XGID=-AB-aBC-BBC--a------dcbbb-:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X |
| X X X | | X X X |
| X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 97 O: 77 X-O: 0-0
Cube: 1
X to play 52

---
Tim Chow

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

On 1/5/2023 8:26 AM, Timothy Chow wrote:

XGID=-AB-aBC-BBC--a------dcbbb-:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
 +13-14-15-16-17-18------19-20-21-22-23-24-+
 | O                |   |    O  O  O  O  O |
 |                  |   |    O  O  O  O  O |
 |                  |   |    O  O          |
 |                  |   |    O             |
 |                  |   |                  |
 |                  |BAR|                  |
 |                  |   |                  |
 |                  |   |                  |
 |       X          |   | X                |
 |       X  X  X    |   | X  X        X    |
 |       X  X  X    |   | X  X  O     X  X |
 +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 97  O: 77 X-O: 0-0
Cube: 1
X to play 52

O's board looks too strong to hit loose and leave two blots. 9/4*/2
buries a checker on the deuce and leaves a blot against a strong board,
so I don't like that play.

I'll cover the ace and play 10/8 to keep checkers in front of the
runner. If O doesn't roll a three X is in good shape.

10/8 6/1.

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

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

XGID=-AB-aBC-BBC--a------dcbbb-:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X |
| X X X | | X X X |
| X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 97 O: 77 X-O: 0-0
Cube: 1
X to play 52

In ah...clem's post, he considered and rejected both the loose hit and
the pick-and-pass play, but did not mention PoH.

It is often the case during containment that if you're behind in the pip
count (or even approximately equal), then hitting is worth the risk even
if it gives the opponent a direct shot in return. The reasoning goes
something like this: if your opponent dances then you are a huge
favorite, so even if getting hit loses the game for you (via D/P), it's
better than entering a losing race.

That heuristic reasoning fails here, mainly because after the safe play
of 10/8 6/1, X's prime still does a pretty good job of containment. But
it's still a tricky judgment call, in my opinion; see the variant, in
which the rollout favors the PoH play.

1. Rollout¹ 10/8 6/1 eq:+0.282
Player: 58.52% (G:1.27% B:0.02%)
Opponent: 41.48% (G:2.70% B:0.02%)
Confidence: ±0.008 (+0.274..+0.291) - [100.0%]

2. Rollout¹ 9/4* 6/4 eq:+0.141 (-0.142)
Player: 54.72% (G:2.89% B:0.06%)
Opponent: 45.28% (G:10.97% B:0.07%)
Confidence: ±0.009 (+0.132..+0.149) - [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=-ABa-BC-BBBA-a------dcbbb-:0:0:1:53:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| X X X | | X X X |
| X X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 98 O: 78 X-O: 0-0
Cube: 1
X to play 53

1. Rollout¹ 8/3* 6/3 eq:+0.278
Player: 59.15% (G:3.54% B:0.07%)
Opponent: 40.85% (G:13.96% B:0.17%)
Confidence: ±0.008 (+0.270..+0.286) - [100.0%]

2. Rollout¹ 11/8 6/1 eq:+0.226 (-0.052)
Player: 56.34% (G:1.29% B:0.02%)
Opponent: 43.66% (G:3.44% B:0.02%)
Confidence: ±0.006 (+0.220..+0.232) - [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

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

On Saturday, January 7, 2023 at 8:53:31 AM UTC-5, Tim Chow wrote:

XGID=-AB-aBC-BBC--a------dcbbb-:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X |
| X X X | | X X X |
| X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 97 O: 77 X-O: 0-0
Cube: 1
X to play 52
In ah...clem's post, he considered and rejected both the loose hit and
the pick-and-pass play, but did not mention PoH.

It is often the case during containment that if you're behind in the pip count (or even approximately equal), then hitting is worth the risk even
if it gives the opponent a direct shot in return. The reasoning goes something like this: if your opponent dances then you are a huge
favorite, so even if getting hit loses the game for you (via D/P), it's better than entering a losing race.

That heuristic reasoning fails here, mainly because after the safe play
of 10/8 6/1, X's prime still does a pretty good job of containment. But
it's still a tricky judgment call, in my opinion; see the variant, in
which the rollout favors the PoH play.

1. Rollout¹ 10/8 6/1 eq:+0.282
Player: 58.52% (G:1.27% B:0.02%)
Opponent: 41.48% (G:2.70% B:0.02%)
Confidence: ±0.008 (+0.274..+0.291) - [100.0%]

2. Rollout¹ 9/4* 6/4 eq:+0.141 (-0.142)
Player: 54.72% (G:2.89% B:0.06%)
Opponent: 45.28% (G:10.97% B:0.07%)
Confidence: ±0.009 (+0.132..+0.149) - [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=-ABa-BC-BBBA-a------dcbbb-:0:0:1:53:0:0:0:0:10
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| | | X |
| X X X | | X X X |
| X X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 98 O: 78 X-O: 0-0
Cube: 1
X to play 53

1. Rollout¹ 8/3* 6/3 eq:+0.278
Player: 59.15% (G:3.54% B:0.07%)
Opponent: 40.85% (G:13.96% B:0.17%)
Confidence: ±0.008 (+0.270..+0.286) - [100.0%]

2. Rollout¹ 11/8 6/1 eq:+0.226 (-0.052)
Player: 56.34% (G:1.29% B:0.02%)
Opponent: 43.66% (G:3.44% B:0.02%)
Confidence: ±0.006 (+0.220..+0.232) - [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

A series I never got around to writing because it's a lot of work is when to attack the last checker in similar situations loose. The race matters, of course, but that's only one of the main pieces of the puzzle. Most people don't realize how much it
matters the type of containment that is still in front of that checker if you decide not to hit. (a 3 prime? a broken 3 prime with the midpoint still? a 4 prime, a broken 4 prime, etc...)

Stick

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

On Saturday, January 7, 2023 at 1:53:31 PM UTC, Tim Chow wrote:

XGID=-AB-aBC-BBC--a------dcbbb-:0:0:1:52:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O | | O O O O O |
| | | O O O O O |
| | | O O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| X | | X |
| X X X | | X X X |
| X X X | | X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 97 O: 77 X-O: 0-0
Cube: 1
X to play 52
In ah...clem's post, he considered and rejected both the loose hit and
the pick-and-pass play, but did not mention PoH.

It is often the case during containment that if you're behind in the pip count (or even approximately equal), then hitting is worth the risk even
if it gives the opponent a direct shot in return. The reasoning goes something like this: if your opponent dances then you are a huge
favorite, so even if getting hit loses the game for you (via D/P), it's better than entering a losing race.

That heuristic reasoning fails here, mainly because after the safe play
of 10/8 6/1, X's prime still does a pretty good job of containment. But
it's still a tricky judgment call, in my opinion; see the variant, in
which the rollout favors the PoH play.

I think I would have (wrongly) played PoH here.
Perhaps XG can calculate the probability that, given the PoH play,
XG hits a shot in one of its next 4 rolls? (I'm hopeless at using XG
in any sophisticated way, and furthermore, my computer that has XG installed
is busted.)
I think a big problem with the PoH play is that XG gets an eventual shot with
a probability far higher than the baseline 11/36.
XG has 13/36 hits right away when you consider 63.
Also XG has 16/36 dances on the 4 point board and we then have lots of
numbers that don't cover the ace.
The variant is favourable in this respect in that XG has 12 immediate hits rather than 13,
and with checkers covering 8 to 11 instead of 8 to 10, the variant is more favourable
to covering the ace point.
Of course, the containment is a big factor too.

Paul

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

On 1/8/2023 6:43 AM, peps...@gmail.com wrote:

Perhaps XG can calculate the probability that, given the PoH play,
XG hits a shot in one of its next 4 rolls?

I don't think so. But GNU can at least estimate the probability of
hitting a shot sometime during the rest of the game (after each play),
which may be a reasonable proxy for what you're looking for?

---
Tim Chow

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

On 1/7/2023 4:14 PM, Stick Rice wrote:

A series I never got around to writing because it's a lot of work is when to attack the last checker in similar situations loose. The race matters, of course, but that's only one of the main pieces of the puzzle. Most people don't realize how much it

matters the type of containment that is still in front of that checker if you decide not to hit. (a 3 prime? a broken 3 prime with the midpoint still? a 4 prime, a broken 4 prime, etc...)

In 2007, Douglas Zare wrote a GammonVillage article on this topic,
"Serious Backgammon Errors - Late Loose Hits." But there is
certainly room for much more to be written about it.

---
Tim Chow

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