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

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.

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