XGID=-B-C-A------a----b-fdb--A-: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

---
Tim Chow

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

On Saturday, June 10, 2023 at 3:04:11 AM UTC+1, Timothy Chow wrote:

XGID=-B-C-A------a----b-fdb--A-: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

D/P for me but the problem is very difficult (for me) and I
could hardly be less confident.

We need to double because a pottle followed by an opponent's miss is a huge market loser.
Any roll of the form 6-x or 1-5, 2-4 means the opponent needs to hit.
I will count the probability of losing the market this way:
66 miss has probability 7/432
65 miss has probability 25/648
64 miss has probability 1/27
63 miss has probability 11/324
62 miss has probability 7/216
61/51/24 miss has probability 1/18.

Total probability of losing market this way is approx 21.4%
This total is admittedly anti-Ohaganistic but we can do
a subHagan double if the threats repeat roll after roll.
If we don't get the escape now, we are likely to have another
attempt on the next shake.

So double.
With 8 checkers off, we probably have around 50% winning probability if
closed out. This is where my theoretical knowledge is very vague.
I vaguely remember something about 7/8 checkers off as being the 50/50
point but we need a world-class theorist to clarify.
So this is where a Stickism would be of huge benefit to the future of humanity or alternatively Tim might educate us in his follow-up.
I could even google but I need to prepare for a SQL test as part of a job application.
[BTW, they won't be easy select-type statements. There will be ultra-finicky nested queries and nasty joins involved -- these tests are designed to weed people out.]

But is it a take? The opponent is far from a closeout but doesn't have wasted checkers either.
It appears to me that eventually escaping and eventually being closed out are of roughly equal probability.
Furthermore the opponent has winning possibilities based on our inner board blot.

If my two 50/50 theories are correct -- the opponent's winning probability is 25% -- 50 to get the closeout
* 50 to win once having achieved it.
This would give the opponent a take because the cube vig is considerable and we might pick up the other checker.

Final reflection time: It seems that the escaping parlay is far more likely than the closeout parlay.
With 21% each time, we can escape somewhat soon, whereas closing out is a huge ask for the opponent.
My 50/50 theory about closeout and escaping being equally likely seems totally wrong.

D/P

Paul

--- SoupGate-Win32 v1.05
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XGID=-B-C-A------a----b-fdb--A-: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

I don't know that there's a way to analyze these sorts of positions
other than by accumulating examples and studying them. Paul made a
valiant effort to analyze this position using "standard" facts, and
did a pretty good job, but the crucial question of how likely O is
to successfully contain X is hard to judge. XG says it's an easy
take.

Paul did raise the question about the winning probability after a
closeout. With all of X's checkers on low points, the game is
about even when X has four checkers borne off:

http://www.gammonlife.com/writers/07tardieuart1.htm

Here, though, things are more favorable for O in the sense that she
has some chances of picking up another checkers in a blot-hitting
contest.

Analyzed in Rollout
No double
Player Winning Chances: 68.68% (G:9.67% B:0.44%)
Opponent Winning Chances: 31.32% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 69.00% (G:9.27% B:0.41%)
Opponent Winning Chances: 31.00% (G:0.00% B:0.00%)

Cubeful Equities:
No double: +0.548 (-0.162)
Double/Take: +0.710
Double/Pass: +1.000 (+0.290)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.009 (+0.539..+0.557)
Confidence Double: ± 0.012 (+0.698..+0.722)

eXtreme Gammon Version: 2.19.211.pre-release

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

XGID=-B-C-A------a----b-fdbA---: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 38 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 73.46% (G:7.08% B:0.32%)
Opponent Winning Chances: 26.54% (G:0.00% B:0.00%)
Double/Take
Player Winning Chances: 73.70% (G:7.15% B:0.34%)
Opponent Winning Chances: 26.30% (G:0.00% B:0.00%)

Cubeful Equities:
No double: +0.580 (-0.309)
Double/Take: +0.889
Double/Pass: +1.000 (+0.111)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 4-ply, cube decisions: XG Roller+
Search interval: Large
Confidence No Double: ± 0.007 (+0.574..+0.587)
Confidence Double: ± 0.008 (+0.881..+0.897)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

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

On 6/9/2023 10:04 PM, Timothy Chow wrote:

XGID=-B-C-A------a----b-fdb--A-: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-+
 |             O    |   | O  O  O        X |
 |             O    |   | O  O  O          |
 |                  |   | O  O             |
 |                  |   | O  O             |
 |                  |   | 6                |
 |                  |BAR|                  |
 |                  |   |                  |
 |                  |   |                  |
 |                  |   |          X       |
 |                  |   |          X     X |
 | O                |   |    X     X     X |
 +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 40  O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

With 8 off, X will be about 50% to win if O closes him out. So we can
file that under "no really bad sequences". 15 rolls escape, but X gets
hit about 1/3 of those, making for about ten market losers.

O'Hagen's law seems to narrowly imply a cube, but 66 is not the great
roll that one would expect and the blot on the five gives O enough extra
wins by picking up a second checker that I'll hold.

ND/T

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

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

On 6/11/2023 8:51 AM, Timothy Chow wrote:
With all of X's checkers on low points, the game is

about even when X has four checkers borne off:

http://www.gammonlife.com/writers/07tardieuart1.htm

You mean eight checkers, not four.

I remember this as:
8 off implies 50%
Add or subtract 10 percentage points for the first two additional or
fewer checkers off, then 7 percentage points for each additional checker.


It gives:


off GWC
4 16
5 23
6 30
7 40
8 50
9 60
10 70
11 77
12 84

Which is close enough to the table in the gammonlife article for most
practical purposes and a lot easier to remember.

Of course, it only works when the remaining checkers are on low points
so there are few "misses" when bearing off.

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

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

On Sunday, June 11, 2023 at 11:26:07 AM UTC-4, ah....Clem wrote:

On 6/9/2023 10:04 PM, Timothy Chow wrote:

XGID=-B-C-A------a----b-fdb--A-: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

With 8 off, X will be about 50% to win if O closes him out. So we can
file that under "no really bad sequences". 15 rolls escape, but X gets
hit about 1/3 of those, making for about ten market losers.

O'Hagen's law seems to narrowly imply a cube, but 66 is not the great
roll that one would expect and the blot on the five gives O enough extra wins by picking up a second checker that I'll hold.

ND/T

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

It's O'Hagan. And [66] is not that great of a roll?! Unless I'm misunderstanding who you're giving the [66] too it's by far the best roll there is.

Stick

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

On 6/28/2023 10:52 AM, Stick Rice wrote:

On Sunday, June 11, 2023 at 11:26:07 AM UTC-4, ah....Clem wrote:

On 6/9/2023 10:04 PM, Timothy Chow wrote:

XGID=-B-C-A------a----b-fdb--A-: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-+
| O | | O O O X |
| O | | O O O |
| | | O O |
| | | O O |
| | | 6 |
| |BAR| |
| | | |
| | | |
| | | X |
| | | X X |
| O | | X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 93 X-O: 0-0
Cube: 1
X on roll, cube action

With 8 off, X will be about 50% to win if O closes him out. So we can
file that under "no really bad sequences". 15 rolls escape, but X gets
hit about 1/3 of those, making for about ten market losers.

O'Hagen's law seems to narrowly imply a cube, but 66 is not the great
roll that one would expect and the blot on the five gives O enough extra
wins by picking up a second checker that I'll hold.

ND/T

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

It's O'Hagan. And [66] is not that great of a roll?! Unless I'm misunderstanding who you're giving the [66] too it's by far the best roll there is.

I suspect ah...Clem just meant to say that 66 gives O a return
shot from the bar.

---
Tim Chow

--- SoupGate-Win32 v1.05
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