This is my attempt to respond to ah...clem's request for positions
that offer---or at least might seem to offer---the opportunity for
what Chris Bray might call a "one-roll proposition."

XGID=--aBBCBB----A-A-----fcBbc-:1:-1:1:62:0:0:0:0:10

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 | +---+
| | | O O X O O | | 2 |
| | | O O O | +---+
| | | O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X |
| X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 125 O: 72 X-O: 0-0
Cube: 2, O own cube
X to play 62

---
Tim Chow

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

On 10/6/2023 8:25 PM, Timothy Chow wrote:

This is my attempt to respond to ah...clem's request for positions
that offer---or at least might seem to offer---the opportunity for
what Chris Bray might call a "one-roll proposition."

XGID=--aBBCBB----A-A-----fcBbc-:1:-1:1:62:0:0:0:0:10

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 | +---+  |                  |   |    O  O  X  O  O | | 2 |  |                  |   |    O  O        O | +---+
 |                  |   |    O             |
 |                  |   |    6             |
 |                  |BAR|                  |
 |                  |   |                  |
 |                  |   |                  |
 |                  |   |    X             |
 |                X |   | X  X  X  X       |
 | X              X |   | X  X  X  X  O    |  +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 125  O: 72 X-O: 0-0
Cube: 2, O own cube
X to play 62

Slotting the back of the prime is classic play, and since 6s are good
rolls for O anyway, might as well recirculate for more contact if she
leaps out.

5/3 gives more rolls to make the 8 point while 12/10 doesn't improve the
number of POH rolls, so I'll go with 14/8 5/3.

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

XGID=--aBBCBB----A-A-----fcBbc-:1:-1:1:62:0:0:0:0:10

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 | +---+
| | | O O X O O | | 2 |
| | | O O O | +---+
| | | O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X |
| X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 125 O: 72 X-O: 0-0
Cube: 2, O own cube
X to play 62

This first problem is a negative example, in the sense that XG does
not slot the 8pt. Although O's board has started to crunch, she
still has a four-point board, and getting hit could be disastrous
for X. A pedestrian play such as 12/6 5/3 or 12/4 still does a
pretty good job of keeping O contained, and gives O a chance to
roll something that causes her position to deteriorate further.

In the variant, I have weakened O's board.

1. Rollout¹ 12/6 5/3 eq:+0.293
Player: 68.90% (G:6.69% B:0.19%)
Opponent: 31.10% (G:6.68% B:0.06%)
Confidence: ±0.005 (+0.288..+0.298) - [98.9%]

2. Rollout¹ 12/4 eq:+0.285 (-0.008)
Player: 68.52% (G:6.70% B:0.19%)
Opponent: 31.48% (G:6.75% B:0.06%)
Confidence: ±0.005 (+0.280..+0.290) - [1.1%]

3. Rollout¹ 14/8 12/10 eq:+0.218 (-0.075)
Player: 66.56% (G:7.03% B:0.20%)
Opponent: 33.44% (G:12.97% B:0.15%)
Confidence: ±0.005 (+0.213..+0.223) - [0.0%]

4. Rollout¹ 22/14 eq:+0.215 (-0.078)
Player: 64.98% (G:8.78% B:0.26%)
Opponent: 35.02% (G:10.32% B:0.05%)
Confidence: ±0.006 (+0.209..+0.220) - [0.0%]

5. Rollout¹ 22/16 14/12 eq:+0.212 (-0.081)
Player: 64.19% (G:8.38% B:0.26%)
Opponent: 35.81% (G:8.67% B:0.06%)
Confidence: ±0.006 (+0.206..+0.218) - [0.0%]

6. Rollout¹ 14/8 5/3 eq:+0.200 (-0.093)
Player: 66.31% (G:7.14% B:0.20%)
Opponent: 33.69% (G:14.19% B:0.20%)
Confidence: ±0.005 (+0.195..+0.206) - [0.0%]

7. Rollout¹ 14/6 eq:+0.194 (-0.099)
Player: 64.61% (G:6.54% B:0.18%)
Opponent: 35.39% (G:6.36% B:0.06%)
Confidence: ±0.005 (+0.190..+0.199) - [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=--aBBCBB----A-A-----fdBac-:1:-1:1:62:0:0:0:0:10

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 | +---+
| | | O O X O | | 2 |
| | | O O O | +---+
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X |
| X X | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 125 O: 74 X-O: 0-0
Cube: 2, O own cube
X to play 62

1. Rollout¹ 14/8 12/10 eq:+0.368
Player: 72.58% (G:7.94% B:0.25%)
Opponent: 27.42% (G:9.77% B:0.14%)
Confidence: ±0.002 (+0.365..+0.370) - [78.2%]

2. Rollout¹ 22/14 eq:+0.366 (-0.002)
Player: 71.67% (G:7.35% B:0.23%)
Opponent: 28.33% (G:6.58% B:0.05%)
Confidence: ±0.003 (+0.363..+0.369) - [21.8%]

3. Rollout² 22/16 5/3 eq:+0.353 (-0.015)
Player: 71.46% (G:7.03% B:0.23%)
Opponent: 28.54% (G:8.78% B:0.11%)
Confidence: ±0.007 (+0.346..+0.360) - [0.0%]

4. Rollout² 22/16 12/10 eq:+0.346 (-0.022)
Player: 71.02% (G:7.31% B:0.20%)
Opponent: 28.98% (G:8.40% B:0.13%)
Confidence: ±0.006 (+0.340..+0.352) - [0.0%]

5. Rollout² 12/6 5/3 eq:+0.343 (-0.025)
Player: 71.09% (G:6.93% B:0.21%)
Opponent: 28.91% (G:6.35% B:0.06%)
Confidence: ±0.006 (+0.337..+0.349) - [0.0%]

6. Rollout² 14/8 5/3 eq:+0.339 (-0.028)
Player: 71.63% (G:7.76% B:0.26%)
Opponent: 28.37% (G:11.43% B:0.18%)
Confidence: ±0.005 (+0.335..+0.344) - [0.0%]

7. Rollout² 12/4 eq:+0.333 (-0.034)
Player: 70.83% (G:6.78% B:0.20%)
Opponent: 29.17% (G:6.61% B:0.06%)
Confidence: ±0.006 (+0.327..+0.339) - [0.0%]

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

² 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)