XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51

---
Tim Chow

On Friday, November 4, 2022 at 1:47:44 PM UTC, Tim Chow wrote:
> XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X X X O | | O O O O O |
> | X X O | | O O O O |
> | | | O O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X |
> | | | X |
> | X X | | X O X |
> | X X | | X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 132 O: 101 X-O: 0-0
> Cube: 1
> X to play 51
>
> ---
> Tim Chow

This one _looks_ very easy. But note the emphasis on "looks".
With O's board being very strong, any indirect shot giving 5.5% hits
would have to be very well motivated to be correct.
There is only one legal play here which is safe in the sense that
that none of O's possible next-rolls enable a legal blot hit.
I see absolutely no reason not to make this safe play, particularly
since it doesn't seem to introduce any weaknesses whatsoever.

Solution:
1. Find the unique play which is completely safe.
2. Make that play.

Note on Solution:
If it happens to be the case that the number of completely safe plays
is different to 1 (and, after all, I could have made a mistake),
then simply mark my solution as wrong. (And, of course, I'm also
wrong if we should play unsafely.)

Paul

On Friday, November 4, 2022 at 11:09:01 AM UTC-4, peps...@gmail.com wrote:
> On Friday, November 4, 2022 at 1:47:44 PM UTC, Tim Chow wrote:
> > XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
> >
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | X X X O | | O O O O O |
> > | X X O | | O O O O |
> > | | | O O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | X |
> > | | | X |
> > | X X | | X O X |
> > | X X | | X O X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 132 O: 101 X-O: 0-0
> > Cube: 1
> > X to play 51
> >
> > ---
> > Tim Chow
> This one _looks_ very easy. But note the emphasis on "looks".
> With O's board being very strong, any indirect shot giving 5.5% hits
> would have to be very well motivated to be correct.
> There is only one legal play here which is safe in the sense that
> that none of O's possible next-rolls enable a legal blot hit.
> I see absolutely no reason not to make this safe play, particularly
> since it doesn't seem to introduce any weaknesses whatsoever.
>
> Solution:
> 1. Find the unique play which is completely safe.
> 2. Make that play.
>
> Note on Solution:
> If it happens to be the case that the number of completely safe plays
> is different to 1 (and, after all, I could have made a mistake),
> then simply mark my solution as wrong. (And, of course, I'm also
> wrong if we should play unsafely.)
>
> Paul

The weakness this play introduces is you have to play the rest of the game out. How is the rest of the game going to pan out? Your opponent is going to have to run off his anchor and he's going to have to do it very soon. When he does so he'll still have a killer board and what will you have? A mess you just created by dumping a checker so low. (and a slightly harder time with containment in the outfield since you stacked your checkers up so inflexibly)

Stick

On Friday, November 4, 2022 at 7:28:52 PM UTC, Stick Rice wrote:
> On Friday, November 4, 2022 at 11:09:01 AM UTC-4, peps...@gmail.com wrote:
> > On Friday, November 4, 2022 at 1:47:44 PM UTC, Tim Chow wrote:
> > > XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
> > >
> > > Score is X:0 O:0. Unlimited Game
> > > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > > | X X X O | | O O O O O |
> > > | X X O | | O O O O |
> > > | | | O O |
> > > | | | |
> > > | | | |
> > > | |BAR| |
> > > | | | |
> > > | | | X |
> > > | | | X |
> > > | X X | | X O X |
> > > | X X | | X O X |
> > > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > > Pip count X: 132 O: 101 X-O: 0-0
> > > Cube: 1
> > > X to play 51
> > >
> > > ---
> > > Tim Chow
> > This one _looks_ very easy. But note the emphasis on "looks".
> > With O's board being very strong, any indirect shot giving 5.5% hits
> > would have to be very well motivated to be correct.
> > There is only one legal play here which is safe in the sense that
> > that none of O's possible next-rolls enable a legal blot hit.
> > I see absolutely no reason not to make this safe play, particularly
> > since it doesn't seem to introduce any weaknesses whatsoever.
> >
> > Solution:
> > 1. Find the unique play which is completely safe.
> > 2. Make that play.
> >
> > Note on Solution:
> > If it happens to be the case that the number of completely safe plays
> > is different to 1 (and, after all, I could have made a mistake),
> > then simply mark my solution as wrong. (And, of course, I'm also
> > wrong if we should play unsafely.)
> >
> > Paul
> The weakness this play introduces is you have to play the rest of the game out. How is the rest of the game going to pan out? Your opponent is going to have to run off his anchor and he's going to have to do it very soon. When he does so he'll still have a killer board and what will you have? A mess you just created by dumping a checker so low. (and a slightly harder time with containment in the outfield since you stacked your checkers up so inflexibly)

My opponent won't jump out before I make my ace point.
And I'll win through my 3 point board.

"Pump it up until you can feel it.
Pump it up when you don't really need it."

Paul

On 11/4/2022 9:47 AM, Timothy Chow wrote:

XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51

O is way ahead in the race so it seems like X's game plan should be to
hold her runners until she crunches or has to run into a shot. Her
board is strong, so offering a direct shot now seems wrong. I don't
like playing to the ace point so I'll clear the eight point. I think I
want to keep the blot on the 16 to get a triple shot if she runs.

XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 101 X-O: 0-0
Cube: 1
X to play 51

I called this a "holding game," but who's holding whom? X is the one
who is well behind in the pip count, so it's X who wants to get and hit
a shot. So he wants to arrange his checkers for containment purposes,
but he also has to be wary of leaving too many shots because O's board
is rather strong.

The safest play is 16/15 6/1, but it leaves a blot in X's board. Does
O's blot in her own board allow X to play more boldly than that?
According to the rollout below, yes. I tried 13/7, trying for more
diversity in the outfield at the cost of 2 extra immediate shots and
some additional blotting danger in the future; XG says that's too bold.
The equity differences are big, showing how delicate this decision is.

See also the variant, in which O's board is perfect.

1. Rollout¹ 16/15 13/8 eq:-0.288
Player: 40.20% (G:4.50% B:0.17%)
Opponent: 59.80% (G:14.93% B:0.19%)
Confidence: ±0.015 (-0.303..-0.273) - [100.0%]

2. Rollout¹ 16/15 6/1 eq:-0.426 (-0.139)
Player: 38.59% (G:4.37% B:0.13%)
Opponent: 61.41% (G:15.67% B:0.24%)
Confidence: ±0.013 (-0.439..-0.414) - [0.0%]

3. Rollout¹ 13/7 eq:-0.442 (-0.154)
Player: 39.00% (G:4.66% B:0.17%)
Opponent: 61.00% (G:19.40% B:0.30%)
Confidence: ±0.016 (-0.458..-0.426) - [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=---B-bDBB----B-BA-bcbbbb--:0:0:1:51:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X X X O | | O O O O O |
| X X O | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X X | | X O X |
| X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 132 O: 100 X-O: 0-0
Cube: 1
X to play 51

1. Rollout¹ 16/15 13/8 eq:-0.478
Player: 37.41% (G:3.65% B:0.12%)
Opponent: 62.59% (G:16.88% B:0.18%)
Confidence: ±0.014 (-0.492..-0.464) - [68.1%]

2. Rollout¹ 16/15 6/1 eq:-0.483 (-0.005)
Player: 37.20% (G:4.08% B:0.11%)
Opponent: 62.80% (G:16.24% B:0.31%)
Confidence: ±0.013 (-0.496..-0.469) - [31.9%]

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

On Sunday, November 6, 2022 at 12:43:19 PM UTC, Tim Chow wrote:
> XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X X X O | | O O O O O |
> | X X O | | O O O O |
> | | | O O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X |
> | | | X |
> | X X | | X O X |
> | X X | | X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 132 O: 101 X-O: 0-0
> Cube: 1
> X to play 51
> I called this a "holding game," but who's holding whom? X is the one
> who is well behind in the pip count, so it's X who wants to get and hit
> a shot. So he wants to arrange his checkers for containment purposes,
> but he also has to be wary of leaving too many shots because O's board
> is rather strong.
>
> The safest play is 16/15 6/1, but it leaves a blot in X's board. Does
> O's blot in her own board allow X to play more boldly than that?
> According to the rollout below, yes. I tried 13/7, trying for more
> diversity in the outfield at the cost of 2 extra immediate shots and
> some additional blotting danger in the future; XG says that's too bold.
> The equity differences are big, showing how delicate this decision is.
>
> See also the variant, in which O's board is perfect.
>
> 1. Rollout¹ 16/15 13/8 eq:-0.288
> Player: 40.20% (G:4.50% B:0.17%)
> Opponent: 59.80% (G:14.93% B:0.19%)
> Confidence: ±0.015 (-0.303..-0.273) - [100.0%]
>
> 2. Rollout¹ 16/15 6/1 eq:-0.426 (-0.139)
> Player: 38.59% (G:4.37% B:0.13%)
> Opponent: 61.41% (G:15.67% B:0.24%)
> Confidence: ±0.013 (-0.439..-0.414) - [0.0%]
>
> 3. Rollout¹ 13/7 eq:-0.442 (-0.154)
> Player: 39.00% (G:4.66% B:0.17%)
> Opponent: 61.00% (G:19.40% B:0.30%)
> Confidence: ±0.016 (-0.458..-0.426) - [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=---B-bDBB----B-BA-bcbbbb--:0:0:1:51:0:0:0:0:10
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X X X O | | O O O O O |
> | X X O | | O O O O O |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X |
> | | | X |
> | X X | | X O X |
> | X X | | X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 132 O: 100 X-O: 0-0
> Cube: 1
> X to play 51
> 1. Rollout¹ 16/15 13/8 eq:-0.478
> Player: 37.41% (G:3.65% B:0.12%)
> Opponent: 62.59% (G:16.88% B:0.18%)
> Confidence: ±0.014 (-0.492..-0.464) - [68.1%]
>
> 2. Rollout¹ 16/15 6/1 eq:-0.483 (-0.005)
> Player: 37.20% (G:4.08% B:0.11%)
> Opponent: 62.80% (G:16.24% B:0.31%)
> Confidence: ±0.013 (-0.496..-0.469) - [31.9%]
>
> 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

The fact that you can so effortlessly variantize to make my
play optimal (or at least quite possibly optimal) tells me that
Stick's argument is too crude -- it applies just as well to your variantization
where, if we believe the equities, the conclusion of the argument is false.

Paul

On Monday, November 7, 2022 at 4:09:57 PM UTC-5, peps...@gmail.com wrote:
> On Sunday, November 6, 2022 at 12:43:19 PM UTC, Tim Chow wrote:
> > XGID=---B-bDBB----B-BA-bccabb--:0:0:1:51:0:0:0:0:10
> >
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | X X X O | | O O O O O |
> > | X X O | | O O O O |
> > | | | O O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | X |
> > | | | X |
> > | X X | | X O X |
> > | X X | | X O X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 132 O: 101 X-O: 0-0
> > Cube: 1
> > X to play 51
> > I called this a "holding game," but who's holding whom? X is the one
> > who is well behind in the pip count, so it's X who wants to get and hit
> > a shot. So he wants to arrange his checkers for containment purposes,
> > but he also has to be wary of leaving too many shots because O's board
> > is rather strong.
> >
> > The safest play is 16/15 6/1, but it leaves a blot in X's board. Does
> > O's blot in her own board allow X to play more boldly than that?
> > According to the rollout below, yes. I tried 13/7, trying for more
> > diversity in the outfield at the cost of 2 extra immediate shots and
> > some additional blotting danger in the future; XG says that's too bold.
> > The equity differences are big, showing how delicate this decision is.
> >
> > See also the variant, in which O's board is perfect.
> >
> > 1. Rollout¹ 16/15 13/8 eq:-0.288
> > Player: 40.20% (G:4.50% B:0.17%)
> > Opponent: 59.80% (G:14.93% B:0.19%)
> > Confidence: ±0.015 (-0.303..-0.273) - [100.0%]
> >
> > 2. Rollout¹ 16/15 6/1 eq:-0.426 (-0.139)
> > Player: 38.59% (G:4.37% B:0.13%)
> > Opponent: 61.41% (G:15.67% B:0.24%)
> > Confidence: ±0.013 (-0.439..-0.414) - [0.0%]
> >
> > 3. Rollout¹ 13/7 eq:-0.442 (-0.154)
> > Player: 39.00% (G:4.66% B:0.17%)
> > Opponent: 61.00% (G:19.40% B:0.30%)
> > Confidence: ±0.016 (-0.458..-0.426) - [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=---B-bDBB----B-BA-bcbbbb--:0:0:1:51:0:0:0:0:10
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | X X X O | | O O O O O |
> > | X X O | | O O O O O |
> > | | | O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | | |
> > | | | X |
> > | | | X |
> > | X X | | X O X |
> > | X X | | X O X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 132 O: 100 X-O: 0-0
> > Cube: 1
> > X to play 51
> > 1. Rollout¹ 16/15 13/8 eq:-0.478
> > Player: 37.41% (G:3.65% B:0.12%)
> > Opponent: 62.59% (G:16.88% B:0.18%)
> > Confidence: ±0.014 (-0.492..-0.464) - [68.1%]
> >
> > 2. Rollout¹ 16/15 6/1 eq:-0.483 (-0.005)
> > Player: 37.20% (G:4.08% B:0.11%)
> > Opponent: 62.80% (G:16.24% B:0.31%)
> > Confidence: ±0.013 (-0.496..-0.469) - [31.9%]
> >
> > 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
> The fact that you can so effortlessly variantize to make my
> play optimal (or at least quite possibly optimal) tells me that
> Stick's argument is too crude -- it applies just as well to your variantization
> where, if we believe the equities, the conclusion of the argument is false.
>
> Paul

Variants may be effortless to conjure up but that doesn't mean from original to variant it's not a big freakin' change! If by making that change you also only get your play to equal, that should further argue that in general, if an in general can be applied, that the original 'rule' should be followed. Also, my answers are often quippy not going into the full detail of what's meant/how it should be applied/what the exceptions are etc... and what is in my head because who has time for that...

Stick

On 11/7/2022 4:09 PM, peps...@gmail.com wrote:
> The fact that you can so effortlessly variantize to make my
> play optimal (or at least quite possibly optimal) tells me that
> Stick's argument is too crude -- it applies just as well to your variantization
> where, if we believe the equities, the conclusion of the argument is false.

Actually, if you take what Stick wrote at face value, without
reading between the lines, all he did was to point out the
weaknesses of your play. He did not explicitly draw the
conclusion that your play was wrong, let alone explicitly
say that your play was wrong *because* of the features he
mentioned.

---
Tim Chow

On Tuesday, November 8, 2022 at 5:20:48 AM UTC, Tim Chow wrote:
> On 11/7/2022 4:09 PM, peps...@gmail.com wrote:
> > The fact that you can so effortlessly variantize to make my
> > play optimal (or at least quite possibly optimal) tells me that
> > Stick's argument is too crude -- it applies just as well to your variantization
> > where, if we believe the equities, the conclusion of the argument is false.
> Actually, if you take what Stick wrote at face value, without
> reading between the lines, all he did was to point out the
> weaknesses of your play. He did not explicitly draw the
> conclusion that your play was wrong, let alone explicitly
> say that your play was wrong *because* of the features he
> mentioned.

I see your point, but I don't share your interpretation.
If my play was not wrong, then surely it couldn't be described as
"creating a mess".
For example, suppose you roll a horrible 44 that crunches you in what was
a crushing blitzy postion. Then your position is a mess, but no one would
say that you "created the mess" [unless they were faulting you for overlooking
the 44].
So, I think Stick was fairly clear in saying my play was wrong, even if he
wasn't as clear as possible.
Certainly, if my play was correct in the initial position, I would consider that I
was vindicated, and that he had made a mistake.

Stick's beginning also makes clear that Stick is asserting a mistake on my part:
"The weakness this play introduces is you have to play the rest of the game out. How is the rest of the game going to pan out?"
If a player causes a weakness owing to not planning ahead, then clearly the play is criticized.

If someone says "The weakness of your play is that it loses pips in the race" then you'd be right --
the person asserting the weakness might like the play anyway because of its compensating strengths.
But that's not the case here.

It isn't exactly "reading between the lines" to conclude that Stick is critical of my play.
If somebody says to me that "You look like you've eaten way too many hamburgers" then
I think it's fair to characterize them as saying that I'm overweight, even though it's technically
possible to argue for a different interpretation.

Paul