On 4/13/2022 8:51 AM, I wrote:

Interestingly, XG 3-ply doubles here.

Over the years, I have found that there is just one important exception
to Stick's rule.  Even in a position where you win a lot of gammons, it
can be a double if the following two conditions are satisfied: (1) your opponent wins very few gammons (~5% or less) and (2) the position is
close to the take/pass borderline.  The variant below is a case in
point.  Of course, to make use of this exception OTB, you have to
develop a sense for when such a position is close to the take/pass borderline.

Oh, I forgot to say one thing. I was the 7-away player here, playing
against XG 3-ply. When it doubled, I assumed that it was probably close
to the take/pass borderline because otherwise XG 3-ply wouldn't double
in such a gammonish position. Not having a good sense myself for
whether it was a take, I passed, figuring that it would be a small error
at worst. But XG overturned its own verdict upon rollout.

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XGID=-baBBCB-A--A-B--bd-cbB-a--:0:0:1:00:4:0:0:7:10

X:Player 2 O:Player 1
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O |
| X O O | | O O X |
| O | | O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X X X O |
| X X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 128 O: 151 X-O: 4-0/7
Cube: 1
X on roll, cube action

Stick's rule for 3-away/many-away cube actions is, the 3-away player
should not double when gammons are still possible, because you'll
usually be either too good or not good enough. Doubling reduces the
value of your own gammons and gives your opponent an opportunity to
win 8 points by winning a redoubled gammon.

While others surely were aware of this rule, implicitly if not
explicitly, I myself learned it from Stick, and I don't recall seeing
other backgammon authors stating any rule of this sort before Stick did.

In general I have found this to be an excellent rule. The position
here is a case in point. Against a human you might consider doubling
because you may get a pass. But according to the rollout, it's an
easy take and a big ND. Interestingly, XG 3-ply doubles here.

Over the years, I have found that there is just one important exception
to Stick's rule. Even in a position where you win a lot of gammons, it
can be a double if the following two conditions are satisfied: (1) your opponent wins very few gammons (~5% or less) and (2) the position is
close to the take/pass borderline. The variant below is a case in
point. Of course, to make use of this exception OTB, you have to
develop a sense for when such a position is close to the take/pass
borderline.

Analyzed in Rollout
No double
Player Winning Chances: 74.31% (G:30.57% B:5.31%)
Opponent Winning Chances: 25.69% (G:5.11% B:0.23%)
Double/Take
Player Winning Chances: 73.78% (G:31.85% B:11.05%)
Opponent Winning Chances: 26.22% (G:5.15% B:0.28%)

Cubeful Equities:
No double: +0.791
Double/Take: +0.704 (-0.087)
Double/Pass: +1.000 (+0.209)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 22.8%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.013 (+0.778..+0.804)
Confidence Double: ± 0.022 (+0.682..+0.726)

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

-------
Variant
-------

XGID=-baBBCBB-----B--bd-cbB-a--:0:0:1:00:4:0:0:7:10

X:Player 2 O:Player 1
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O |
| X O O | | O O X |
| O | | O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X O |
| X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 151 X-O: 4-0/7
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 79.33% (G:31.21% B:4.48%)
Opponent Winning Chances: 20.67% (G:3.43% B:0.16%)
Double/Take
Player Winning Chances: 78.03% (G:33.42% B:12.19%)
Opponent Winning Chances: 21.97% (G:3.53% B:0.33%)

Cubeful Equities:
No double: +0.935 (-0.065)
Double/Take: +1.055 (+0.055)
Double/Pass: +1.000

Best Cube action: Double / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.012 (+0.924..+0.947)
Confidence Double: ± 0.022 (+1.033..+1.076)

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

---
Tim Chow

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Wednesday, April 13, 2022 at 8:51:40 AM UTC-4, Tim Chow wrote:

XGID=-baBBCB-A--A-B--bd-cbB-a--:0:0:1:00:4:0:0:7:10

X:Player 2 O:Player 1
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O |
| X O O | | O O X |
| O | | O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X X X O |
| X X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 128 O: 151 X-O: 4-0/7
Cube: 1
X on roll, cube action
Stick's rule for 3-away/many-away cube actions is, the 3-away player
should not double when gammons are still possible, because you'll
usually be either too good or not good enough. Doubling reduces the
value of your own gammons and gives your opponent an opportunity to
win 8 points by winning a redoubled gammon.

While others surely were aware of this rule, implicitly if not
explicitly, I myself learned it from Stick, and I don't recall seeing
other backgammon authors stating any rule of this sort before Stick did.

In general I have found this to be an excellent rule. The position
here is a case in point. Against a human you might consider doubling
because you may get a pass. But according to the rollout, it's an
easy take and a big ND. Interestingly, XG 3-ply doubles here.

Over the years, I have found that there is just one important exception
to Stick's rule. Even in a position where you win a lot of gammons, it
can be a double if the following two conditions are satisfied: (1) your opponent wins very few gammons (~5% or less) and (2) the position is
close to the take/pass borderline. The variant below is a case in
point. Of course, to make use of this exception OTB, you have to
develop a sense for when such a position is close to the take/pass borderline.

Analyzed in Rollout
No double
Player Winning Chances: 74.31% (G:30.57% B:5.31%)
Opponent Winning Chances: 25.69% (G:5.11% B:0.23%)
Double/Take
Player Winning Chances: 73.78% (G:31.85% B:11.05%)
Opponent Winning Chances: 26.22% (G:5.15% B:0.28%)

Cubeful Equities:
No double: +0.791
Double/Take: +0.704 (-0.087)
Double/Pass: +1.000 (+0.209)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 22.8%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.013 (+0.778..+0.804)
Confidence Double: ± 0.022 (+0.682..+0.726)

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

-------
Variant
-------

XGID=-baBBCBB-----B--bd-cbB-a--:0:0:1:00:4:0:0:7:10
X:Player 2 O:Player 1
Score is X:4 O:0 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X O |
| X O O | | O O X |
| O | | O |
| O | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X O |
| X | | X X X X O O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 123 O: 151 X-O: 4-0/7
Cube: 1
X on roll, cube action
Analyzed in Rollout
No double
Player Winning Chances: 79.33% (G:31.21% B:4.48%)
Opponent Winning Chances: 20.67% (G:3.43% B:0.16%)
Double/Take
Player Winning Chances: 78.03% (G:33.42% B:12.19%)
Opponent Winning Chances: 21.97% (G:3.53% B:0.33%)

Cubeful Equities:
No double: +0.935 (-0.065)
Double/Take: +1.055 (+0.055)
Double/Pass: +1.000

Best Cube action: Double / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.012 (+0.924..+0.947)
Confidence Double: ± 0.022 (+1.033..+1.076)

eXtreme Gammon Version: 2.19.207.pre-release, MET: Kazaross XG2

---
Tim Chow

To be specific, the rule is meant for 3a 7a or greater. If you apply it to 3a 6a it will get clunky. It can be in the back of your mind at 3a 6a but it isn't nearly as on point as 3a 7a or greater. It should not be used for 3a 5a or 3a 4a.

Stick

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)