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T4 Variant

Posted By: Nack Ballard
Date: Tuesday, 21 April 2026, at 4:29 a.m.

In Response To: Position of the Day 04-06-26 - Rollout - Almost Nack'ed! (Stick)

A couple of terms:

T4 = Technical four-score position: a position for which there is a different best play at each of the four main scores (Money/unlimited, DMP, GS and GG).

R4 = Real four-score position: Same definition as T4, except that each best play clears the bar of not being "tied" with the best play at any of the other three main scores. The tied cusps are: Money = .01, DMP = .0045, GS = .007, and GG = .007. (Recent research suggests that a more accurate number for GS and GG may be .0075.)

Stick coined the alternative term of "Nacked" as an adjective and perhaps "Nack" as a verb. I suggest the further distinction that a position is technically Nacked (when it is a T4) or really Nacked (when it is an R4).

I believe that, conservatively, over a hundred T4's exist for each R4. That is, an R4 is much rarer.

The Blue-to-play-42 position that Stick posted in this thread (with pipcount 157 - 142) falls short of being a T4 (technically Nacked) and well short of being an R4 (really Nacked).

I tweaked Stick's positions by moving White's checkers 5 pips (3 forward and 2 backward) and Blue's checkers 2 pips. Below, you'll find a rollout at each of the four main scores. At three out of four scores, the best play is "tied," and so even my adjusted position does not come close to qualifying as an R4. In fact, it does not even qualify as a T4 as it stands, because the rollouts would need to be extended until each best play reaches 99.6+% (if it does).

I would try to convert this position to an R4 if I were still motivated. It would require many more checker adjustments, and in this case I think the original position would be largely unrecognizable.

On and off, over the last 20 years, I've created at least one R4 for each of the 21 rolls (more than twice that number in total). Many or most are scattered about in the BGOnline archives. (If you are interested, search under my name, with "Four Score" in the subject header.)

Refer to the set of likely-T4 rollouts below, with 3R settings and shown to the fourth decimal place.

Nack





White is Player 2

score: 0
pip: 141
Unlimited Game
Jacoby Beaver
pip: 157
score: 0

Blue is Player 1
XGID=-a---aE-CA-AdC----cb-bBb--:0:0:1:42:0:0:3:0:10
Money

1.Rollout113/9 11/9eq: -0.1700
Player:
Opponent:		45.45% (G:9.11% B:0.32%)
54.55% (G:11.15% B:0.38%)		Conf.: ±0.0065 (-0.1765...-0.1634) - [79.2%]
Duration: 1 hour 40 minutes
2.Rollout111/7 9/7eq: -0.1737 (-0.0038)
Player:
Opponent:		45.33% (G:9.09% B:0.30%)
54.67% (G:11.05% B:0.36%)		Conf.: ±0.0063 (-0.1800...-0.1674) - [20.8%]
Duration: 1 hour 40 minutes
3.Rollout28/4 6/4eq: -0.2276 (-0.0577)
Player:
Opponent:		44.93% (G:11.75% B:0.43%)
55.07% (G:16.29% B:0.66%)		Conf.: ±0.0142 (-0.2418...-0.2134) - [0.0%]
Duration: 20 minutes 57 seconds
4.Rollout213/11 9/5* eq: -0.2330 (-0.0631)
Player:
Opponent:		44.70% (G:12.19% B:0.40%)
55.30% (G:16.63% B:0.66%)		Conf.: ±0.0157 (-0.2487...-0.2173) - [0.0%]
Duration: 23 minutes 29 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 434344
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 434344
Moves: 3-ply, cube decisions: XG Roller
White is Player 2

score: 0
pip: 141
1 point match
pip: 157
score: 0

Blue is Player 1
XGID=-a---aE-CA-AdC----cb-bBb--:0:0:1:42:0:0:0:1:10
DMP

1.Rollout18/4 6/4eq: -0.0834
Player:
Opponent:		45.83% (G:11.23% B:1.18%)
54.17% (G:23.28% B:2.24%)		Conf.: ±0.0026 (-0.0861...-0.0808) - [71.0%]
Duration: 1 hour 07 minutes
2.Rollout113/9 11/9eq: -0.0848 (-0.0014)
Player:
Opponent:		45.76% (G:8.71% B:0.68%)
54.24% (G:14.03% B:1.02%)		Conf.: ±0.0024 (-0.0872...-0.0824) - [19.2%]
Duration: 58 minutes 17 seconds
3.Rollout111/7 9/7eq: -0.0853 (-0.0019)
Player:
Opponent:		45.73% (G:8.90% B:0.68%)
54.27% (G:15.01% B:0.91%)		Conf.: ±0.0023 (-0.0876...-0.0831) - [9.7%]
Duration: 56 minutes 06 seconds
4.Rollout113/11 9/5* eq: -0.0893 (-0.0058)
Player:
Opponent:		45.54% (G:11.70% B:1.06%)
54.46% (G:22.91% B:2.36%)		Conf.: ±0.0027 (-0.0920...-0.0866) - [0.0%]
Duration: 1 hour 40 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 66618975
Moves: 3-ply, cube decisions: XG Roller
White is Player 2

score: 0
pip: 141
2 point match
Crawford
pip: 157
score: 1

Blue is Player 1
XGID=-a---aE-CA-AdC----cb-bBb--:0:0:1:42:1:0:1:2:10
Gammon Save

1.Rollout111/7 9/7eq: -0.2912
Player:
Opponent:		44.26% (G:8.71% B:0.68%)
55.74% (G:8.82% B:0.53%)		Conf.: ±0.0028 (-0.2941...-0.2884) - [59.5%]
Duration: 57 minutes 07 seconds
2.Rollout113/9 11/9eq: -0.2917 (-0.0005)
Player:
Opponent:		44.44% (G:8.45% B:0.52%)
55.56% (G:9.02% B:0.70%)		Conf.: ±0.0030 (-0.2947...-0.2888) - [40.5%]
Duration: 54 minutes 33 seconds
3.Rollout213/11 9/5* eq: -0.4078 (-0.1166)
Player:
Opponent:		42.85% (G:10.00% B:0.81%)
57.15% (G:13.24% B:1.15%)		Conf.: ±0.0067 (-0.4145...-0.4011) - [0.0%]
Duration: 22 minutes 22 seconds
4.Rollout28/4 6/4eq: -0.4129 (-0.1216)
Player:
Opponent:		43.61% (G:11.91% B:1.33%)
56.39% (G:14.25% B:2.17%)		Conf.: ±0.0067 (-0.4196...-0.4062) - [0.0%]
Duration: 21 minutes 37 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 61075634
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 61075634
Moves: 3-ply, cube decisions: XG Roller
White is Player 2

score: 1
pip: 141
2 point match
Crawford
pip: 157
score: 0

Blue is Player 1
XGID=-a---aE-CA-AdC----cb-bBb--:0:0:1:42:0:1:1:2:10
Gammon Go

1.Rollout113/11 9/5* eq: +0.1677
Player:
Opponent:		45.42% (G:12.96% B:0.88%)
54.58% (G:24.41% B:2.57%)		Conf.: ±0.0039 (+0.1638...+0.1716) - [100.0%]
Duration: 1 hour 30 minutes
2.Rollout18/4 6/4eq: +0.1577 (-0.0100)
Player:
Opponent:		45.53% (G:12.36% B:0.95%)
54.47% (G:22.82% B:2.23%)		Conf.: ±0.0037 (+0.1540...+0.1614) - [0.0%]
Duration: 1 hour 21 minutes
3.Rollout211/7 9/7eq: +0.1039 (-0.0638)
Player:
Opponent:		45.49% (G:9.70% B:0.76%)
54.51% (G:15.75% B:0.88%)		Conf.: ±0.0065 (+0.0974...+0.1104) - [0.0%]
Duration: 20 minutes 06 seconds
4.Rollout213/9 11/9eq: +0.1006 (-0.0671)
Player:
Opponent:		45.28% (G:9.75% B:0.64%)
54.72% (G:15.02% B:1.14%)		Conf.: ±0.0062 (+0.0944...+0.1068) - [0.0%]
Duration: 19 minutes 24 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 4779754
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 4779754
Moves: 3-ply, cube decisions: XG Roller

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