XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10

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 O O O O O |
| | | O O O O O |
| | | O O O |
| | | O |
| | X | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 54 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

On 9/11/2022 9:31 AM, Timothy Chow wrote:
> XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10
>
> 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  O  O  O  O  O |
>  |                  |   | O  O  O  O  O    |
>  |                  |   |    O     O  O    |
>  |                  |   |          O       |
>  |                  | X |                  |
>  |                  |BAR|                  |
>  |                  |   |                  |
>  |                  |   |                  |
>  |                  |   |                  | +---+
>  |                  |   |                  | | 2 |
>  |                  |   |             X    | +---+
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 27  O: 54 X-O: 0-0
> Cube: 2, X own cube
> X on roll, cube action

Closed out on the bar with 12 checkers off is 84% GWC. And you have 13
off, so it's clearly D/P. She still has 15 checkers on the board, so
there is the remote chance of entering with a hit and scrambling around
the board to win a gammon. But hitting gives her a great chance to send
a second checker to the roof and hen X's winning chances go by the
wayside. So I don't think it's TG even though X will still have a cash
almost all the time next roll.

So, I"d just cash this now. 1x followed by 2x loses the game (about 10%)
and that seems more likely than the rare gammon wins for X.

R/P.

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

On 9/12/2022 11:14 AM, ah....Clem wrote:
> On 9/11/2022 9:31 AM, Timothy Chow wrote:
>> XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10
>>
>> 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  O  O  O  O  O |
>>   |                  |   | O  O  O  O  O    |
>>   |                  |   |    O     O  O    |
>>   |                  |   |          O       |
>>   |                  | X |                  |
>>   |                  |BAR|                  |
>>   |                  |   |                  |
>>   |                  |   |                  |
>>   |                  |   |                  | +---+
>>   |                  |   |                  | | 2 |
>>   |                  |   |             X    | +---+
>>   +12-11-10--9--8--7-------6--5--4--3--2--1-+
>> Pip count  X: 27  O: 54 X-O: 0-0
>> Cube: 2, X own cube
>> X on roll, cube action
>
> Closed out on the bar with 12 checkers off is 84% GWC. And you have 13
> off, so it's clearly D/P. She still has 15 checkers on the board, so
> there is the remote chance of entering with a hit and scrambling around
> the board to win a gammon. But hitting gives her a great chance to send
> a second checker to the roof and hen X's winning chances go by the
> wayside. So I don't think it's TG even though X will still have a cash
> almost all the time next roll.
>
> So, I"d just cash this now. 1x followed by 2x loses the game (about 10%)
> and that seems more likely than the rare gammon wins for X.
>
> R/P.

Thinking about this some more, the "closed out on the bar with N
checkers off" reference positions are for all the other checkers to be
on the ace point. With a blot to shoot at, it's probably less than with
two checkers on the ace. Since O wins by picking up another checker, we
might want to add those 10% wins to her ~15% wins to arrive at 25%. And
since exchanges of hits can happen for multiple rolls, add more than 10%
to push this into take territory.

I'd still ship it. Some will pass.

R/T.

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

On Monday, September 12, 2022 at 6:50:12 PM UTC+1, ah....Clem wrote:
> On 9/12/2022 11:14 AM, ah....Clem wrote:
> > On 9/11/2022 9:31 AM, Timothy Chow wrote:
> >> XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10
> >>
> >> 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 O O O O O |
> >> | | | O O O O O |
> >> | | | O O O |
> >> | | | O |
> >> | | X | |
> >> | |BAR| |
> >> | | | |
> >> | | | |
> >> | | | | +---+
> >> | | | | | 2 |
> >> | | | X | +---+
> >> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> >> Pip count X: 27 O: 54 X-O: 0-0
> >> Cube: 2, X own cube
> >> X on roll, cube action
> >
> > Closed out on the bar with 12 checkers off is 84% GWC. And you have 13
> > off, so it's clearly D/P. She still has 15 checkers on the board, so
> > there is the remote chance of entering with a hit and scrambling around
> > the board to win a gammon. But hitting gives her a great chance to send
> > a second checker to the roof and hen X's winning chances go by the
> > wayside. So I don't think it's TG even though X will still have a cash
> > almost all the time next roll.
> >
> > So, I"d just cash this now. 1x followed by 2x loses the game (about 10%)
> > and that seems more likely than the rare gammon wins for X.
> >
> > R/P.
> Thinking about this some more, the "closed out on the bar with N
> checkers off" reference positions are for all the other checkers to be
> on the ace point. With a blot to shoot at, it's probably less than with
> two checkers on the ace. Since O wins by picking up another checker, we
> might want to add those 10% wins to her ~15% wins to arrive at 25%. And
> since exchanges of hits can happen for multiple rolls, add more than 10%
> to push this into take territory.
>
> I'd still ship it. Some will pass.

Yes, I know for a fact that some will pass because I will pass this.
Clearly, it's not TG because there are significant losses by the opponent putting
2 on the bar. I agree mainly with the way you're thinking about this, but I don't see
a take here. Sorry. RD/P.

Paul

XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10

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 O O O O O |
| | | O O O O O |
| | | O O O |
| | | O |
| | X | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 54 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

This is a corner of backgammon which, despite being "standard" in
some sense, I have never really studied before. I knew the standard
reference position when I have on checker closed out (with the
opponent's spares on 4/5/6) and 3 checkers on my ace point, then it's
a borderline RD/NRD. When I have 13 checkers off, however, a lot
depends on the chances that my opponent can pick up the second checker.
If my checker on the bar hits when coming in, it's a double-edged sword.
On the one hand, I gain valuable pips in the race, but on the other
hand, I risk getting the second checker sent back. How do these two
factors trade off against each other?

According to the rollout below (with somewhat stronger settings than
the default), the position above is RD/T. But see the two other
positions that I was faced with on subsequent rolls.

Analyzed in Rollout
No redouble
Player Winning Chances: 75.67% (G:2.20% B:0.30%)
Opponent Winning Chances: 24.33% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 75.60% (G:2.06% B:0.31%)
Opponent Winning Chances: 24.40% (G:0.00% B:0.00%)

Cubeful Equities:
No redouble: +0.828 (-0.054)
Redouble/Take: +0.882
Redouble/Pass: +1.000 (+0.118)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.010 (+0.819..+0.838)
Confidence Double: ± 0.017 (+0.865..+0.900)

eXtreme Gammon Version: 2.19.207.pre-release

---------
Next turn
---------

XGID=--A----------------bbcccaA:1:1:1:00:0:0:0:0:10

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 O O O O O | O
| | | O O O O O |
| | | O O O |
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 50 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 74.87% (G:0.00% B:0.00%)
Opponent Winning Chances: 25.13% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 74.79% (G:0.00% B:0.00%)
Opponent Winning Chances: 25.21% (G:0.00% B:0.00%)

Cubeful Equities:
No redouble: +0.801
Redouble/Take: +0.794 (-0.007)
Redouble/Pass: +1.000 (+0.199)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 3.2%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.010 (+0.790..+0.811)
Confidence Double: ± 0.016 (+0.778..+0.810)

eXtreme Gammon Version: 2.19.207.pre-release

---------
Next turn
---------

XGID=--A----------------abccbaA:1:1:1:00:0:0:0:0:10

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 O O O O O | O
| | | O O O O | O
| | | O O | O
| | | |
| | X | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 42 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 81.28% (G:0.00% B:0.00%)
Opponent Winning Chances: 18.72% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 80.99% (G:0.00% B:0.00%)
Opponent Winning Chances: 19.01% (G:0.00% B:0.00%)

Cubeful Equities:
No redouble: +0.898 (-0.102)
Redouble/Take: +1.108 (+0.108)
Redouble/Pass: +1.000

Best Cube action: Redouble / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.007 (+0.891..+0.904)
Confidence Double: ± 0.015 (+1.093..+1.123)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

On 9/13/2022 8:50 AM, Timothy Chow wrote:
> XGID=--A----------------bcbdcaA:1:1:1:00:0:0:0:0:10
>
> 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  O  O  O  O  O |
>  |                  |   | O  O  O  O  O    |
>  |                  |   |    O     O  O    |
>  |                  |   |          O       |
>  |                  | X |                  |
>  |                  |BAR|                  |
>  |                  |   |                  |
>  |                  |   |                  |
>  |                  |   |                  | +---+
>  |                  |   |                  | | 2 |
>  |                  |   |             X    | +---+
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 27  O: 54 X-O: 0-0
> Cube: 2, X own cube
> X on roll, cube action

>
> According to the rollout below (with somewhat stronger settings than
> the default), the position above is RD/T.  But see the two other
> positions that I was faced with on subsequent rolls.

The two big questions I had about this position were whether gammons
mattered and how big a factor was the possibility of picking up another
checker. Your first variant seems to indicate that the 2% gammmon
chances tips it to being a cube (O with one checker off barely changes
the GWC, but the gammons go away.)

In the variant below, I've given X a second checker on the deuce point
so that picking up a second checker is much rarer. This pushes it
(barely) into TG territory with the take being a triple whopper with
cheese. The chance for O to pick up a second checker appears to make a
huge difference.

XGID=--B----------------bcbdcaA:1:1:1:00:0:0:0:0:10

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 O O O O O |
| | | O O O O O |
| | | O O O |
| | | O |
| | X | |
| |BAR| |
| | | |
| | | |
| | | | +---+
| | | X | | 2 |
| | | X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 29 O: 54 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble
Player Winning Chances: 84.63% (G:3.31% B:0.22%)
Opponent Winning Chances: 15.37% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 84.73% (G:2.96% B:0.31%)
Opponent Winning Chances: 15.27% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.728, Double=+1.454

Cubeful Equities:
No redouble: +1.014
Redouble/Take: +1.361 (+0.347)
Redouble/Pass: +1.000 (-0.014)

Best Cube action: Too good to redouble / Pass
Percentage of wrong take needed to make the double decision right: 3.9%

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.001 (+1.013..+1.015)
Confidence Double: ± 0.010 (+1.350..+1.371)

Double Decision confidence: 100.0%
Take Decision confidence: 100.0%

Duration: 8.4 seconds

eXtreme Gammon Version: 2.10

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