HINT: there are three points to "anchor" on.

XGID=------E-B---eEb--bAdbA-A--:1:1:1:52:0:0:0:0:10

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 X X |
| X O O | | O O |
| X | | O |
| X | | O |
| X | | |
| |BAR| |
| O | | X |
| O | | X |
| O | | X | +---+
| O X | | X | | 2 |
| O X | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 173 O: 137 X-O: 0-0
Cube: 2, X own cube
X to play 52

On 10/12/2023 1:23 PM, ah...Clem wrote:
>
> HINT: there are three points to "anchor" on.
>
> XGID=------E-B---eEb--bAdbA-A--:1:1:1:52:0:0:0:0:10
>
> 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 X X |
> | X O O | | O O |
> | X | | O |
> | X | | O |
> | X | | |
> | |BAR| |
> | O | | X |
> | O | | X |
> | O | | X | +---+
> | O X | | X | | 2 |
> | O X | | X | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 173 O: 137 X-O: 0-0
> Cube: 2, X own cube
> X to play 52

Normally, the bar-point "anchor" is a very valuable point to make
in the early game, but X is so far behind in the pip count that I
worry that it's not enough contact. I do think we need to anchor,
since otherwise we're too vulnerable to being attacked. I would
play 23/21. As for the 5, the obvious 5 is 18/13, but again I
think we need to play for more contact, so I'd try 13/8 instead,
which unstacks the midpoint instead of plopping down yet another
checker on it.

---
Tim Chow

XGID=------E-B---eEb--bAdbA-A--:1:1:1:52:0:0:0:0:10

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 X X |
| X O O | | O O |
| X | | O |
| X | | O |
| X | | |
| |BAR| |
| O | | X |
| O | | X |
| O | | X | +---+
| O X | | X | | 2 |
| O X | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 173 O: 137 X-O: 0-0
Cube: 2, X own cube
X to play 52

X is way behind in the race and that implies maintaining contact. At
first glance, anchoring on the 21 point appears to maximize contact
since it's farther back than either the 18 or 16. But, as NeilKaz
observed the 18 provides more of a nuisance to O than the 21 - an anchor
on the 21 only provides a direct shot at one of O's outfield points
while anchoring on the 18 observes three of O's points. And the 17 point
can be cleared by dumping behind the anchor, or just waiting until X is
forced off the anchor. That, and O would really like to make the bar point.

Once you anchor on the bar point, 13/11 or 6/4 is basically a wash -
unstack vs slot a valuable homeboard point. Even the odd looking 8/6 is
better than anchoring on the 21.

Wil Snellings, who is no slouch, advocated for making the 16 point, but
the race is too lopsided to give up that much contact.

I impulsively went with the 21 point since "anchor up" is obvious, and
then liked unstacking more than moving the bar point blot to safety. At
least I got that part right.

1. Rollout¹ 23/18 6/4 eq:-0.501
Player: 24.48% (G:2.79% B:0.10%)
Opponent: 75.52% (G:9.54% B:0.17%)
Confidence: ±0.007 (-0.508..-0.493) - [97.4%]
Duration: 6 minutes 52 seconds

2. Rollout¹ 23/18 13/11 eq:-0.511 (-0.010)
Player: 24.35% (G:2.75% B:0.10%)
Opponent: 75.65% (G:9.78% B:0.27%)
Confidence: ±0.007 (-0.518..-0.504) - [2.6%]
Duration: 6 minutes 56 seconds

3. Rollout¹ 23/18 8/6 eq:-0.535 (-0.035)
Player: 23.17% (G:2.50% B:0.09%)
Opponent: 76.83% (G:9.62% B:0.25%)
Confidence: ±0.008 (-0.543..-0.528) - [0.0%]
Duration: 6 minutes 12 seconds

4. Rollout¹ 23/21 13/8 eq:-0.569 (-0.068)
Player: 22.78% (G:2.81% B:0.10%)
Opponent: 77.22% (G:12.69% B:0.30%)
Confidence: ±0.007 (-0.576..-0.562) - [0.0%]
Duration: 6 minutes 30 seconds

5. Rollout¹ 23/21 18/13 eq:-0.581 (-0.081)
Player: 20.29% (G:1.51% B:0.05%)
Opponent: 79.71% (G:5.87% B:0.19%)
Confidence: ±0.005 (-0.586..-0.576) - [0.0%]
Duration: 6 minutes 20 seconds

6. Rollout¹ 21/16 18/16 eq:-0.607 (-0.106)
Player: 24.39% (G:3.77% B:0.13%)
Opponent: 75.61% (G:22.13% B:0.39%)
Confidence: ±0.008 (-0.615..-0.598) - [0.0%]
Duration: 6 minutes 04 seconds

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

eXtreme Gammon Version: 2.10

One thing that I noticed in the original position, but did not pay
enough attention to, is that the bar-point anchor is six pips away
from O's midpoint checkers, but the 4pt anchor is not six pips or
even five pips away from any of O's points. If we shift O's checkers
on her 11pt to her 10pt, the story changes:

XGID=------E-B---eE-b-bAdbA-A--:1:1:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O X | | O O X X |
| X O O | | O O |
| X | | O |
| X | | O |
| X | | |
| |BAR| |
| O | | X |
| O | | X |
| O | | X | +---+
| O X | | X | | 2 |
| O X | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 173 O: 135 X-O: 0-0
Cube: 2, X own cube
X to play 52

1. Rollout¹ 23/21 13/8 eq:-0.556
Player: 23.28% (G:2.97% B:0.10%)
Opponent: 76.72% (G:12.74% B:0.34%)
Confidence: ±0.004 (-0.560..-0.553) - [72.7%]

2. Rollout¹ 23/18 6/4 eq:-0.558 (-0.002)
Player: 23.14% (G:2.83% B:0.11%)
Opponent: 76.86% (G:12.41% B:0.26%)
Confidence: ±0.004 (-0.562..-0.554) - [27.0%]

3. Rollout¹ 23/18 13/11 eq:-0.563 (-0.006)
Player: 22.83% (G:2.71% B:0.10%)
Opponent: 77.17% (G:12.10% B:0.26%)
Confidence: ±0.004 (-0.566..-0.559) - [0.3%]

4. Rollout¹ 23/21 18/13 eq:-0.569 (-0.012)
Player: 20.95% (G:1.86% B:0.06%)
Opponent: 79.05% (G:6.73% B:0.21%)
Confidence: ±0.003 (-0.571..-0.566) - [0.0%]

¹ 5184 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