XGID=---C-bC-E-B-bB---a-daabb--:0:0:1:63:0:0:0:0:10

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-+
| X O | | O O O O O |
| X | | O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| X | | |
| X | | |
| X | | X X |
| O X X | | X O X |
| O X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 117 X-O: 0-0
Cube: 1
X to play 63

---
Tim Chow

On 9/10/2022 8:15 AM, Timothy Chow wrote:
> XGID=---C-bC-E-B-bB---a-daabb--:0:0:1:63:0:0:0:0:10
>
> 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-+
>  | X           O    |   | O  O  O  O  O    |
>  | X                |   | O        O  O    |
>  |                  |   | O                |
>  |                  |   | O                |
>  |                  |   |                  |
>  |                  |BAR|                  |
>  |             X    |   |                  |
>  |             X    |   |                  |
>  |             X    |   | X        X       |
>  | O     X     X    |   | X  O     X       |
>  | O     X     X    |   | X  O     X       |
>  +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count  X: 113  O: 117 X-O: 0-0
> Cube: 1
> X to play 63

O has two juicy homeboard blots to shoot at if X leaves a shot and gets
hit. So, 13/4 looks tempting - ahead by 13 pips with all runners
escaped when misses.

But if O hits with a 12, 13, 14, or 44 there's only one blot to shoot at
and if hit with a 11 there are no blots to shoot at.

That makes me adverse to volunteering a shot. After 8/2 6/3 X is still
ahead by 13 pips with only the midpoint to clear, and O's midpoint won't
be there for long. So, 8/2 6/3.

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

On Saturday, September 10, 2022 at 3:56:17 PM UTC-4, ah....Clem wrote:
> On 9/10/2022 8:15 AM, Timothy Chow wrote:
> > XGID=---C-bC-E-B-bB---a-daabb--:0:0:1:63:0:0:0:0:10
> >
> > 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-+
> > | X O | | O O O O O |
> > | X | | O O O |
> > | | | O |
> > | | | O |
> > | | | |
> > | |BAR| |
> > | X | | |
> > | X | | |
> > | X | | X X |
> > | O X X | | X O X |
> > | O X X | | X O X |
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 113 O: 117 X-O: 0-0
> > Cube: 1
> > X to play 63
> O has two juicy homeboard blots to shoot at if X leaves a shot and gets
> hit. So, 13/4 looks tempting - ahead by 13 pips with all runners
> escaped when misses.
>
> But if O hits with a 12, 13, 14, or 44 there's only one blot to shoot at
> and if hit with a 11 there are no blots to shoot at.
>
> That makes me adverse to volunteering a shot. After 8/2 6/3 X is still
> ahead by 13 pips with only the midpoint to clear, and O's midpoint won't
> be there for long. So, 8/2 6/3.
>
>
> --
> Ah....Clem
> The future is fun, the future is fair.

If you were going to pay now wouldn't 10, 7 be far superior to 13/4?

Stick

XGID=---C-bC-E-B-bB---a-daabb--:0:0:1:63:0:0:0:0:10

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-+
| X O | | O O O O O |
| X | | O O O |
| | | O |
| | | O |
| | | |
| |BAR| |
| X | | |
| X | | |
| X | | X X |
| O X X | | X O X |
| O X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 113 O: 117 X-O: 0-0
Cube: 1
X to play 63

To me, most of the indicators for paying now or paying later seemed
to be pointing to paying now. O's board is currently weak and it
rates to get stronger in the next couple of rolls. Paying now with
13/10 13/7 gives O only 11 shots (the minimum) and gives X quite a
good chance of bringing everything home safely without ever leaving
a shot again if he is missed now. Playing 8/2 6/3 seems very awkward,
stripping the last spare from his 6pt and creating a blot in his board,
which will give O more leeway for leaving a blot on her midpoint.

Nevertheless, XG pays later. Part of the point is that despite X's
inflexible-looking position after 8/2 6/3, on the next roll, only 63
forces him to blot immediately. If O clears her midpoint soon, then
X may never have to leave a direct shot. Still, I don't know that I
would be able to accurately judge a similar position if it were to
come up OTB again.

1. Rollout¹ 8/2 6/3 eq:+0.306
Player: 58.89% (G:2.50% B:0.07%)
Opponent: 41.11% (G:4.50% B:0.08%)
Confidence: ±0.009 (+0.298..+0.315) - [100.0%]

2. Rollout¹ 13/10 13/7 eq:+0.231 (-0.075)
Player: 57.18% (G:4.22% B:0.25%)
Opponent: 42.82% (G:6.66% B:0.09%)
Confidence: ±0.009 (+0.222..+0.240) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

On Monday, September 12, 2022 at 9:13:06 AM UTC-4, Tim Chow wrote:
> XGID=---C-bC-E-B-bB---a-daabb--:0:0:1:63:0:0:0:0:10
>
> 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-+
> | X O | | O O O O O |
> | X | | O O O |
> | | | O |
> | | | O |
> | | | |
> | |BAR| |
> | X | | |
> | X | | |
> | X | | X X |
> | O X X | | X O X |
> | O X X | | X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 113 O: 117 X-O: 0-0
> Cube: 1
> X to play 63
> To me, most of the indicators for paying now or paying later seemed
> to be pointing to paying now. O's board is currently weak and it
> rates to get stronger in the next couple of rolls. Paying now with
> 13/10 13/7 gives O only 11 shots (the minimum) and gives X quite a
> good chance of bringing everything home safely without ever leaving
> a shot again if he is missed now. Playing 8/2 6/3 seems very awkward,
> stripping the last spare from his 6pt and creating a blot in his board,
> which will give O more leeway for leaving a blot on her midpoint.
>
> Nevertheless, XG pays later. Part of the point is that despite X's
> inflexible-looking position after 8/2 6/3, on the next roll, only 63
> forces him to blot immediately. If O clears her midpoint soon, then
> X may never have to leave a direct shot. Still, I don't know that I
> would be able to accurately judge a similar position if it were to
> come up OTB again.
>
> 1. Rollout¹ 8/2 6/3 eq:+0.306
> Player: 58.89% (G:2.50% B:0.07%)
> Opponent: 41.11% (G:4.50% B:0.08%)
> Confidence: ±0.009 (+0.298..+0.315) - [100.0%]
>
> 2. Rollout¹ 13/10 13/7 eq:+0.231 (-0.075)
> Player: 57.18% (G:4.22% B:0.25%)
> Opponent: 42.82% (G:6.66% B:0.09%)
> Confidence: ±0.009 (+0.222..+0.240) - [0.0%]
>
> ¹ 1296 Games rolled with Variance Reduction.
> Dice Seed: 271828
> Moves: 3-ply, cube decisions: XG Roller
>
> eXtreme Gammon Version: 2.19.207.pre-release
>
> ---
> Tim Chow

While yes, paying now is easy to clean up a couple things we can't forget even when the opponent has a blotted home board. First, how many of the hitting numbers hit and cover. Here we see 7/11 hit and cover at least one blot and the opponent is still happy to hit with the other 4 rolls since he still has the stronger board. Another thing to remember is while "and gives X quite a good chance of bringing everything home safely without ever leaving a shot again if he is missed now" it's true, it's also that our racing lead isn't as big as we'd like (we aren't cashing any time soon or even doubling most likely). As you also mentioned and needs to be reemphasized as a big piece of the puzzle, the opponent has no timing in his outfield checkers _since_ he is close enough in the race. He will have to pull those checkers from the midpoint almost immediately in most sequences and now we can get by with leaving just an indirect if we so choose.

Stick