I'm sorry but I don't know how to create diagrams so please just listen
to my verbal descriptions without complaining too much. Ok?

Your opponent has all 15 checkers and is on roll.
All her checkers are in her inner board. Her ace point is
empty and she has 3 checkers on all her other inner board points.

You have 15 checkers. Your task is to find the optimal position for
your checkers under the constraint that at least one of your checkers
must be on her acepoint.
The four variants are:
1) DMP
2) Money -- cube in centre.
3) Money -- she owns cube.
4) Money -- you own cube.

It could be that she can double you out with access to the cube whatever
you do -- in fact I think that's likely. But the other two variants are interesting
(to me).

Paul

On Friday, October 20, 2023 at 5:39:26 PM UTC-4, peps...@gmail.com wrote:
> I'm sorry but I don't know how to create diagrams so please just listen
> to my verbal descriptions without complaining too much. Ok?
>
> Your opponent has all 15 checkers and is on roll.
> All her checkers are in her inner board. Her ace point is
> empty and she has 3 checkers on all her other inner board points.
>
> You have 15 checkers. Your task is to find the optimal position for
> your checkers under the constraint that at least one of your checkers
> must be on her acepoint.
> The four variants are:
> 1) DMP
> 2) Money -- cube in centre.
> 3) Money -- she owns cube.
> 4) Money -- you own cube.
>
> It could be that she can double you out with access to the cube whatever
> you do -- in fact I think that's likely. But the other two variants are interesting
> (to me).
>
> Paul

Yes, ignore the two list items where the opponent has cube access as they will be DP. (unless you're bad enough to settle on a position where you opponent is actually TG)

Without even thinking about it at dmp I'll have an anchor on the 24pt, a checker on the 18pt, and a 6 prime from the 4pt to the 9pt.

For money I suspect everything will be TG with the anchor made regardless of how you put your offensive position so we can only have one checker back and the gammon save a certainty so it'll have to go DP. (one checker on the 24pt, full board, spares reasonable)

Stick

On Saturday, October 21, 2023 at 5:13:33 AM UTC+1, Stick Rice wrote:
> On Friday, October 20, 2023 at 5:39:26 PM UTC-4, peps...@gmail.com wrote:
> > I'm sorry but I don't know how to create diagrams so please just listen
> > to my verbal descriptions without complaining too much. Ok?
> >
> > Your opponent has all 15 checkers and is on roll.
> > All her checkers are in her inner board. Her ace point is
> > empty and she has 3 checkers on all her other inner board points.
> >
> > You have 15 checkers. Your task is to find the optimal position for
> > your checkers under the constraint that at least one of your checkers
> > must be on her acepoint.
> > The four variants are:
> > 1) DMP
> > 2) Money -- cube in centre.
> > 3) Money -- she owns cube.
> > 4) Money -- you own cube.
> >
> > It could be that she can double you out with access to the cube whatever
> > you do -- in fact I think that's likely. But the other two variants are interesting
> > (to me).
> >
> > Paul
> Yes, ignore the two list items where the opponent has cube access as they will be DP. (unless you're bad enough to settle on a position where you opponent is actually TG)
>
> Without even thinking about it at dmp I'll have an anchor on the 24pt, a checker on the 18pt, and a 6 prime from the 4pt to the 9pt.
>
> For money I suspect everything will be TG with the anchor made regardless of how you put your offensive position so we can only have one checker back and the gammon save a certainty so it'll have to go DP. (one checker on the 24pt, full board, spares reasonable)
>
> Stick

For money, how about trying to win the race?
10 checkers on your own ace point, 4 on your 2 point?

Paul

On 10/21/2023 6:25 AM, peps...@gmail.com wrote:
> On Saturday, October 21, 2023 at 5:13:33 AM UTC+1, Stick Rice wrote:
>> Without even thinking about it at dmp I'll have an anchor on the 24pt, a checker on the 18pt, and a 6 prime from the 4pt to the 9pt.

It appears that giving X even more timing than that is an improvement.
I didn't work too hard to optimize, but see below for example.

XGID=-----AADBBA-----A-AcccccB-:0:0:1:21:0:0:0:1:10

Score is X:0 O:0 1 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X | | O O O O O X |
| | | O O O O O X |
| | | O O O O O |
| | | |
| | | |
| |BAR| |
| | | |
| X | | |
| X | | |
| X X X | | |
| X X X X | | X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 165 O: 60 X-O: 0-0/1
Cube: 1
X to play 21

1. Rollout¹ 7/6 7/5 eq:-0.531
Player: 23.44% (G:0.00% B:0.00%)
Opponent: 76.56% (G:56.98% B:30.73%)
Confidence: ±0.005 (-0.537..-0.526) - [100.0%]

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, MET: Kazaross XG2

-----------------------------------------------------------------

XGID=----AADBBB--------AcccccB-:0:0:1:21:0:0:0:1:10

Score is X:0 O:0 1 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O O O O X |
| | | O O O O O X |
| | | O O O O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X X | | X |
| X X X | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 147 O: 60 X-O: 0-0/1
Cube: 1
X to play 21

1. Rollout¹ 6/5 6/4 eq:-0.567
Player: 21.64% (G:0.00% B:0.00%)
Opponent: 78.36% (G:52.36% B:22.79%)
Confidence: ±0.004 (-0.571..-0.563) - [100.0%]

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, MET: Kazaross XG2

>> For money I suspect everything will be TG with the anchor made regardless of how you put your offensive position so we can only have one checker back and the gammon save a certainty so it'll have to go DP. (one checker on the 24pt, full board, spares reasonable)
>>
>> Stick
>
> For money, how about trying to win the race?
> 10 checkers on your own ace point, 4 on your 2 point?

The above two positions roll out about the same. But it seems that
it's actually slightly better for us to have an anchor.

Just because Position A is TG (for the opponent owning the cube)
and Position B is D/P (again, for the opponent owning the cube)
doesn't automatically mean that Position A is better than Position B
(for the opponent) if we own the cube.

XGID=-BBBBCB--A---------cccccA-:1:1:1:12:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O X |
| | | O O O O O |
| | | O O O O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X | +---+
| | | X X X X X X | | 2 |
| X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 80 O: 60 X-O: 0-0
Cube: 2, X own cube
X to play 12

1. Rollout¹ 9/6 eq:-0.904
Player: 4.99% (G:0.00% B:0.00%)
Opponent: 95.01% (G:1.82% B:0.03%)
Confidence: ±0.002 (-0.906..-0.903) - [100.0%]

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

-----------------------------------------------------------------

XGID=-ICB---------------cccccA-:1:1:1:12:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O X |
| | | O O O O O |
| | | O O O O O |
| | | |
| | | |
| |BAR| |
| | | 9 |
| | | X |
| | | X X | +---+
| | | X X X | | 2 |
| | | X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 45 O: 60 X-O: 0-0
Cube: 2, X own cube
X to play 12

1. Rollout¹ 3/2 3/1 eq:-0.907
Player: 5.53% (G:0.00% B:0.00%)
Opponent: 94.47% (G:3.07% B:0.05%)
Confidence: ±0.002 (-0.909..-0.905) - [100.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.211.pre-release

-----------------------------------------------------------------

XGID=--BBBBBB---A-------cccccB-:1:1:1:12:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O O O X |
| | | O O O O O X |
| | | O O O O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| X | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 60 X-O: 0-0
Cube: 2, X own cube
X to play 12

1. Rollout¹ 11/8 eq:-0.888
Player: 12.57% (G:0.00% B:0.00%)
Opponent: 87.43% (G:18.18% B:0.71%)
Confidence: ±0.003 (-0.892..-0.885) - [100.0%]

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