XGID=-----bE-D-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O X |
| X O | | O O |
| X O | | O O |
| | | O |
| | | O |
| |BAR| |
| | | X |
| X | | X |
| X | | X |
| O X X | | X O |
| O X X | | X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 145 O: 135 X-O: 0-0
Cube: 1
X to play 51

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=-----bE-D-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O X |
| X O | | O O |
| X O | | O O |
| | | O |
| | | O |
| |BAR| |
| | | X |
| X | | X |
| X | | X |
| O X X | | X O |
| O X X | | X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 145 O: 135 X-O: 0-0
Cube: 1
X to play 51

Given that X is behind in the race, I didn't think that Pottling was
the right idea here. The trouble is that the alternative play 8/2
is so weak. Take a look at the variant for comparison.

1. Rollout¹ 24/18 eq:-0.414
Player: 40.99% (G:4.20% B:0.18%)
Opponent: 59.01% (G:16.61% B:0.26%)
Confidence: ±0.012 (-0.426..-0.402) - [100.0%]

2. Rollout¹ 8/2 eq:-0.527 (-0.113)
Player: 38.61% (G:5.65% B:0.22%)
Opponent: 61.39% (G:20.20% B:0.40%)
Confidence: ±0.013 (-0.539..-0.514) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

-------
Variant
-------

XGID=--A--bE-C-B-bC---c-ec---A-:0:0:1:51:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O X |
| X O | | O O |
| X O | | O O |
| | | O |
| | | O |
| |BAR| |
| | | X |
| | | X |
| X | | X |
| O X X | | X O |
| O X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 139 O: 135 X-O: 0-0
Cube: 1
X to play 51

1. Rollout¹ 6/1 2/1 eq:-0.371
Player: 41.92% (G:5.96% B:0.21%)
Opponent: 58.08% (G:16.79% B:0.29%)
Confidence: ±0.010 (-0.381..-0.360) - [90.4%]

2. Rollout¹ 24/18 eq:-0.381 (-0.011)
Player: 41.86% (G:4.45% B:0.19%)
Opponent: 58.14% (G:16.59% B:0.34%)
Confidence: ±0.012 (-0.393..-0.369) - [9.6%]

3. Rollout¹ 8/2 eq:-0.394 (-0.023)
Player: 41.46% (G:5.70% B:0.22%)
Opponent: 58.54% (G:17.05% B:0.35%)
Confidence: ±0.010 (-0.405..-0.384) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Pottle

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=---CBCC-A-b-cB-----dAcba--:0:0:1:42:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O |
| X | | O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | X X X |
| O O | | X X X X |
| O O X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 104 O: 113 X-O: 0-0
Cube: 1
X to play 42

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XG 3-ply plays 5/1 3/1.


XGID=---CBCC-A-b-cB-----dAcba--:0:0:1:42:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O X O O O |
| X | | O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | X X X |
| O O | | X X X X |
| O O X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 104 O: 113 X-O: 0-0
Cube: 1
X to play 42

It's thematic to race when ahead in the race, and O's 2's and 4's
are duplicated to hit and cover if X plays 20/14. But should X pay
now or pay later? XG 3-ply plays 5/1 3/1, but the rollout below
disagrees.

1. Rollout¹ 20/14 eq:+0.287
Player: 58.35% (G:9.35% B:0.22%)
Opponent: 41.65% (G:3.35% B:0.07%)
Confidence: ±0.008 (+0.279..+0.295) - [100.0%]

2. Rollout¹ 5/1 3/1 eq:+0.204 (-0.083)
Player: 55.85% (G:10.37% B:0.13%)
Opponent: 44.15% (G:4.28% B:0.08%)
Confidence: ±0.011 (+0.193..+0.215) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Since ah_clem seems to be currently interested in "Pottle or not"
problems, here's one to ponder.

XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O X O O O |
| X O | | O O O |
| X | | O |
| X | | |
| | | |
| |BAR| |
| | | |
| O | | X |
| O | | X |
| O X X | | X X |
| O X X | | X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 140 O: 123 X-O: 0-0
Cube: 1
X to play 32

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 9/20/2022 8:27 AM, Timothy Chow wrote:

Since ah_clem seems to be currently interested in "Pottle or not"
problems, here's one to ponder.

XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

X:Player 1   O:Player 2
Score is X:0 O:0. Unlimited Game  +13-14-15-16-17-18------19-20-21-22-23-24-+
 | X           O    |   | O  X  O  O     O |
 | X           O    |   | O     O        O |
 | X                |   | O                |  | X                |   |                  |
 |                  |   |                  |
 |                  |BAR|                  |
 |                  |   |                  |
 | O                |   | X                |  | O                |   | X                |  | O  X        X    |   | X        X       |
 | O  X        X    |   | X        X     O |  +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 140  O: 123 X-O: 0-0
Cube: 1
X to play 32

My understanding is that Pottling is more favored when ahead or roughly
even in the race, but when behind it can be better to hang back for more contact.

X is behind in the race, so perhaps it's better to do something other
than run the straggler. But, I'm not seeing anything "very constructive"
so Pottling would be correct according to the letter of the rule. Also,
with O's homeboard blot getting hit in the outfield gives X lots of counterplay, so I'll Pottle here.

20/15.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=-a-B--D-B--BdD---b-cAba-b-:0:0:1:32:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O X O O O |
| X O | | O O O |
| X | | O |
| X | | |
| | | |
| |BAR| |
| | | |
| O | | X |
| O | | X |
| O X X | | X X |
| O X X | | X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 140 O: 123 X-O: 0-0
Cube: 1
X to play 32

As ah_clem said, sometimes being behind in the pip count can be a
reason not to Pottle. The idea is that if you disengage into a
pure race then you'll be losing, and Pottling is a step toward
disengaging. But there are a couple of other factors to take into
account:

1. If your straggler is in danger of being attacked, then Pottling
may be the lesser of two evils.

2. If you're well positioned to contain the checker (or checkers)
that your opponent has not yet escaped, then Pottling does not
really disengage, and may even help, by bringing another checker
into the containment effort.

These factors can be difficult to judge. The rollout belows deems
that anything other than 20/15 is a whopper, but if I shift the
blot in O's home board by just one pip to the 2pt, then 20/15 is
tied with 13/11 13/10 (see variant below).

1. Rollout¹ 20/15 eq:-0.267
Player: 43.87% (G:6.46% B:0.27%)
Opponent: 56.13% (G:18.13% B:0.19%)
Confidence: ±0.010 (-0.277..-0.257) - [100.0%]

2. Rollout¹ 13/8 eq:-0.369 (-0.102)
Player: 42.11% (G:7.60% B:0.32%)
Opponent: 57.89% (G:22.17% B:0.26%)
Confidence: ±0.010 (-0.379..-0.358) - [0.0%]

3. Rollout¹ 13/11 13/10 eq:-0.386 (-0.119)
Player: 42.04% (G:8.68% B:0.39%)
Opponent: 57.96% (G:25.23% B:0.36%)
Confidence: ±0.012 (-0.398..-0.374) - [0.0%]

4. Rollout¹ 6/1* eq:-0.413 (-0.146)
Player: 40.95% (G:9.86% B:0.35%)
Opponent: 59.05% (G:24.39% B:0.50%)
Confidence: ±0.012 (-0.425..-0.401) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

-------
Variant
-------

XGID=-a-B--D-B--BdD---b-cAb-ab-:0:0:1:32:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O X O O O |
| X O | | O O O |
| X | | O |
| X | | |
| | | |
| |BAR| |
| | | |
| O | | X |
| O | | X |
| O X X | | X X |
| O X X | | X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 140 O: 122 X-O: 0-0
Cube: 1
X to play 32

1. Rollout¹ 20/15 eq:-0.304
Player: 43.20% (G:6.59% B:0.28%)
Opponent: 56.80% (G:18.73% B:0.18%)
Confidence: ±0.005 (-0.309..-0.299) - [67.5%]

2. Rollout¹ 13/11 13/10 eq:-0.306 (-0.002)
Player: 44.06% (G:10.40% B:0.53%)
Opponent: 55.94% (G:24.75% B:0.34%)
Confidence: ±0.006 (-0.312..-0.300) - [32.5%]

3. Rollout¹ 13/8 eq:-0.317 (-0.013)
Player: 43.67% (G:8.64% B:0.40%)
Opponent: 56.33% (G:21.60% B:0.21%)
Confidence: ±0.005 (-0.322..-0.312) - [0.0%]

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:41:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O |
| X O | | O O |
| X O | | O |
| | | |
| | X | |
| |BAR| |
| | | X |
| | | X |
| X X | | X |
| O X X | | X O |
| O X X | | X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 139 O: 162 X-O: 0-0
Cube: 1
X to play 41

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:41:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O |
| X O | | O O |
| X O | | O |
| | | |
| | X | |
| |BAR| |
| | | X |
| | | X |
| X X | | X |
| O X X | | X O |
| O X X | | X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 139 O: 162 X-O: 0-0
Cube: 1
X to play 41

Stepping up into a quadruple shot can be the right idea if it is a
distraction play. But stepping up to the 5pt isn't a distraction play
because that's the point O wants to make.

In the variant, I have changed the roll to 52.

1. Rollout¹ Bar/24 6/2* eq:+0.035
Player: 51.07% (G:13.29% B:0.52%)
Opponent: 48.93% (G:13.06% B:0.47%)
Confidence: ±0.016 (+0.019..+0.051) - [100.0%]

2. Rollout¹ Bar/20 eq:-0.069 (-0.104)
Player: 48.57% (G:11.99% B:0.47%)
Opponent: 51.43% (G:14.62% B:0.42%)
Confidence: ±0.016 (-0.085..-0.053) - [0.0%]

3. Rollout¹ Bar/24 7/3 eq:-0.075 (-0.110)
Player: 48.60% (G:11.84% B:0.47%)
Opponent: 51.40% (G:14.25% B:0.53%)
Confidence: ±0.013 (-0.089..-0.062) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

-------
Variant
-------

XGID=--a-b-ECC---bCaa-c-c-b---A:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O |
| X O | | O O |
| X O | | O |
| | | |
| | X | |
| |BAR| |
| | | X |
| | | X |
| X X | | X |
| O X X | | X O |
| O X X | | X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 139 O: 162 X-O: 0-0
Cube: 1
X to play 52

1. Rollout¹ Bar/18 eq:+0.041
Player: 51.23% (G:12.55% B:0.55%)
Opponent: 48.77% (G:12.78% B:0.43%)
Confidence: ±0.016 (+0.026..+0.057) - [99.9%]

2. Rollout¹ Bar/23 13/8 eq:+0.008 (-0.033)
Player: 49.88% (G:12.86% B:0.51%)
Opponent: 50.12% (G:11.96% B:0.40%)
Confidence: ±0.015 (-0.006..+0.023) - [0.1%]

3. Rollout¹ Bar/23 6/1 eq:-0.052 (-0.094)
Player: 48.69% (G:12.95% B:0.38%)
Opponent: 51.31% (G:13.66% B:0.44%)
Confidence: ±0.016 (-0.068..-0.037) - [0.0%]

4. Rollout¹ Bar/23 7/2* eq:-0.060 (-0.101)
Player: 48.33% (G:13.05% B:0.49%)
Opponent: 51.67% (G:13.95% B:0.45%)
Confidence: ±0.017 (-0.077..-0.043) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)