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Amazing Odd-Even Parity

Posted By: Nack Ballard
Date: Thursday, 2 November 2023, at 7:45 p.m.

In Response To: Position of the Day 10-22-23 - Rollout (Stick)

There is a remarkable progression of odd-even parity that stems from the position Stick posted.

The progression starts with the position below, where White's "floating checker" is a spare on her 4pt. Without making any other change in the position, we're going to move that floating checker one pip at a time, to a higher and higher point, until it can go no further on White's side of the board.

When the floating checker is on an odd-numbered point, the position appears on the LEFT side of your screen. When it is on an even-numbered point, the position appears on the RIGHT side of your screen. (If your window isn't wide enough, then you'll have to grasp the better-play progression through alternation.)

------------------------------------------------------------
L/R.....Position#.....Point#...Better play

LEFT....Odd-numbered....Odd....P (Point, 8/5 6/5)
RIGHT...Even-numbered...Even...X (hit and split, 24/23 6/3*)
------------------------------------------------------------

The only position in which another play is better than both of the featured plays is in the position that the "original" one Stick posted, marked here as "Position 6." Even there, X is better than P, honoring its evenness in the parity.

Pos.1 [P p37 X54 Z117 B134].....Pos.2 [X p3 P35 B138 Z147]
Pos.3 [P p31 X39 B109 Z125].....Pos.4 [X p11 P17 B46 Z57]
Pos.5 [P p160 B236 Z236 X239]...Pos.6 [B X13 p16 P30]
Pos.7 [P X7 p18 B30 Z35]........Pos.8 [X Z5 P6 p14 B16]

Above is a nacbrac summary for all eight rollouts: Positions #1 through #8.
Below are the details of those rollouts (odd-numbered positions on the left).

Nack





White is Player 2

score: 0
pip: 135
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--a-bcbc--A-:0:0:1:31:0:0:3:0:10
Position 1:.. 5pt is better than hit-and-split

1.Rollout18/5 6/5eq: -0.606
Player:
Opponent:		37.80% (G:8.90% B:0.50%)
62.20% (G:29.19% B:0.94%)		Conf.: ± 0.017 (-0.623...-0.588) - [99.5%]
Duration: 44 minutes 10 seconds
2.Rollout113/10 11/10eq: -0.643 (-0.037)
Player:
Opponent:		36.70% (G:8.55% B:0.45%)
63.30% (G:28.31% B:0.99%)		Conf.: ± 0.021 (-0.664...-0.622) - [0.4%]
Duration: 43 minutes 52 seconds
3.Rollout124/23 6/3* eq: -0.660 (-0.054)
Player:
Opponent:		37.94% (G:9.02% B:0.53%)
62.06% (G:32.40% B:0.98%)		Conf.: ± 0.030 (-0.690...-0.630) - [0.1%]
Duration: 47 minutes 52 seconds
4.Rollout124/23 13/10eq: -0.723 (-0.117)
Player:
Opponent:		36.37% (G:8.32% B:0.57%)
63.63% (G:31.57% B:1.14%)		Conf.: ± 0.021 (-0.744...-0.702) - [0.0%]
Duration: 46 minutes 17 seconds
5.Rollout124/23 11/8eq: -0.739 (-0.134)
Player:
Opponent:		36.08% (G:7.55% B:0.40%)
63.92% (G:30.59% B:0.66%)		Conf.: ± 0.018 (-0.757...-0.722) - [0.0%]
Duration: 41 minutes 19 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 49734356
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10




White is Player 2

score: 0
pip: 136
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--a-bccb--A-:0:0:1:31:0:0:3:0:10
Position 2:.. hit-and-split is better than 5pt

1.Rollout124/23 6/3* eq: -0.635
Player:
Opponent:		38.05% (G:8.87% B:0.55%)
61.95% (G:31.79% B:0.98%)		Conf.: ± 0.011 (-0.646...-0.624) - [63.9%]
Duration: 51 minutes 11 seconds
2.Rollout113/10 11/10eq: -0.638 (-0.003)
Player:
Opponent:		36.69% (G:8.18% B:0.41%)
63.31% (G:27.58% B:0.91%)		Conf.: ± 0.010 (-0.648...-0.627) - [36.1%]
Duration: 45 minutes 25 seconds
3.Rollout28/5 6/5eq: -0.670 (-0.035)
Player:
Opponent:		36.54% (G:8.89% B:0.49%)
63.46% (G:29.19% B:1.01%)		Conf.: ± 0.018 (-0.688...-0.652) - [0.0%]
Duration: 7 minutes 15 seconds
4.Rollout224/23 11/8eq: -0.773 (-0.138)
Player:
Opponent:		35.49% (G:7.33% B:0.40%)
64.51% (G:30.53% B:0.66%)		Conf.: ± 0.018 (-0.791...-0.755) - [0.0%]
Duration: 8 minutes 12 seconds
5.Rollout224/23 13/10eq: -0.782 (-0.147)
Player:
Opponent:		35.80% (G:8.04% B:0.48%)
64.20% (G:32.01% B:1.09%)		Conf.: ± 0.023 (-0.804...-0.759) - [0.0%]
Duration: 8 minutes 54 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 13579
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 13579
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10





White is Player 2

score: 0
pip: 137
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--a-bdbb--A-:0:0:1:31:0:0:3:0:10
Position 3:.. 5pt is better than hit-and-split

1.Rollout18/5 6/5eq: -0.530
Player:
Opponent:		38.47% (G:9.11% B:0.48%)
61.53% (G:25.58% B:0.96%)		Conf.: ± 0.015 (-0.545...-0.515) - [99.8%]
Duration: 43 minutes 26 seconds
2.Rollout113/10 11/10eq: -0.561 (-0.031)
Player:
Opponent:		37.80% (G:8.57% B:0.42%)
62.20% (G:25.22% B:0.93%)		Conf.: ± 0.013 (-0.575...-0.548) - [0.1%]
Duration: 46 minutes 21 seconds
3.Rollout124/23 6/3* eq: -0.569 (-0.039)
Player:
Opponent:		38.63% (G:9.47% B:0.53%)
61.37% (G:30.60% B:0.96%)		Conf.: ± 0.019 (-0.588...-0.550) - [0.1%]
Duration: 47 minutes 06 seconds
4.Rollout124/23 11/8eq: -0.639 (-0.109)
Player:
Opponent:		37.35% (G:7.19% B:0.42%)
62.65% (G:28.47% B:0.64%)		Conf.: ± 0.016 (-0.656...-0.623) - [0.0%]
Duration: 41 minutes 24 seconds
5.Rollout124/23 13/10eq: -0.655 (-0.125)
Player:
Opponent:		37.14% (G:8.42% B:0.52%)
62.86% (G:29.65% B:1.10%)		Conf.: ± 0.020 (-0.674...-0.635) - [0.0%]
Duration: 44 minutes 35 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 74657175
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10




White is Player 2

score: 0
pip: 138
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--a-ccbb--A-:0:0:1:31:0:0:3:0:10
Position 4:.. hit-and-spli is better than 5pt

1.Rollout124/23 6/3* eq: -0.554
Player:
Opponent:		38.71% (G:9.49% B:0.55%)
61.29% (G:30.17% B:0.99%)		Conf.: ± 0.011 (-0.565...-0.544) - [94.7%]
Duration: 1 hour 31 minutes
2.Rollout113/10 11/10eq: -0.565 (-0.011)
Player:
Opponent:		37.38% (G:8.55% B:0.39%)
62.62% (G:23.73% B:0.90%)		Conf.: ± 0.008 (-0.573...-0.558) - [4.7%]
Duration: 30 minutes 55 seconds
3.Rollout18/5 6/5eq: -0.571 (-0.017)
Player:
Opponent:		37.36% (G:8.90% B:0.47%)
62.64% (G:26.29% B:0.98%)		Conf.: ± 0.009 (-0.581...-0.562) - [0.6%]
Duration: 1 hour 22 minutes
4.Rollout224/23 11/8eq: -0.600 (-0.046)
Player:
Opponent:		37.29% (G:7.72% B:0.42%)
62.71% (G:27.46% B:0.59%)		Conf.: ± 0.017 (-0.617...-0.583) - [0.0%]
Duration: 12 minutes 10 seconds
5.Rollout224/23 13/10eq: -0.612 (-0.057)
Player:
Opponent:		37.60% (G:8.33% B:0.46%)
62.40% (G:28.66% B:0.87%)		Conf.: ± 0.020 (-0.632...-0.591) - [0.0%]
Duration: 13 minutes 19 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 12345
Moves: 3-ply, cube decisions: XG Roller

2 1296 Games rolled with Variance Reduction.
Dice Seed: 12345
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10





White is Player 2

score: 0
pip: 139
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--aabcbb--A-:0:0:1:31:0:0:3:0:10
Position 5:.. 5pt is better than hit-and-split

1.Rollout18/5 6/5eq: -0.520
Player:
Opponent:		37.45% (G:9.24% B:0.55%)
62.55% (G:24.94% B:1.15%)		Conf.: ± 0.026 (-0.546...-0.494) - [100.0%]
Duration: 43 minutes 27 seconds
2.Rollout113/10 11/10eq: -0.680 (-0.160)
Player:
Opponent:		34.51% (G:8.45% B:0.41%)
65.49% (G:24.48% B:1.07%)		Conf.: ± 0.019 (-0.699...-0.661) - [0.0%]
Duration: 42 minutes 13 seconds
3.Rollout124/23 11/8eq: -0.756 (-0.236)
Player:
Opponent:		34.06% (G:7.88% B:0.43%)
65.94% (G:27.01% B:0.73%)		Conf.: ± 0.019 (-0.774...-0.737) - [0.0%]
Duration: 39 minutes 31 seconds
4.Rollout124/23 13/10eq: -0.756 (-0.236)
Player:
Opponent:		34.93% (G:8.30% B:0.45%)
65.07% (G:29.03% B:1.07%)		Conf.: ± 0.022 (-0.778...-0.734) - [0.0%]
Duration: 43 minutes 09 seconds
5.Rollout124/23 6/3* eq: -0.759 (-0.239)
Player:
Opponent:		35.67% (G:8.83% B:0.56%)
64.33% (G:32.16% B:1.00%)		Conf.: ± 0.019 (-0.778...-0.740) - [0.0%]
Duration: 45 minutes 10 seconds
1 1296 Games rolled with Variance Reduction.
Dice Seed: 24503777
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10





White is Player 2

score: 0
pip: 140
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC--b-bcbb--A-:0:0:1:31:0:0:3:0:10
Position 6:.. hit-and-split is better than 5pt

1.Rollout124/23 11/8eq: -0.588
Player:
Opponent:		37.14% (G:7.79% B:0.41%)
62.86% (G:26.33% B:0.64%)		Conf.: ± 0.009 (-0.597...-0.579) - [95.8%]
Duration: 16 minutes 53 seconds
2.Rollout124/23 6/3* eq: -0.601 (-0.013)
Player:
Opponent:		37.59% (G:9.45% B:0.58%)
62.41% (G:29.31% B:1.03%)		Conf.: ± 0.010 (-0.611...-0.591) - [3.1%]
Duration: 18 minutes 51 seconds
3.Rollout113/10 11/10eq: -0.604 (-0.016)
Player:
Opponent:		35.97% (G:8.64% B:0.40%)
64.03% (G:24.28% B:0.97%)		Conf.: ± 0.010 (-0.614...-0.593) - [1.1%]
Duration: 17 minutes 14 seconds
4.Rollout28/5 6/5eq: -0.618 (-0.030)
Player:
Opponent:		35.92% (G:8.53% B:0.38%)
64.08% (G:25.04% B:1.01%)		Conf.: ± 0.013 (-0.631...-0.605) - [0.0%]
Duration: 8 minutes 04 seconds
1 5184 Games rolled with Variance Reduction.
Dice Seed: 97859455
Moves: 3-ply, cube decisions: XG Roller

2 2592 Games rolled with Variance Reduction.
Dice Seed: 97859455
Moves: 3-ply, cube decisions: XG Roller





White is Player 2

score: 0
pip: 141
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbC-aa-bcbb--A-:0:0:1:31:0:0:3:0:10
Position 7:.. 5pt is better than hit-and-split

1.Rollout18/5 6/5eq: -0.562
Player:
Opponent:		37.39% (G:8.88% B:0.46%)
62.61% (G:23.00% B:0.99%)		Conf.: ± 0.007 (-0.569...-0.555) - [87.5%]
Duration: 1 hour 37 minutes
2.Rollout124/23 6/3* eq: -0.569 (-0.007)
Player:
Opponent:		38.14% (G:9.17% B:0.55%)
61.86% (G:28.61% B:0.95%)		Conf.: ± 0.010 (-0.579...-0.559) - [12.5%]
Duration: 1 hour 51 minutes
3.Rollout113/10 11/10eq: -0.580 (-0.018)
Player:
Opponent:		36.43% (G:9.17% B:0.48%)
63.57% (G:22.85% B:0.96%)		Conf.: ± 0.008 (-0.588...-0.573) - [0.0%]
Duration: 2 hours 12 minutes
4.Rollout124/23 11/8eq: -0.592 (-0.030)
Player:
Opponent:		36.72% (G:7.97% B:0.44%)
63.28% (G:25.63% B:0.67%)		Conf.: ± 0.009 (-0.601...-0.583) - [0.0%]
Duration: 2 hours 05 minutes
5.Rollout224/23 13/10eq: -0.597 (-0.035)
Player:
Opponent:		36.87% (G:8.65% B:0.53%)
63.13% (G:26.87% B:0.98%)		Conf.: ± 0.014 (-0.611...-0.583) - [0.0%]
Duration: 1 hour 24 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 1111
Moves: 3-ply, cube decisions: XG Roller

2 2592 Games rolled with Variance Reduction.
Dice Seed: 1111
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10




White is Player 2

score: 0
pip: 142
Unlimited Game
Jacoby Beaver
pip: 145
score: 0

Blue is Player 1
XGID=-a-a--EBB--BbCa-a-bcbb--A-:0:0:1:31:0:0:3:0:10
Position 8:.. hit-and-split is better than 5pt

1.Rollout124/23 6/3* eq: -0.567
Player:
Opponent:		38.45% (G:9.02% B:0.55%)
61.55% (G:26.00% B:0.96%)		Conf.: ± 0.007 (-0.574...-0.559) - [72.3%]
Duration: 2 hours 27 minutes
2.Rollout124/23 13/10eq: -0.572 (-0.005)
Player:
Opponent:		37.06% (G:8.76% B:0.49%)
62.94% (G:25.82% B:0.99%)		Conf.: ± 0.010 (-0.582...-0.562) - [17.7%]
Duration: 2 hours 24 minutes
3.Rollout18/5 6/5eq: -0.572 (-0.006)
Player:
Opponent:		37.10% (G:9.05% B:0.49%)
62.90% (G:23.26% B:1.00%)		Conf.: ± 0.007 (-0.580...-0.565) - [10.0%]
Duration: 2 hours 20 minutes
4.Rollout113/10 11/10eq: -0.581 (-0.014)
Player:
Opponent:		36.47% (G:9.04% B:0.50%)
63.53% (G:22.47% B:0.92%)		Conf.: ± 0.008 (-0.589...-0.573) - [0.1%]
Duration: 2 hours 35 minutes
5.Rollout124/23 11/8eq: -0.583 (-0.016)
Player:
Opponent:		37.24% (G:8.12% B:0.45%)
62.76% (G:24.49% B:0.66%)		Conf.: ± 0.007 (-0.590...-0.576) - [0.0%]
Duration: 2 hours 20 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 25496287
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

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