Four-One and variants, ROLLOUTS

White is Player 2

score: 0
pip: 202

Unlimited Game
Jacoby Beaver

pip: 173
score: 0

Blue is Player 1

XGID=-ab-b-E-C--BcB--ac-c---AB-:0:0:1:41:0:0:3:0:10

32S-63H-32H-51U-62X-31H-21H-41H-
-21H-41H-65R-52X-65H-22P-41D-41

4 3 1 [W V7 P11 U34 H50] "<=62**10 5

Rollout¹

24/20 6/5

eq: +0.119

Player:
Opponent:

52.22% (G:16.43% B:0.85%)
47.78% (G:12.45% B:0.69%)

Conf.: ± 0.003 (+0.116...+0.122) - [99.9%]
Duration: 1 day 02 hours 22 minutes

Rollout¹

24/20 23/22

eq: +0.112 (-0.007)

Player:
Opponent:

51.80% (G:17.30% B:0.82%)
48.20% (G:12.61% B:0.65%)

Conf.: ± 0.003 (+0.109...+0.115) - [0.1%]
Duration: 23 hours 27 minutes

Rollout¹

11/7 8/7

eq: +0.108 (-0.011)

Player:
Opponent:

51.45% (G:18.33% B:0.96%)
48.55% (G:13.05% B:0.71%)

Conf.: ± 0.003 (+0.105...+0.111) - [0.0%]
Duration: 20 hours 31 minutes

Rollout²

23/18

eq: +0.085 (-0.034)

Player:
Opponent:

50.94% (G:17.54% B:0.84%)
49.06% (G:12.97% B:0.69%)

Conf.: ± 0.008 (+0.078...+0.093) - [0.0%]
Duration: 3 hours 58 minutes

Rollout³

6/1*

eq: +0.069 (-0.050)

Player:
Opponent:

50.49% (G:17.59% B:0.75%)
49.51% (G:13.06% B:0.71%)

Conf.: ± 0.011 (+0.058...+0.080) - [0.0%]
Duration: 1 hour 49 minutes

¹ 62208 Games rolled with Variance Reduction.
Dice Seed: 92861368
Moves: 3-ply, cube decisions: XG Roller

² 10368 Games rolled with Variance Reduction.
Dice Seed: 92861368
Moves: 3-ply, cube decisions: XG Roller

³ 5184 Games rolled with Variance Reduction.
Dice Seed: 92861368
Moves: 3-ply, cube decisions: XG Roller

P (Point, making the 7pt) makes a three-point prime in front of five checkers, and is typically the standout play. However, stripping the 8pt while leaving a five-checker stack on the 6pt is rather stiff; it tempts one to look around for another move.

Even so, slotting into a triple shot is not something one should do frivolously! I was a bit surprised at how unqualifyingly wild some of the W (Wild, 24/20 6/5) players seemed to be, though W does win the rollout (narrowly, over V and P).

Duplication matters. Indeed, it's pivotal. That's why I chose this exact position: the five-checker stack on the 6pt alone does not dictate Blue's course. It is the perfect duplication of 4s, 3s and 1s (aided by the support of the 11pt, as Neil points out) that promotes W from a blunder to a tiny winner.

Look what happens when we change just one of the duplicated numbers. In the first position diagrammed below (on the left, if you widen your window), White's 9pt checker has been moved back to the 11pt. Now, instead of rolling out best, W becomes a .053 error!

In the second position diagrammed below, I've removed a second duplicated number (so that now only aces are duped). Although W regains most of its lost ground relative to P (due in part to the increased incentive to advance back checker(s) against White's made 7pt), W is an even larger error -- it has crossed into blunder territory.

In the third position diagrammed below (the right-hand one of the trio, if you widen your window enough), even the duplicated aces are nullified. The three numbers that hit on one side of the board are all different from the three numbers that hit on the other side. Now W is a whopper!

Below is a nacbracs summary of the four positions. (The codes of "4 3 1," etc., denote the number of pips that White's builders are from her 5pt.)

........4 3 1 [W V7 P11 U34 H50] "<=62**10 5
........6 3 1 [P V50 U52 W53 H76] "<=5
........6 2 1 [U V25 P64 H76 W76] "<=5
........6 5 2 [U V40 H71 P77 W112] "<=5

Key: W = Wild (24/20 6/5), U = Up (23/18) and V = Variant up (24/20 23/22) [or with 18pt blocked, U = 24/20 23/22 and V = 24/23 24/20], P = Point (11/7 8/7), H = Hit (6/1*).

White is Player 2

score: 0
pip: 204

Unlimited Game
Jacoby Beaver

pip: 173
score: 0

Blue is Player 1

XGID=-ab-b-E-C--BcBa--c-c---AB-:0:0:1:41:0:0:3:0:10

6 3 1 [P V50 U52 W53 H76] "<=5

Rollout¹

11/7 8/7

eq: +0.144

Player:
Opponent:

52.03% (G:18.75% B:0.98%)
47.97% (G:12.57% B:0.64%)

Conf.: ± 0.023 (+0.121...+0.167) - [100.0%]
Duration: 4 hours 21 minutes

Rollout¹

24/20 23/22

eq: +0.094 (-0.050)

Player:
Opponent:

51.16% (G:18.06% B:0.87%)
48.84% (G:12.48% B:0.64%)

Conf.: ± 0.010 (+0.083...+0.104) - [0.0%]
Duration: 4 hours 43 minutes

Rollout¹

23/18

eq: +0.092 (-0.052)

Player:
Opponent:

51.02% (G:17.77% B:0.87%)
48.98% (G:12.76% B:0.63%)

Conf.: ± 0.011 (+0.081...+0.103) - [0.0%]
Duration: 4 hours 38 minutes

Rollout¹

24/20 6/5

eq: +0.091 (-0.053)

Player:
Opponent:

51.52% (G:16.27% B:0.79%)
48.48% (G:12.73% B:0.70%)

Conf.: ± 0.010 (+0.081...+0.102) - [0.0%]
Duration: 5 hours 02 minutes

Rollout¹

6/1*

eq: +0.068 (-0.076)

Player:
Opponent:

50.62% (G:17.53% B:0.76%)
49.38% (G:12.94% B:0.70%)

Conf.: ± 0.010 (+0.058...+0.079) - [0.0%]
Duration: 4 hours 38 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 70757351
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 201

Unlimited Game
Jacoby Beaver

pip: 173
score: 0

Blue is Player 1

XGID=-ab-b-E-C--BcBa---cc---AB-:0:0:1:41:0:0:3:0:10

6 2 1 [U V25 P64 H76 W76] "<=5

Rollout¹

24/20 23/22

eq: +0.118

Player:
Opponent:

51.51% (G:18.31% B:0.89%)
48.49% (G:12.38% B:0.65%)

Conf.: ± 0.011 (+0.108...+0.129) - [99.9%]
Duration: 4 hours 46 minutes

Rollout¹

24/23 24/20

eq: +0.094 (-0.025)

Player:
Opponent:

51.30% (G:17.41% B:0.83%)
48.70% (G:12.70% B:0.66%)

Conf.: ± 0.010 (+0.084...+0.104) - [0.1%]
Duration: 4 hours 26 minutes

Rollout¹

11/7 8/7

eq: +0.054 (-0.064)

Player:
Opponent:

50.19% (G:17.96% B:0.96%)
49.81% (G:13.76% B:0.78%)

Conf.: ± 0.010 (+0.044...+0.065) - [0.0%]
Duration: 4 hours 08 minutes

Rollout¹

6/1*

eq: +0.042 (-0.076)

Player:
Opponent:

49.93% (G:17.43% B:0.84%)
50.07% (G:13.50% B:0.76%)

Conf.: ± 0.011 (+0.032...+0.053) - [0.0%]
Duration: 4 hours 35 minutes

Rollout¹

24/20 6/5

eq: +0.042 (-0.076)

Player:
Opponent:

50.71% (G:15.32% B:0.75%)
49.29% (G:13.56% B:0.75%)

Conf.: ± 0.011 (+0.032...+0.053) - [0.0%]
Duration: 5 hours 04 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 43835611
Moves: 3-ply, cube decisions: XG Roller

White is Player 2

score: 0
pip: 205

Unlimited Game
Jacoby Beaver

pip: 173
score: 0

Blue is Player 1

XGID=-ab-b-E-C--BcBaa--cb---AB-:0:0:1:41:0:0:3:0:10

6 5 2 [U V40 H71 P77 W112]"<=5

Rollout¹

24/20 23/22

eq: +0.114

Player:
Opponent:

51.14% (G:18.83% B:0.92%)
48.86% (G:12.43% B:0.69%)

Conf.: ± 0.014 (+0.099...+0.128) - [100.0%]
Duration: 3 hours 58 minutes

Rollout¹

24/23 24/20

eq: +0.073 (-0.040)

Player:
Opponent:

50.63% (G:17.62% B:0.88%)
49.37% (G:12.61% B:0.63%)

Conf.: ± 0.012 (+0.062...+0.085) - [0.0%]
Duration: 3 hours 37 minutes

Rollout¹

6/1*

eq: +0.042 (-0.071)

Player:
Opponent:

49.64% (G:18.24% B:0.78%)
50.36% (G:13.09% B:0.71%)

Conf.: ± 0.011 (+0.031...+0.053) - [0.0%]
Duration: 3 hours 44 minutes

Rollout¹

11/7 8/7

eq: +0.037 (-0.077)

Player:
Opponent:

49.43% (G:18.51% B:1.03%)
50.57% (G:13.28% B:0.71%)

Conf.: ± 0.012 (+0.025...+0.048) - [0.0%]
Duration: 3 hours 33 minutes

Rollout¹

24/20 6/5

eq: +0.002 (-0.112)

Player:
Opponent:

49.80% (G:15.30% B:0.74%)
50.20% (G:14.15% B:0.85%)

Conf.: ± 0.011 (-0.010...+0.013) - [0.0%]
Duration: 4 hours 08 minutes

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 85570326
Moves: 3-ply, cube decisions: XG Roller

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