-63r-21K-53-11A.-21-54J-52 [8 9203 7278 K353] "<=5"

1.	Rollout1	Bar/23* 13/8	eq: +0.209
	Player: Opponent: 56.41% (G:16.34% B:0.96%) 43.59% (G:23.28% B:3.22%) Conf.: ± 0.009 (+0.200...+0.218) - [100.0%] Duration: 1 hour 34 minutes
2.	Rollout1	Bar/23* 14/9	eq: +0.005 (-0.203)
	Player: Opponent: 53.12% (G:14.92% B:0.83%) 46.88% (G:24.48% B:1.70%) Conf.: ± 0.009 (-0.004...+0.015) - [0.0%] Duration: 1 hour 41 minutes
3.	Rollout1	Bar/23* 12/7	eq: -0.069 (-0.278)
	Player: Opponent: 50.64% (G:15.08% B:0.90%) 49.36% (G:25.98% B:2.38%) Conf.: ± 0.009 (-0.078...-0.060) - [0.0%] Duration: 1 hour 34 minutes
4.	Rollout1	Bar/23* 7/2*	eq: -0.144 (-0.353)
	Player: Opponent: 47.13% (G:17.20% B:1.40%) 52.87% (G:28.73% B:4.31%) Conf.: ± 0.009 (-0.153...-0.135) - [0.0%] Duration: 1 hour 40 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 75310303 Moves: 3-ply, cube decisions: XG Roller

Sorry for the delay in posting answers. Recently, life's been busy.

As Tim and Stick opined (a few months ago), the answers to my problems have often been deducible by QF. To be a bit less predictable, I posted a problem where the correct play is best at all scores... and this ploy "worked" to some extent. Be that (sidelight) as it may, this position demonstrates that in prime-vs-prime positions, frequently the key idea is to "put the checkers where they want to go."

Below are some of the more insightful comments (in order of response):

Joe Russell: Bar-23, 13-8 looks right in all scenarios, other than possibly GS. Other, more passive plays, just seem weak, as white will hit on its 2-point with entering 6's anyway ...Bar-23, 13-8 threatens to make a serious counter prime and, also, leaves a plethora of numbers to complete the prime if missed or hit back if white hits a fly shot on the 8-point.

Ian Dunstan: The move I want to make foremost is b/23* 13/8. Attempting to make a 5th consecutive part of the prime looks paramount to me. This is the move I want to make before thinking about cube position and score.

Igor: First, my DMP move is bar/23* 13/8 ...attempt to counterprime white since we now both have two checkers back. I don't see any factors that would make me change this move for money, regardless of the position of the cube.

Robert Chow: My play is 13/8 in all situations except at gammon save where I would play 14/9. Even at gammon save, 13/8 might be right because the need to make the 8 point may outweigh the danger of having five blots scooped up in the worst case scenario.

If White fans after Blue plays "8" (8pt, bar/23* 13/8), Blue can offer a powerful redouble (by rollout, 8-F-R is .93). If White fans after any other play, Blue will not even have a double (9-F-C, which is closest, is only .57).

Above is the rollout for money, center cube. Below are rollouts with the other cube positions and scores. Following that is a nacbracs summary, and a cusp variant (with more rollouts).

+C (money, owning cube)

		White is Player 2 score: 0 pip: 99 Unlimited Game Jacoby Beaver pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:1:1:1:52:0:0:3:0:10
+C[8 986 7175 K284] "<=5

1.	Rollout1	Bar/23* 13/8	eq: +0.273
	Player: Opponent: 56.20% (G:16.58% B:1.02%) 43.80% (G:23.66% B:3.54%) Conf.: ± 0.009 (+0.265...+0.282) - [100.0%] Duration: 1 hour 29 minutes
2.	Rollout1	Bar/23* 14/9	eq: +0.187 (-0.086)
	Player: Opponent: 53.21% (G:15.28% B:0.83%) 46.79% (G:24.21% B:1.58%) Conf.: ± 0.006 (+0.181...+0.194) - [0.0%] Duration: 1 hour 29 minutes
3.	Rollout1	Bar/23* 12/7	eq: +0.099 (-0.175)
	Player: Opponent: 50.62% (G:15.34% B:0.94%) 49.38% (G:26.08% B:2.50%) Conf.: ± 0.006 (+0.093...+0.105) - [0.0%] Duration: 1 hour 20 minutes
4.	Rollout1	Bar/23* 7/2*	eq: -0.011 (-0.284)
	Player: Opponent: 47.01% (G:17.32% B:1.39%) 52.99% (G:28.62% B:4.43%) Conf.: ± 0.007 (-0.018...-0.004) - [0.0%] Duration: 1 hour 32 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 85576101 Moves: 3-ply, cube decisions: XG Roller

–C (money with Opp owning cube)

		White is Player 2 score: 0 pip: 99 Unlimited Game Jacoby Beaver pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:1:-1:1:52:0:0:3:0:10
–C[8 988 7167 K267] "<=5

1.	Rollout1	Bar/23* 13/8	eq: -0.091
	Player: Opponent: 56.25% (G:16.64% B:1.02%) 43.75% (G:23.67% B:3.47%) Conf.: ± 0.006 (-0.097...-0.085) - [100.0%] Duration: 1 hour 31 minutes
2.	Rollout1	Bar/23* 14/9	eq: -0.179 (-0.088)
	Player: Opponent: 53.40% (G:15.33% B:0.89%) 46.60% (G:24.14% B:1.62%) Conf.: ± 0.007 (-0.186...-0.172) - [0.0%] Duration: 1 hour 27 minutes
3.	Rollout1	Bar/23* 12/7	eq: -0.258 (-0.167)
	Player: Opponent: 50.96% (G:15.20% B:0.94%) 49.04% (G:25.76% B:2.41%) Conf.: ± 0.006 (-0.264...-0.252) - [0.0%] Duration: 1 hour 15 minutes
4.	Rollout1	Bar/23* 7/2*	eq: -0.358 (-0.267)
	Player: Opponent: 47.14% (G:17.34% B:1.46%) 52.86% (G:28.55% B:4.36%) Conf.: ± 0.007 (-0.365...-0.351) - [0.0%] Duration: 1 hour 35 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 85576101 Moves: 3-ply, cube decisions: XG Roller

d (double match point)

		White is Player 2 score: 0 pip: 99 1 point match pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:0:0:1:52:0:0:0:1:10
d[8 753] "<=5

1.	Rollout1	Bar/23* 13/8	eq: +0.135
	Player: Opponent: 56.76% (G:15.07% B:1.99%) 43.24% (G:26.13% B:5.96%) Conf.: ± 0.003 (+0.132...+0.139) - [100.0%] Duration: 1 hour 00 minute
2.	Rollout1	Bar/23* 14/9	eq: +0.082 (-0.053)
	Player: Opponent: 54.09% (G:14.31% B:2.00%) 45.91% (G:26.59% B:4.79%) Conf.: ± 0.003 (+0.078...+0.085) - [0.0%] Duration: 56 minutes 18 seconds
1 5184 Games rolled with Variance Reduction. Dice Seed: 49207271 Moves: 3-ply, cube decisions: XG Roller

s (gammon save)

		White is Player 2 score: 0 pip: 99 2 point match Crawford pip: 157 score: 1 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:0:0:1:52:1:0:1:2:10
s[8 961] "<=5

1.	Rollout1	Bar/23* 13/8	eq: -0.341
	Player: Opponent: 55.98% (G:15.58% B:2.33%) 44.02% (G:23.04% B:5.29%) Conf.: ± 0.005 (-0.346...-0.336) - [100.0%] Duration: 1 hour 21 minutes
2.	Rollout1	Bar/23* 14/9	eq: -0.402 (-0.061)
	Player: Opponent: 52.99% (G:14.51% B:2.18%) 47.01% (G:23.10% B:3.34%) Conf.: ± 0.005 (-0.407...-0.397) - [0.0%] Duration: 1 hour 13 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 49207271 Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

g (gammon go)

		White is Player 2 score: 1 pip: 99 2 point match Crawford pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA-aacbbbbaAA:0:0:1:52:0:1:1:2:10
g[8 970 7120 K150] "<=5

1.	Rollout1	Bar/23* 13/8	eq: +0.461
	Player: Opponent: 55.79% (G:17.26% B:2.21%) 44.21% (G:26.38% B:6.13%) Conf.: ± 0.005 (+0.456...+0.466) - [100.0%] Duration: 1 hour 16 minutes
2.	Rollout1	Bar/23* 14/9	eq: +0.391 (-0.070)
	Player: Opponent: 53.04% (G:16.50% B:2.55%) 46.96% (G:27.03% B:4.84%) Conf.: ± 0.005 (+0.386...+0.395) - [0.0%] Duration: 1 hour 13 minutes
3.	Rollout1	Bar/23* 12/7	eq: +0.340 (-0.120)
	Player: Opponent: 50.61% (G:16.42% B:2.64%) 49.39% (G:28.69% B:5.39%) Conf.: ± 0.005 (+0.336...+0.345) - [0.0%] Duration: 1 hour 14 minutes
4.	Rollout1	Bar/23* 7/2*	eq: +0.311 (-0.150)
	Player: Opponent: 47.13% (G:18.42% B:3.48%) 52.87% (G:31.67% B:10.18%) Conf.: ± 0.005 (+0.306...+0.316) - [0.0%] Duration: 1 hour 24 minutes
1 5184 Games rolled with Variance Reduction. Dice Seed: 49207271 Moves: 3-ply, cube decisions: XG Roller

......NACBRACS SUMMARY (5k rollouts, XG2 3-ply checker with roller cube)

...... m[8 9203 7278 K353]......n[8 9153] (not diagrammed)
......+C[8 986 7175 K284]
......–C[8 988 7167 K267]
...... d[8 753]
...... s[8 961]
...... g[8 970 7120 K150]

Play Key: 8 = 8pt (bar/23* 13/8), 9 = 9pt (bar/23* 14/9), 7 = 7pt (bar/23* 12/7, K = Kill (bar/23* 7/2*).

Score Key: m = money (center cube), n = unlimited no Jacoby no beavers (center cube), +C = money owning cube, –C = money with Opp owning cube, d = dmp, s = gammon save, g = gammon go.

Nactation tutorial • explanation of nacbracs

If we advance White's 9pt and 8pt blots 2 pips each, thereby giving her good 4s (and softening the duplication of 61 and 62), Blue's decision to play "8" or "9" is much closer, in fact "tied" when the score is +C (money, owning cube) or s (gammon save).

The results for this variant are:

..... m[8 985] "<=5 ...... n[8 953] "<=5
.....+C[9 8-5] "<=20
.....–C[8 922] "<=5
..... d[8 923] "<=5
..... s[8=9] "<=20
..... g[8 918] "<=5

For this variant, detailed rollout results for +C and s can be found below.

Nack

		White is Player 2 score: 0 pip: 95 Unlimited Game Jacoby Beaver pip: 157 score: 0 Blue is Player 1
XGID=--a-BBBB----BBA---dcbbbaAA:1:1:1:52:0:0:3:0:10
Variant: +C[9 8-5] "<=20

1.	Rollout1	Bar/23* 14/9	eq: +0.137
	Player: Opponent: 52.60% (G:13.52% B:0.61%) 47.40% (G:26.10% B:1.61%) Conf.: ± 0.003 (+0.134...+0.140) - [98.3%] Duration: 6 hours 02 minutes
2.	Rollout1	Bar/23* 13/8	eq: +0.132 (-0.005)
	Player: Opponent: 53.73% (G:13.29% B:0.58%) 46.27% (G:27.03% B:4.14%) Conf.: ± 0.003 (+0.129...+0.135) - [1.7%] Duration: 5 hours 55 minutes
1 20736 Games rolled with Variance Reduction. Dice Seed: 46465363 Moves: 3-ply, cube decisions: XG Roller

		White is Player 2 score: 0 pip: 95 2 point match Crawford pip: 157 score: 1 Blue is Player 1
XGID=--a-BBBB----BBA---dcbbbaAA:0:0:1:52:1:0:1:2:10
Variant: s[8=9] "<=20

1.	Rollout1	Bar/23* 13/8	eq: -0.449
	Player: Opponent: 53.72% (G:11.28% B:1.15%) 46.28% (G:26.16% B:6.24%) Conf.: ± 0.003 (-0.451...-0.446) - [56.8%] Duration: 5 hours 13 minutes
2.	Rollout1	Bar/23* 14/9	eq: -0.449 (0.000)
	Player: Opponent: 52.44% (G:11.74% B:1.27%) 47.56% (G:24.90% B:3.24%) Conf.: ± 0.002 (-0.452...-0.447) - [43.2%] Duration: 5 hours 05 minutes
1 20736 Games rolled with Variance Reduction. Dice Seed: 49207271 Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

Messages In This Thread

• Prime-versus-Prime, challenge #1
  Nack Ballard -- Monday, 18 August 2014, at 1:08 a.m.
  • Prime-versus-Prime, challenge #1
    Joe Russell -- Monday, 18 August 2014, at 1:37 a.m.
  • Prime-versus-Prime, challenge #1
    BenF -- Monday, 18 August 2014, at 2:58 a.m.
    • Prime-versus-Prime, challenge #1 (semi-spoiler)
      BenF -- Monday, 18 August 2014, at 3:04 a.m.
  • Prime-versus-Prime, challenge #1
    scotty -- Monday, 18 August 2014, at 10:48 p.m.
    • Prime-versus-Prime, challenge #1
      scotty -- Monday, 18 August 2014, at 10:53 p.m.
  • Prime-versus-Prime, challenge #1
    Ian Dunstan -- Tuesday, 19 August 2014, at 9:40 a.m.
  • Prime-versus-Prime, challenge #1
    hominid -- Tuesday, 19 August 2014, at 10:17 a.m.
  • Prime-versus-Prime, challenge #1
    Igor -- Tuesday, 19 August 2014, at 3:01 p.m.
  • Prime-versus-Prime, challenge #1
    Robert Chow -- Tuesday, 19 August 2014, at 6:40 p.m.
  • Prime-versus-Prime, challenge #1, ROLLOUTS
    Nack Ballard -- Monday, 1 September 2014, at 4:26 p.m.