No cows were harmed in the making of this backgammon position.

XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10

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 O O | +---+
| X | | O O O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X X |
| | | X X X |
| O | | X X X X O |
| O | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 82 O: 107 X-O: 0-0
Cube: 2, O own cube
X to play 51

---
Tim Chow

On 8/26/2022 9:52 AM, Timothy Chow wrote:
> No cows were harmed in the making of this backgammon position.
>
> XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10
>
> 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  O  O | +---+
>  |    X             |   | O     O  O  O  O | | 2 |
>  |                  |   |                O | +---+
>  |                  |   |                  |
>  |                  |   |                  |
>  |                  |BAR|                  |
>  |                  |   |                  |
>  |                  |   |    X     X       |
>  |                  |   | X  X     X       |
>  | O                |   | X  X     X  X  O |
>  | O                |   | X  X     X  X  O |
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 82  O: 107 X-O: 0-0
> Cube: 2, O own cube
> X to play 51

14/9 is forced. I count four shots to hit on either the 9 or 8 points,
11 to hit on the 13, and 12 to hit on the 14.

Perhaps it's worth the extra shot to unstack the three point, but I'm
unconvinced, so 14/9 14/13.

XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10

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 O O | +---+
| X | | O O O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X X |
| | | X X X |
| O | | X X X X O |
| O | | X X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 82 O: 107 X-O: 0-0
Cube: 2, O own cube
X to play 51

I was rather surprised at how much difference there is among the
possible plays here. 14/9 3/2 lets O hit with any 2 as well as
53 and 11, for a total of 14 shots. 14/8 lets O hit with any 2
as well as 61, 43, and 11, for a total of 16 shots. 14/13 14/9
lets O hit with any ace as well as 62, 53, 66 and 33, for a total
of 17 shots. So picking the play that leaves the fewest shots
will lead you to the top play of the rollout below. But I think
it's also true that O is particularly happy to hit from her 24pt
since it lets her escape with tempo.

1. Rollout¹ 14/9 3/2 eq:+0.309
Player: 68.07% (G:10.09% B:0.35%)
Opponent: 31.93% (G:6.03% B:0.12%)
Confidence: ±0.005 (+0.304..+0.314) - [100.0%]

2. Rollout¹ 14/9 6/5 eq:+0.243 (-0.066)
Player: 65.50% (G:9.03% B:0.32%)
Opponent: 34.50% (G:6.21% B:0.13%)
Confidence: ±0.005 (+0.238..+0.248) - [0.0%]

3. Rollout¹ 14/8 eq:+0.224 (-0.084)
Player: 65.21% (G:9.84% B:0.36%)
Opponent: 34.79% (G:6.37% B:0.12%)
Confidence: ±0.005 (+0.219..+0.229) - [0.0%]

4. Rollout¹ 14/13 14/9 eq:+0.154 (-0.155)
Player: 62.75% (G:8.72% B:0.29%)
Opponent: 37.25% (G:6.96% B:0.14%)
Confidence: ±0.004 (+0.149..+0.158) - [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

On Sunday, August 28, 2022 at 1:37:36 PM UTC+1, Tim Chow wrote:
> XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10
>
> 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 O O | +---+
> | X | | O O O O O | | 2 |
> | | | O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X X |
> | | | X X X |
> | O | | X X X X O |
> | O | | X X X X O |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 82 O: 107 X-O: 0-0
> Cube: 2, O own cube
> X to play 51
> I was rather surprised at how much difference there is among the
> possible plays here. 14/9 3/2 lets O hit with any 2 as well as
> 53 and 11, for a total of 14 shots. 14/8 lets O hit with any 2
> as well as 61, 43, and 11, for a total of 16 shots. 14/13 14/9
> lets O hit with any ace as well as 62, 53, 66 and 33, for a total
> of 17 shots. So picking the play that leaves the fewest shots
> will lead you to the top play of the rollout below. But I think
> it's also true that O is particularly happy to hit from her 24pt
> since it lets her escape with tempo.
>
> 1. Rollout¹ 14/9 3/2 eq:+0.309
> Player: 68.07% (G:10.09% B:0.35%)
> Opponent: 31.93% (G:6.03% B:0.12%)
> Confidence: ±0.005 (+0.304..+0.314) - [100.0%]
>
> 2. Rollout¹ 14/9 6/5 eq:+0.243 (-0.066)
> Player: 65.50% (G:9.03% B:0.32%)
> Opponent: 34.50% (G:6.21% B:0.13%)
> Confidence: ±0.005 (+0.238..+0.248) - [0.0%]
>
> 3. Rollout¹ 14/8 eq:+0.224 (-0.084)
> Player: 65.21% (G:9.84% B:0.36%)
> Opponent: 34.79% (G:6.37% B:0.12%)
> Confidence: ±0.005 (+0.219..+0.229) - [0.0%]
>
> 4. Rollout¹ 14/13 14/9 eq:+0.154 (-0.155)
> Player: 62.75% (G:8.72% B:0.29%)
> Opponent: 37.25% (G:6.96% B:0.14%)
> Confidence: ±0.004 (+0.149..+0.158) - [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

ah..Clem had exactly the right idea of minimizing shots but, bizarrely, he miscounted really badly
and confused leaving maximum shots with leaving minimum shots to end up with the worst play.

With 14/9 3/2, the top choice, there are no trade-offs. We really have our cake and eat it, and this
is surely a trivial problem for anyone who can (and does) count shots.
3/2 helps our position by building for the acepoint and unstacking (as ah..Clem correctly noted). And also, this play minimizes shots, too.

It would be a more interesting problem if the 3/2 play didn't also minimize shots.

Paul

On 8/28/2022 2:48 PM, peps...@gmail.com wrote:

> It would be a more interesting problem if the 3/2 play didn't also minimize shots.

What I found interesting was not the ranking of the plays but
the size of the equity differences.

---
Tim Chow

On Monday, August 29, 2022 at 1:43:51 AM UTC+1, Tim Chow wrote:
> On 8/28/2022 2:48 PM, peps...@gmail.com wrote:
>
> > It would be a more interesting problem if the 3/2 play didn't also minimize shots.
> What I found interesting was not the ranking of the plays but
> the size of the equity differences.
>
> ---
> Tim Chow

Not me. If you choose a play which subjects you to more shots, and fails to develop
the position by unstacking, then you expect to get batttered.

Paul

On Monday, August 29, 2022 at 1:43:51 AM UTC+1, Tim Chow wrote:
> On 8/28/2022 2:48 PM, peps...@gmail.com wrote:
>
> > It would be a more interesting problem if the 3/2 play didn't also minimize shots.
> What I found interesting was not the ranking of the plays but
> the size of the equity differences.
>
> ---
> Tim Chow

If I remember rightly, this type of trade-off that makes a position interesting,
occurs in the opening if you slot to the opponent's bar with 62/63/64 and the
continuation is 55, dance.
These positions are all somewhat marginal between D/P and D/T.
(I can't remember which of the 3 are takes (if any).)
(Perhaps naively), I would have thought that cuber's position increases in strength
depending on the number of shots they have. But this turns out not to be true.
The 9 point builder after 13/9 has value if this checker doesn't get hit, so I don't think
64 is the worst of the 3 games for the underdog.

Paul

On Sunday, August 28, 2022 at 8:37:36 AM UTC-4, Tim Chow wrote:
> XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10
>
> 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 O O | +---+
> | X | | O O O O O | | 2 |
> | | | O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X X |
> | | | X X X |
> | O | | X X X X O |
> | O | | X X X X O |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 82 O: 107 X-O: 0-0
> Cube: 2, O own cube
> X to play 51
> I was rather surprised at how much difference there is among the
> possible plays here. 14/9 3/2 lets O hit with any 2 as well as
> 53 and 11, for a total of 14 shots. 14/8 lets O hit with any 2
> as well as 61, 43, and 11, for a total of 16 shots. 14/13 14/9
> lets O hit with any ace as well as 62, 53, 66 and 33, for a total
> of 17 shots. So picking the play that leaves the fewest shots
> will lead you to the top play of the rollout below. But I think
> it's also true that O is particularly happy to hit from her 24pt
> since it lets her escape with tempo.
>
> 1. Rollout¹ 14/9 3/2 eq:+0.309
> Player: 68.07% (G:10.09% B:0.35%)
> Opponent: 31.93% (G:6.03% B:0.12%)
> Confidence: ±0.005 (+0.304..+0.314) - [100.0%]
>
> 2. Rollout¹ 14/9 6/5 eq:+0.243 (-0.066)
> Player: 65.50% (G:9.03% B:0.32%)
> Opponent: 34.50% (G:6.21% B:0.13%)
> Confidence: ±0.005 (+0.238..+0.248) - [0.0%]
>
> 3. Rollout¹ 14/8 eq:+0.224 (-0.084)
> Player: 65.21% (G:9.84% B:0.36%)
> Opponent: 34.79% (G:6.37% B:0.12%)
> Confidence: ±0.005 (+0.219..+0.229) - [0.0%]
>
> 4. Rollout¹ 14/13 14/9 eq:+0.154 (-0.155)
> Player: 62.75% (G:8.72% B:0.29%)
> Opponent: 37.25% (G:6.96% B:0.14%)
> Confidence: ±0.004 (+0.149..+0.158) - [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

While this and these situations are generally easily solved when there's a difference in the amount of shots left, it should be recognized here that by making the correct play, 3/2, and not 14/13, we make the opponent's immediate aces pretty disgusting.

Stick

On Tuesday, August 30, 2022 at 7:56:57 PM UTC+1, Stick Rice wrote:
> On Sunday, August 28, 2022 at 8:37:36 AM UTC-4, Tim Chow wrote:
> > XGID=-bBD-DC-----b-B----b-bbbc-:1:-1:1:51:0:0:0:0:10
> >
> > 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 O O | +---+
> > | X | | O O O O O | | 2 |
> > | | | O | +---+
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | X X |
> > | | | X X X |
> > | O | | X X X X O |
> > | O | | X X X X O |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 82 O: 107 X-O: 0-0
> > Cube: 2, O own cube
> > X to play 51
> > I was rather surprised at how much difference there is among the
> > possible plays here. 14/9 3/2 lets O hit with any 2 as well as
> > 53 and 11, for a total of 14 shots. 14/8 lets O hit with any 2
> > as well as 61, 43, and 11, for a total of 16 shots. 14/13 14/9
> > lets O hit with any ace as well as 62, 53, 66 and 33, for a total
> > of 17 shots. So picking the play that leaves the fewest shots
> > will lead you to the top play of the rollout below. But I think
> > it's also true that O is particularly happy to hit from her 24pt
> > since it lets her escape with tempo.
> >
> > 1. Rollout¹ 14/9 3/2 eq:+0.309
> > Player: 68.07% (G:10.09% B:0.35%)
> > Opponent: 31.93% (G:6.03% B:0.12%)
> > Confidence: ±0.005 (+0.304..+0.314) - [100.0%]
> >
> > 2. Rollout¹ 14/9 6/5 eq:+0.243 (-0.066)
> > Player: 65.50% (G:9.03% B:0.32%)
> > Opponent: 34.50% (G:6.21% B:0.13%)
> > Confidence: ±0.005 (+0.238..+0.248) - [0.0%]
> >
> > 3. Rollout¹ 14/8 eq:+0.224 (-0.084)
> > Player: 65.21% (G:9.84% B:0.36%)
> > Opponent: 34.79% (G:6.37% B:0.12%)
> > Confidence: ±0.005 (+0.219..+0.229) - [0.0%]
> >
> > 4. Rollout¹ 14/13 14/9 eq:+0.154 (-0.155)
> > Player: 62.75% (G:8.72% B:0.29%)
> > Opponent: 37.25% (G:6.96% B:0.14%)
> > Confidence: ±0.004 (+0.149..+0.158) - [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
> While this and these situations are generally easily solved when there's a difference in the amount of shots left, it should be recognized here that by making the correct play, 3/2, and not 14/13, we make the opponent's immediate aces pretty disgusting.
>
> Stick

Good point, and it's an excellent example of a key difference between intermediates and experts.
Intermediates typically focus only on minimizing the opponent's jokers but often ignore the opponent's anti-jokers
whereas stronger players pay attention to all luck events: opponent's jokers, opponent's anti-jokers, our own jokers, our own
anti-jokers. (And rolls with luck outcomes in between, of course.)

Paul

On 8/31/2022 4:04 AM, peps...@gmail.com wrote:
> On Tuesday, August 30, 2022 at 7:56:57 PM UTC+1, Stick Rice wrote:
>> While this and these situations are generally easily solved when there's a difference in the amount of shots left, it should be recognized here that by making the correct play, 3/2, and not 14/13, we make the opponent's immediate aces pretty disgusting.
>>
>> Stick
>
> Good point, and it's an excellent example of a key difference between intermediates and experts.
> Intermediates typically focus only on minimizing the opponent's jokers but often ignore the opponent's anti-jokers
> whereas stronger players pay attention to all luck events: opponent's jokers, opponent's anti-jokers, our own jokers, our own
> anti-jokers. (And rolls with luck outcomes in between, of course.)

Stick's observation about aces is a nice one that I had overlooked.
At the same time, I'm not sure how important it is in this position.
In the variant below, reasoning about aces might lead you to reject
15/14 15/10 in favor of 15/9. Not that 15/9 would be a big blunder,
but it suggests to me that other considerations dominate.

The variant below also illustrates why I was surprised by how much
equity difference there was between the plays in the original position,
In this variant, 15/10 3/2 gives O 15 hitting rolls instead of 14, and
while that demotes it to third place, it's not that far behind in
equity.

I think that maybe in the original position, part of the story is that
14/13 turns O's twelves from good rolls into super-jokers.

XGID=-bBD-DC------b-B---b-bbbc-:1:-1:1:51:0:0:0:0:10

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-+
| O X | | O O O O O | +---+
| O X | | O O O O O | | 2 |
| | | O | +---+
| | | |
| | | |
| |BAR| |
| | | |
| | | X X |
| | | X X X |
| | | 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: 84 O: 105 X-O: 0-0
Cube: 2, O own cube
X to play 51

1. Rollout¹ 15/14 15/10 eq:+0.286
Player: 67.73% (G:9.22% B:0.31%)
Opponent: 32.27% (G:6.05% B:0.12%)
Confidence: ±0.004 (+0.282..+0.290) - [100.0%]

2. Rollout¹ 15/9 eq:+0.273 (-0.013)
Player: 66.42% (G:10.36% B:0.34%)
Opponent: 33.58% (G:6.05% B:0.14%)
Confidence: ±0.004 (+0.269..+0.278) - [0.0%]

3. Rollout¹ 15/10 3/2 eq:+0.259 (-0.028)
Player: 66.07% (G:10.86% B:0.45%)
Opponent: 33.93% (G:6.63% B:0.12%)
Confidence: ±0.004 (+0.255..+0.263) - [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

On Wednesday, August 31, 2022 at 7:55:56 AM UTC-4, Tim Chow wrote:
> On 8/31/2022 4:04 AM, peps...@gmail.com wrote:
> > On Tuesday, August 30, 2022 at 7:56:57 PM UTC+1, Stick Rice wrote:
> >> While this and these situations are generally easily solved when there's a difference in the amount of shots left, it should be recognized here that by making the correct play, 3/2, and not 14/13, we make the opponent's immediate aces pretty disgusting.
> >>
> >> Stick
> >
> > Good point, and it's an excellent example of a key difference between intermediates and experts.
> > Intermediates typically focus only on minimizing the opponent's jokers but often ignore the opponent's anti-jokers
> > whereas stronger players pay attention to all luck events: opponent's jokers, opponent's anti-jokers, our own jokers, our own
> > anti-jokers. (And rolls with luck outcomes in between, of course.)
> Stick's observation about aces is a nice one that I had overlooked.
> At the same time, I'm not sure how important it is in this position.
> In the variant below, reasoning about aces might lead you to reject
> 15/14 15/10 in favor of 15/9. Not that 15/9 would be a big blunder,
> but it suggests to me that other considerations dominate.
>
> The variant below also illustrates why I was surprised by how much
> equity difference there was between the plays in the original position,
> In this variant, 15/10 3/2 gives O 15 hitting rolls instead of 14, and
> while that demotes it to third place, it's not that far behind in
> equity.
>
> I think that maybe in the original position, part of the story is that
> 14/13 turns O's twelves from good rolls into super-jokers.
>
> XGID=-bBD-DC------b-B---b-bbbc-:1:-1:1:51:0:0:0:0:10
> 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-+
> | O X | | O O O O O | +---+
> | O X | | O O O O O | | 2 |
> | | | O | +---+
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X X |
> | | | X X X |
> | | | 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: 84 O: 105 X-O: 0-0
> Cube: 2, O own cube
> X to play 51
> 1. Rollout¹ 15/14 15/10 eq:+0.286
> Player: 67.73% (G:9.22% B:0.31%)
> Opponent: 32.27% (G:6.05% B:0.12%)
> Confidence: ±0.004 (+0.282..+0.290) - [100.0%]
>
> 2. Rollout¹ 15/9 eq:+0.273 (-0.013)
> Player: 66.42% (G:10.36% B:0.34%)
> Opponent: 33.58% (G:6.05% B:0.14%)
> Confidence: ±0.004 (+0.269..+0.278) - [0.0%]
>
> 3. Rollout¹ 15/10 3/2 eq:+0.259 (-0.028)
> Player: 66.07% (G:10.86% B:0.45%)
> Opponent: 33.93% (G:6.63% B:0.12%)
> Confidence: ±0.004 (+0.255..+0.263) - [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

The short version with the original position is stick it into XG and look at the dice distribution.

Stick