XGID=-C-CbBB-B---aB---b-bcabb-A:0:0:1:44:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O O O O |
| X O | | O O O O |
| | | O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X O X X |
| O X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 112 X-O: 0-0
Cube: 1
X to play 44

---
Tim Chow

On Saturday, November 4, 2023 at 5:07:56 PM UTC, Timothy Chow wrote:
> XGID=-C-CbBB-B---aB---b-bcabb-A:0:0:1:44:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O | | O O O O O |
> | X O | | O O O O |
> | | | O |
> | | | |
> | | X | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X |
> | X | | X X O X X |
> | O X | | X X O X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 101 O: 112 X-O: 0-0
> Cube: 1
> X to play 44
>
> ---
> Tim Chow
I would play the mundane 13/9 13/5 but I suspect I'm missing something here ....
--
BD

On Sunday, November 5, 2023 at 7:40:54 AM UTC-5, BlueDice wrote:
> On Saturday, November 4, 2023 at 5:07:56 PM UTC, Timothy Chow wrote:
> > XGID=-C-CbBB-B---aB---b-bcabb-A:0:0:1:44:0:0:0:0:10
> >
> > Score is X:0 O:0. Unlimited Game
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | X O | | O O O O O |
> > | X O | | O O O O |
> > | | | O |
> > | | | |
> > | | X | |
> > | |BAR| |
> > | | | |
> > | | | |
> > | | | X X |
> > | X | | X X O X X |
> > | O X | | X X O X X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 101 O: 112 X-O: 0-0
> > Cube: 1
> > X to play 44
> >
> > ---
> > Tim Chow
> I would play the mundane 13/9 13/5 but I suspect I'm missing something here ....
> --
> BD

Being that it's a problem it's a lot easier to find the candidate plays and not let one slip by the catcher. A game I played just this past week was "always make the second best play". It's a variant where your single goal is to make the second best play. It forces you to weigh candidates you normally wouldn't because often times the best play is the best play and it's not close. While I rarely do this OtB, every now and again a confusing position comes up where I do force myself to pick what I would play if I didn't make Play A. This isn't one of the positions where I'd do such a thing OtB but as a problem if you 'think you're missing something' then you should more closely examine the candidate plays.

So, did you consider 13/1 originally?

Stick

XGID=-C-CbBB-B---aB---b-bcabb-A:0:0:1:44:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O O O O |
| X O | | O O O O |
| | | O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X O X X |
| O X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 101 O: 112 X-O: 0-0
Cube: 1
X to play 44

Killing a checker to the 1pt always goes against the grain, but this
nice roll has turned the game around, and we have the opportunity to
press our advantage by hitting a second blot. The alternative of
13/9 13/5 releases the pressure on O's outfield blot.

1. Rollout¹ Bar/21* 13/1 eq:+0.471
Player: 60.33% (G:24.36% B:0.31%)
Opponent: 39.67% (G:9.91% B:0.35%)
Confidence: ±0.008 (+0.463..+0.479) - [100.0%]

2. Rollout¹ Bar/21* 13/9 13/5 eq:+0.407 (-0.064)
Player: 58.42% (G:25.23% B:0.47%)
Opponent: 41.58% (G:10.01% B:0.40%)
Confidence: ±0.007 (+0.400..+0.414) - [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

---
Tim Chow

XGID=aAABBBBA-A-----Abb-bdB-bb-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O O |
| O O | | O O X O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | | +---+
| | | X X X X | | 2 |
| X X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 112 O: 97 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

On Tuesday, November 7, 2023 at 9:35:50 AM UTC-5, Timothy Chow wrote:
> XGID=-C-CbBB-B---aB---b-bcabb-A:0:0:1:44:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O | | O O O O O |
> | X O | | O O O O |
> | | | O |
> | | | |
> | | X | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X |
> | X | | X X O X X |
> | O X | | X X O X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 101 O: 112 X-O: 0-0
> Cube: 1
> X to play 44
> Killing a checker to the 1pt always goes against the grain, but this
> nice roll has turned the game around, and we have the opportunity to
> press our advantage by hitting a second blot. The alternative of
> 13/9 13/5 releases the pressure on O's outfield blot.
>
> 1. Rollout¹ Bar/21* 13/1 eq:+0.471
> Player: 60.33% (G:24.36% B:0.31%)
> Opponent: 39.67% (G:9.91% B:0.35%)
> Confidence: ±0.008 (+0.463..+0.479) - [100.0%]
>
> 2. Rollout¹ Bar/21* 13/9 13/5 eq:+0.407 (-0.064)
> Player: 58.42% (G:25.23% B:0.47%)
> Opponent: 41.58% (G:10.01% B:0.40%)
> Confidence: ±0.007 (+0.400..+0.414) - [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
>
> ---
> Tim Chow

It's not really about the pressure on the opp's outfield blot, it's about the duplication of ones and the amount of shots we leave immediately.

Stick

On Tuesday, November 7, 2023 at 9:36:54 AM UTC-5, Timothy Chow wrote:
> XGID=aAABBBBA-A-----Abb-bdB-bb-:1:1:1:00:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X O O |
> | O O | | O O X O O |
> | | | O |
> | | | O |
> | | | |
> | |BAR| |
> | | O | |
> | | | |
> | | | | +---+
> | | | X X X X | | 2 |
> | X X | | X X X X X X | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 112 O: 97 X-O: 0-0
> Cube: 2, X own cube
> X on roll, cube action
>
> ---
> Tim Chow

If we roll a natural five like [32 41] and decided to cover our two point and the opponent fans is that position a pass?

Stick

XGID=aAABBBBA-A-----Abb-bdB-bb-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O O |
| O O | | O O X O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | | +---+
| | | X X X X | | 2 |
| X X | | X X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 112 O: 97 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

This is a position where O'Hagan's Law might lead you astray, even with
a centered cube. According to XG, there are 14 rolls which, if followed
by a dance, lose X's market (66 65 61 54 53 52 43 33), and there are a
small number of other market-losing sequences as well (e.g., if X rolls
21, played 9/7 2/1, and O rolls 52 from the bar, exposing another blot).
Multiplying 14 by 25/36 gives about 9.7, so we're slightly over
O'Hagan's threshold of 25% for a centered cube. The remaining part of
O'Hagan's law asks if X is doing reasonably well if he doesn't lose his
market. Most of the time, the answer is yes; as long as O dances, X is
doing well, and even if O enters without hitting (because X has played
2/1), it's not so bad for X. However, if O enters with a hit, then that
is bad news for X. It's not easy to judge all these things OTB, but the
rollout indicates a sizable ND, even with a centered cube.

Forgetting about O'Hagan's Law for a moment, and just looking at the
position, it's important that X may still have some trouble escaping
his back checkers. Rolls such as 55 and 44, for example, may look
pretty good at first glance, but come with a risk of crunching X's
board if he can't immediately escape a checker. Even O's checkers on
her 1pt and 2pt aren't useless because she might hit a checker on her
next turn. These sorts of considerations are what allow O to take even
after some of the cover/dance sequences, according to XG.

Analyzed in Rollout
No redouble
Player Winning Chances: 66.01% (G:13.06% B:0.25%)
Opponent Winning Chances: 33.99% (G:9.65% B:0.25%)
Redouble/Take
Player Winning Chances: 65.97% (G:12.82% B:0.26%)
Opponent Winning Chances: 34.03% (G:9.88% B:0.27%)

Cubeful Equities:
No redouble: +0.630
Redouble/Take: +0.474 (-0.156)
Redouble/Pass: +1.000 (+0.370)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 29.7%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.009 (+0.621..+0.639)
Confidence Double: ± 0.015 (+0.459..+0.489)

eXtreme Gammon Version: 2.19.211.pre-release

-------------
Centered cube
-------------

XGID=aAABBBBA-A-----Abb-bdB-bb-:0:0:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O O |
| O O | | O O X O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | |
| | | 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: 112 O: 97 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 65.99% (G:12.79% B:0.23%)
Opponent Winning Chances: 34.01% (G:9.52% B:0.25%)
Double/Take
Player Winning Chances: 65.97% (G:12.82% B:0.26%)
Opponent Winning Chances: 34.03% (G:9.88% B:0.27%)

Cubeful Equities:
No double: +0.567
Double/Take: +0.474 (-0.093)
Double/Pass: +1.000 (+0.433)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 17.8%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.010 (+0.557..+0.578)
Confidence Double: ± 0.015 (+0.459..+0.489)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

XGID=--ACBCBbB----B----ba-bbcc-:0:0:1:43:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O O O O |
| X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X O | | X X X X |
| X O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 88 O: 79 X-O: 0-0
Cube: 1
X to play 43

---
Tim Chow

On 11/7/2023 9:36 AM, Timothy Chow wrote:
> XGID=aAABBBBA-A-----Abb-bdB-bb-:1:1:1:00:0:0:0:0:10
>
> Score is X:0 O:0. Unlimited Game
>  +13-14-15-16-17-18------19-20-21-22-23-24-+
>  |       X  O  O    |   | O  O  X     O  O |
>  |          O  O    |   | O  O  X     O  O |
>  |                  |   |    O             |
>  |                  |   |    O             |
>  |                  |   |                  |
>  |                  |BAR|                  |
>  |                  | O |                  |
>  |                  |   |                  |
>  |                  |   |                  | +---+
>  |                  |   | X  X  X  X       | | 2 |
>  |          X     X |   | X  X  X  X  X  X | +---+
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 112  O: 97 X-O: 0-0
> Cube: 2, X own cube
> X on roll, cube action
>

Any 1, 5, 6, 7, or 8 makes a fifth homeboard point. Seeems like too
many market losers to hold. I don't think it's TG since O has some
counterplay and X has work to do to get his runners around. Plus it
looks like it might be a take.

Ship it for sure and make it O's problem. I'd pass this one due to all
the rolls that make a fifth homeboard point, and even if I can enter and
hit I'm still stuck behind a four or five prime.

R/P

--
Ah....Clem
The future is fun, the future is fair.

XGID=--ACBCBbB----B----ba-bbcc-:0:0:1:43:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O O O O |
| X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X O | | X X X X |
| X O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 88 O: 79 X-O: 0-0
Cube: 1
X to play 43

Who's holding whom? Visually, it might look like O is holding X, but X
is behind in the pip count (if we ignore wastage). The game is roughly
level, and X would be happy to hit a shot. To maximize his chances of
that, he needs to keep his 8pt. The trouble is, keeping his 8pt forces
him to wreck his board somewhat, which means that even if he does hit
a shot, its effectiveness will be diminished.

XG hates 8/5 8/4, and doesn't like the compromise play of 8/4 5/2 much
better. Although 5/2 5/1 or 5/1 4/1 damages X's board, it's still rather
strong, and the weaknesses are not beyond repair. See the variant below,
where the top two plays of the rollout are tied.

1. Rollout¹ 5/2 5/1 eq:+0.199
Player: 56.99% (G:2.45% B:0.07%)
Opponent: 43.01% (G:0.87% B:0.01%)
Confidence: ±0.008 (+0.191..+0.206) - [77.3%]

2. Rollout¹ 5/1 4/1 eq:+0.195 (-0.004)
Player: 56.80% (G:2.25% B:0.06%)
Opponent: 43.20% (G:0.88% B:0.01%)
Confidence: ±0.008 (+0.187..+0.202) - [22.7%]

3. Rollout¹ 6/2 5/2 eq:+0.180 (-0.019)
Player: 56.37% (G:1.82% B:0.04%)
Opponent: 43.63% (G:0.83% B:0.01%)
Confidence: ±0.008 (+0.173..+0.188) - [0.0%]

4. Rollout¹ 8/4 5/2 eq:+0.139 (-0.060)
Player: 55.00% (G:5.00% B:0.13%)
Opponent: 45.00% (G:1.23% B:0.01%)
Confidence: ±0.008 (+0.131..+0.147) - [0.0%]

5. Rollout¹ 8/5 8/4 eq:+0.115 (-0.084)
Player: 54.56% (G:2.07% B:0.05%)
Opponent: 45.44% (G:0.54% B:0.01%)
Confidence: ±0.008 (+0.107..+0.123) - [0.0%]

6. Rollout¹ 8/1 eq:+0.106 (-0.093)
Player: 53.81% (G:6.22% B:0.21%)
Opponent: 46.19% (G:2.27% B:0.04%)
Confidence: ±0.008 (+0.098..+0.114) - [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=--ADBBBbB----B----ba-bbcc-:0:0:1:43:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O | | O O O O O |
| X O | | O O O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X |
| X O | | X X X X |
| X O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 86 O: 79 X-O: 0-0
Cube: 1
X to play 43

1. Rollout¹ 5/2 5/1 eq:+0.173
Player: 55.85% (G:1.57% B:0.04%)
Opponent: 44.15% (G:0.90% B:0.01%)
Confidence: ±0.006 (+0.167..+0.179) - [70.9%]

2. Rollout¹ 8/5 8/4 eq:+0.171 (-0.002)
Player: 56.13% (G:1.95% B:0.05%)
Opponent: 43.87% (G:0.61% B:0.01%)
Confidence: ±0.006 (+0.165..+0.177) - [29.1%]

¹ 2592 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