With only 3 checkers fewer off than the opponent, the double must be
obvious to any non-beginner.
But should XG take it?

Paul

XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
X:Daniel O:eXtremeGammon

Score is X:14 O:0. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| | | O O O |
| | | O O |
| | | O O |
| | | |
| | | |
| |BAR| |
| | O | |
| | | X |
| | | X | +---+
| | | X X X X | | 4 |
| | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 30 O: 37 X-O: 14-0
Cube: 4, X own cube
X on roll, cube action

On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> X:Daniel O:eXtremeGammon
>
> Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | | | O O O |
> | | | O O |
> | | | O O |
> | | | |
> | | | |
> | |BAR| |
> | | O | |
> | | | X |
> | | | X | +---+
> | | | X X X X | | 4 |
> | | | X X X X X | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 30 O: 37 X-O: 14-0
> Cube: 4, X own cube
> X on roll, cube action

Tough one. I'd probably pass OTB, but let's try to analyze it.
About half the time, X will leave a blot, and about 1/3 of those
times, O will hit it; but even then, O is not assured of winning,
since she has a weak board and might get another checker hit.
Let's say O wins 4 out of 36 games this way. The other half of
the time, X won't blot; on average, X will roll small and take
off just one checker. I will guess that X wins about 5 out of 36
games this way. So maybe this is a take.

---
Tim Chow

On Saturday, July 30, 2022 at 1:55:23 PM UTC+1, Tim Chow wrote:
> On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> > XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> > X:Daniel O:eXtremeGammon
> >
> > Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | | | O O O |
> > | | | O O |
> > | | | O O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | O | |
> > | | | X |
> > | | | X | +---+
> > | | | X X X X | | 4 |
> > | | | X X X X X | +---+
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 30 O: 37 X-O: 14-0
> > Cube: 4, X own cube
> > X on roll, cube action
> Tough one. I'd probably pass OTB, but let's try to analyze it.
> About half the time, X will leave a blot, and about 1/3 of those
> times, O will hit it; but even then, O is not assured of winning,
> since she has a weak board and might get another checker hit.
> Let's say O wins 4 out of 36 games this way. The other half of
> the time, X won't blot; on average, X will roll small and take
> off just one checker. I will guess that X wins about 5 out of 36
> games this way. So maybe this is a take.

Because I like this type of arithmetical exercise, I will work out the immediate blot/ immediate hit
probability exactly and then we can see how/if that affects your answer.
66 gives 11/36 hits.
65/64 both give 13/36 hits.
So does 63 because we must surely play the 3 from the 5 point or may be 6/3 5/off but we're definitely
blotting on the 5.
62 leaves the blot on the 5 too.
55 gives 11/36 hits.
54/53/52 all blot on the 5 to give 13/36 hits.
44 gives 11/36 hits.
43 blots on the 5
No other roll blots.
So we get 1/12 * 11/36 + 4/9 * 13/36 = 241/1296 which is slightly more than 18%.
But this only counts the immediate hits. There's also a significant probability of XG hitting a blot but not on the next shot.
So you underestimate the hitting probability I think, but maybe only slightly.
X leaves an immediate blot 19/36 of the time which is already more than half.

So, although you (correctly) say this is a take, it's probably a bigger take than you think. Passing is quite the whopper.
However, I did (wrongly) expect XG to pass OTB.

Paul

On Saturday, July 30, 2022 at 1:55:23 PM UTC+1, Tim Chow wrote:
> On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> > XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> > X:Daniel O:eXtremeGammon
> >
> > Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | | | O O O |
> > | | | O O |
> > | | | O O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | O | |
> > | | | X |
> > | | | X | +---+
> > | | | X X X X | | 4 |
> > | | | X X X X X | +---+
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 30 O: 37 X-O: 14-0
> > Cube: 4, X own cube
> > X on roll, cube action
> Tough one. I'd probably pass OTB, but let's try to analyze it.
> About half the time, X will leave a blot, and about 1/3 of those
> times, O will hit it; but even then, O is not assured of winning,
> since she has a weak board and might get another checker hit.
> Let's say O wins 4 out of 36 games this way. The other half of
> the time, X won't blot; on average, X will roll small and take
> off just one checker. I will guess that X wins about 5 out of 36
> games this way. So maybe this is a take.
>
> ---
> Tim Chow

In general, 8/36 games would be enough for a take because of cube vig,
but in this particular position, I think cube vig is quite low so you do need 9.
After XG takes, XG is unlikely to get an efficient recube.

Paul

On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> With only 3 checkers fewer off than the opponent, the double must be
> obvious to any non-beginner.
> But should XG take it?
>
> Paul
>
> XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> X:Daniel O:eXtremeGammon
>
> Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | | | O O O |
> | | | O O |
> | | | O O |
> | | | |
> | | | |
> | |BAR| |
> | | O | |
> | | | X |
> | | | X | +---+
> | | | X X X X | | 4 |
> | | | X X X X X | +---+
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 30 O: 37 X-O: 14-0
> Cube: 4, X own cube
> X on roll, cube action

If O fails to hit she's screwed. 62, 63, 64, 65, 66, 52, 53, 54 55, 43,
44, and 33 all leave shots. That's 18 or 50%. O hits about 1/3 so that
gives about a 1/6 chance of hitting. Add in game changers like 44, 66,
and sometimes 55 to incease that 18% to about 25 or 26%. Looks like a
take, and of course you ship it here since some will pass.

R/T.

On Sunday, July 31, 2022 at 5:42:52 PM UTC+1, ah...Clem wrote:
> On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> > With only 3 checkers fewer off than the opponent, the double must be
> > obvious to any non-beginner.
> > But should XG take it?
> >
> > Paul
> >
> > XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> > X:Daniel O:eXtremeGammon
> >
> > Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > | | | O O O |
> > | | | O O |
> > | | | O O |
> > | | | |
> > | | | |
> > | |BAR| |
> > | | O | |
> > | | | X |
> > | | | X | +---+
> > | | | X X X X | | 4 |
> > | | | X X X X X | +---+
> > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > Pip count X: 30 O: 37 X-O: 14-0
> > Cube: 4, X own cube
> > X on roll, cube action
> If O fails to hit she's screwed. 62, 63, 64, 65, 66, 52, 53, 54 55, 43,
> 44, and 33 all leave shots. That's 18 or 50%. O hits about 1/3 so that
> gives about a 1/6 chance of hitting. Add in game changers like 44, 66,
> and sometimes 55 to incease that 18% to about 25 or 26%. Looks like a
> take, and of course you ship it here since some will pass.
>
> R/T.

Some good analysis there!
I'd reword the final part to (something like). "Since the take/pass decision
is in doubt, it must be a cube."
When you say "ship it here since some will pass", it makes it sound like a bluff double
where the doubler is gambling on the opponent passing.
Here, it's a brilliant double even if we're certain the opponent will take.

Paul

On Sunday, July 31, 2022 at 7:10:04 PM UTC+1, peps...@gmail.com wrote:
> On Sunday, July 31, 2022 at 5:42:52 PM UTC+1, ah...Clem wrote:
> > On 7/30/2022 6:09 AM, peps...@gmail.com wrote:
> > > With only 3 checkers fewer off than the opponent, the double must be
> > > obvious to any non-beginner.
> > > But should XG take it?
> > >
> > > Paul
> > >
> > > XGID=aDBB-BA---------------acc-:2:1:1:00:14:0:3:0:10
> > > X:Daniel O:eXtremeGammon
> > >
> > > Score is X:14 O:0. Unlimited Game, Jacoby Beaver
> > > +13-14-15-16-17-18------19-20-21-22-23-24-+
> > > | | | O O O |
> > > | | | O O |
> > > | | | O O |
> > > | | | |
> > > | | | |
> > > | |BAR| |
> > > | | O | |
> > > | | | X |
> > > | | | X | +---+
> > > | | | X X X X | | 4 |
> > > | | | X X X X X | +---+
> > > +12-11-10--9--8--7-------6--5--4--3--2--1-+
> > > Pip count X: 30 O: 37 X-O: 14-0
> > > Cube: 4, X own cube
> > > X on roll, cube action
> > If O fails to hit she's screwed. 62, 63, 64, 65, 66, 52, 53, 54 55, 43,
> > 44, and 33 all leave shots. That's 18 or 50%. O hits about 1/3 so that
> > gives about a 1/6 chance of hitting. Add in game changers like 44, 66,
> > and sometimes 55 to incease that 18% to about 25 or 26%. Looks like a
> > take, and of course you ship it here since some will pass.
> >
> > R/T.
> Some good analysis there!
> I'd reword the final part to (something like). "Since the take/pass decision
> is in doubt, it must be a cube."
> When you say "ship it here since some will pass", it makes it sound like a bluff double
> where the doubler is gambling on the opponent passing.
> Here, it's a brilliant double even if we're certain the opponent will take.
>
> Paul
Analyzed in Rollout
No redouble
Player Winning Chances: 75.34% (G:0.00% B:0.00%)
Opponent Winning Chances: 24.66% (G:0.00% B:0.00%)
Redouble/Take
Player Winning Chances: 75.39% (G:0.00% B:0.00%)
Opponent Winning Chances: 24.61% (G:0.00% B:0.00%)

Cubeless Equities: No Double=+0.507, Double=+1.016

Cubeful Equities:
No redouble: +0.719 (-0.133)
Redouble/Take: +0.852
Redouble/Pass: +1.000 (+0.148)