XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

---
Tim Chow

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

On Sunday, October 31, 2021 at 12:23:37 AM UTC+1, Tim Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

Looks like an easy problem to me. Perhaps I'm missing something and it's not as easy as I think.
Or perhaps Tim's point is that we should take care in non-contact bearoffs and not automatically remove checkers
without thinking. Another alternative is that the problem is aimed at weaker players than myself. However, as far as I know,
none of the regular responders are weaker than I am.

That's quite a lengthy preamble, I know. But so what? If anyone listening is from the UK, they might remember the Two Ronnies, a former TV comedy show(?)
Ronnie Corbett always made a joke whose essence was very short and simple, but he spun out the entertainment for several minutes, by introducing
a lot of apparently extraneous "waffle". So hopefully, I'm following a venerable tradition (and isn't "venerable" a great word choice here?).

With 10 checkers left and a max removal of only a single checker, we can't do better than reach a 5 roll position.
Also we are clearly huge favourites so we have a defensive mindset where we look at ways to avoid possible losses.
If we leave ourselves a gap on the 2 point, we lose a roll with two rolls that contain a 2, and a non-2.
But losing is bad ain't it? I mean it's not as if we're babysitting a five-year-old who will throw a tantrum if she doesn't win.
So it might not be a terrible idea to try to avoid losing by avoiding the gap. So 6/2 is a must and the remainder of the roll must be played 4/2 or 3/1. 3/1 is clearly stacky and inefficient and leaves the same 2-point-gap issue as before.

6/2 4/2 is my play.

"Dunno what to do?
Just move to the two!"

Paul

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

Timothy Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X | +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

---
Tim Chow

My play would be either 6/off or 4/off, 4/2.

6/off gets another checker off and eliminates 5 or 6 as being potential problem.

4/off 4/2 removes a checker and fills in the empty 2 point.

I think 4/off 4/2 is better. Chances are I will get a 6 in the next
couple rolls anyway.

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

On Sunday, October 31, 2021 at 1:51:03 PM UTC, badgolferman wrote:

Timothy Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

---
Tim Chow

My play would be either 6/off or 4/off, 4/2.

6/off gets another checker off and eliminates 5 or 6 as being potential problem.

4/off 4/2 removes a checker and fills in the empty 2 point.

I think 4/off 4/2 is better. Chances are I will get a 6 in the next
couple rolls anyway.

Not sure I'm right. But I do know this much:
You'd agree that (whatever we play) we have a huge advantage.
So the idea is: Look for ways to lose and play to avoid them.

There are five legal plays so I would look at all five and check which is most defensive against opportunities to lose.
Also, it's important to count the rolls.
After playing, we need to be able to bear off in no more rolls than our opponent.

We're not trying to maximise efficiency but to minimise losing opportunities. The fact that our opponent is behind is an essential feature of the position. If the opponent were ahead or level, we would play the roll differently.

Paul

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

On 10/30/2021 7:23 PM, Timothy Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
 |                  |   | O  O  O  O  O  O | +---+
 |                  |   |       O  O     O | | 2 |
 |                  |   |       O  O       | +---+
 |                  |   |       O          |
 |                  |   |                  |
 |                  |BAR|                  |
 |                  |   |          X       |
 |                  |   |          X       |
 |                  |   |          X       |
 |                  |   |       X  X     X |
 |                  |   | X     X  X     X |
 +12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count  X: 31  O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

QF makes me think 6/2 4/2 is the bot play. X needs to bear ten off
while O needs to bear 12 off. 6/2 4/2 makes it almost certain that X
will be off in five rolls while any other play means X may miss taking
two off at some point. If I did QF I'd make that argument. But I don't
do QF.

So, I'll take one off and since I see no point in stacking the ace point
I'll play 6/off. How wrong can it be?

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

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

On Monday, November 1, 2021 at 5:22:19 PM UTC, ah....Clem wrote:

On 10/30/2021 7:23 PM, Timothy Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

QF makes me think 6/2 4/2 is the bot play. X needs to bear ten off
while O needs to bear 12 off. 6/2 4/2 makes it almost certain that X
will be off in five rolls while any other play means X may miss taking
two off at some point. If I did QF I'd make that argument. But I don't
do QF.

So, I'll take one off and since I see no point in stacking the ace point
I'll play 6/off. How wrong can it be?

It might not lose much equity but conceptually it just seems like a really horrible
answer. After all, it might not be particularly wrong to say that pi is rational
since this is wrong by less than 0.0000000000000000000001, but it isn't applying mathematical reasoning or knowledge correctly.

You've just seen that 6/2 4/2 makes you nearly certain to be off in 5 rolls.
So play it then!!!!!!!!!!
Are you really going to abstain from a play for the sole reason that it's QF? Or is your point that you want to follow what you think you would have done OTB even if you know it's wrong?

Paul

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

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42

I have to admit that I didn't even consider 6/2 4/2 and I added it to
the rollout only after I saw respondents here mention it. After X plays
either 6/2 or 4/2, I can't see any justification for not ripping a
checker. Sure, we probably won't miss later, but what do we gain by voluntarily missing now? Nothing that I can see.

For me, the choice was between 4/2 4/off and 6/off. I opted for 6/off, reasoning that 4/2 4/off left me vulnerable to missing with a 5 or a 4,
whereas after 6/off, a 2 can be played rather efficiently as 4/2. But
XG prefers 4/2 4/off. You could arrive at 4/2 4/off just by applying
the simple heuristic that having checkers on 4 different points is
usually better than having checkers on only 3 different points. Maybe
there is a more compelling way to argue that 4/2 4/off is the right play
(for example, maybe it yields a lower probability of missing twice later
on?) but I'm not seeing it right now.

By the way, removing several of O's checkers (in order to make X the
underdog) does not change XG's preference for 4/2 4/off.

1. Rollout¹ 4/2 4/Off eq:+0.580
Player: 81.08% (G:0.00% B:0.00%)
Opponent: 18.92% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.579..+0.581) - [100.0%]

2. Rollout¹ 6/Off eq:+0.552 (-0.028)
Player: 79.87% (G:0.00% B:0.00%)
Opponent: 20.13% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.550..+0.553) - [0.0%]

3. Rollout¹ 6/2 4/2 eq:+0.538 (-0.042)
Player: 79.19% (G:0.00% B:0.00%)
Opponent: 20.81% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.536..+0.539) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

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

On Tuesday, November 2, 2021 at 3:57:10 AM UTC, Tim Chow wrote:

XGID=-B-EB-A------------aadcab-:1:-1:1:42:0:0:0:0:10

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-+
| | | O O O O O O | +---+
| | | O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | X |
| | | X |
| | | X |
| | | X X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 31 O: 40 X-O: 0-0
Cube: 2, O own cube
X to play 42
I have to admit that I didn't even consider 6/2 4/2 and I added it to
the rollout only after I saw respondents here mention it. After X plays either 6/2 or 4/2, I can't see any justification for not ripping a
checker. Sure, we probably won't miss later, but what do we gain by voluntarily missing now? Nothing that I can see.

For me, the choice was between 4/2 4/off and 6/off. I opted for 6/off, reasoning that 4/2 4/off left me vulnerable to missing with a 5 or a 4, whereas after 6/off, a 2 can be played rather efficiently as 4/2. But
XG prefers 4/2 4/off. You could arrive at 4/2 4/off just by applying
the simple heuristic that having checkers on 4 different points is
usually better than having checkers on only 3 different points. Maybe
there is a more compelling way to argue that 4/2 4/off is the right play
(for example, maybe it yields a lower probability of missing twice later
on?) but I'm not seeing it right now.

By the way, removing several of O's checkers (in order to make X the underdog) does not change XG's preference for 4/2 4/off.

Thanks.
There are some bearoff plays where, given the choice between playing a single die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie.
So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?
Thanks,

Paul

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

On 11/2/2021 7:49 AM, peps...@gmail.com wrote:

There are some bearoff plays where, given the choice between playing a single die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie.
So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?

Yes, I have a couple of these. Here's maybe the best example (there is
a similar example in "Backgammon Funfair" I think):

XGID=-CCAD-B-------------cdbba-:1:-1:1:63:0:0:0:0:10

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-+
| | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 42 X-O: 0-0
Cube: 2, O own cube
X to play 63

1. Rollout¹ 6/3 6/Off eq:+0.057
Player: 58.29% (G:0.00% B:0.00%)
Opponent: 41.71% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.056..+0.058) - [100.0%]

2. Rollout¹ 6/Off 3/Off eq:+0.019 (-0.038)
Player: 56.97% (G:0.00% B:0.00%)
Opponent: 43.03% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.018..+0.020) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release

It's important here that X has an odd number of checkers, so that
his voluntary miss with 6/3 doesn't hurt much, whereas playing 3/off
risks missing *twice* later on, if he rolls a 5 and then a 3, or
even three 3's before clearing the 4pt.

Here's another example.

XGID=-CAFA---------------dbccb-:1:-1:1:52:0:0:0:0:10

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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O O | +---+
| | | O |
| | | |
| |BAR| |
| | | 6 |
| | | X |
| | | X X |
| | | X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 45 X-O: 0-0
Cube: 2, O own cube
X to play 52

1. Rollout¹ 4/2 3/Off eq:+0.888
Player: 94.84% (G:0.00% B:0.00%)
Opponent: 5.16% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.887..+0.889) - [100.0%]

2. Rollout¹ 4/Off 2/Off eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

3. Rollout¹ 4/Off 3/1 eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release

Again, X has an odd number of checkers so his voluntary miss 4/2 doesn't
hurt much, and if he doesn't miss now then his chances of missing twice
later on are fairly high.

---
Tim Chow

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

On Thursday, November 4, 2021 at 4:12:17 AM UTC, Tim Chow wrote:

On 11/2/2021 7:49 AM, peps...@gmail.com wrote:

There are some bearoff plays where, given the choice between playing a single
die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie.
So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?

Yes, I have a couple of these. Here's maybe the best example (there is
a similar example in "Backgammon Funfair" I think):

XGID=-CCAD-B-------------cdbba-:1:-1:1:63:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 42 X-O: 0-0
Cube: 2, O own cube
X to play 63

1. Rollout¹ 6/3 6/Off eq:+0.057
Player: 58.29% (G:0.00% B:0.00%)
Opponent: 41.71% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.056..+0.058) - [100.0%]

2. Rollout¹ 6/Off 3/Off eq:+0.019 (-0.038)
Player: 56.97% (G:0.00% B:0.00%)
Opponent: 43.03% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.018..+0.020) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
It's important here that X has an odd number of checkers, so that
his voluntary miss with 6/3 doesn't hurt much, whereas playing 3/off
risks missing *twice* later on, if he rolls a 5 and then a 3, or
even three 3's before clearing the 4pt.

Here's another example.

XGID=-CAFA---------------dbccb-:1:-1:1:52:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O O | +---+
| | | O |
| | | |
| |BAR| |
| | | 6 |
| | | X |
| | | X X |
| | | X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 45 X-O: 0-0
Cube: 2, O own cube
X to play 52

1. Rollout¹ 4/2 3/Off eq:+0.888
Player: 94.84% (G:0.00% B:0.00%)
Opponent: 5.16% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.887..+0.889) - [100.0%]

2. Rollout¹ 4/Off 2/Off eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

3. Rollout¹ 4/Off 3/1 eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
Again, X has an odd number of checkers so his voluntary miss 4/2 doesn't hurt much, and if he doesn't miss now then his chances of missing twice later on are fairly high.

Thanks, I'll look at these.
Here, I think you can actually quantify "best" among the examples.
I think a good metric is that the strength of an example is measured by how much equity the greedy play loses (the more the better the example). So, since 0.047 > 0.038, your second example
is actually stronger than your first.
I don't know where my copy of Backgammon Funfair is right now (although I did buy it). But my guess is that
they would use the same metric I did.
So what is your metric to make the first example best? Instructional value perhaps?

Paul

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

On Thursday, November 4, 2021 at 8:52:09 AM UTC, peps...@gmail.com wrote:

On Thursday, November 4, 2021 at 4:12:17 AM UTC, Tim Chow wrote:

On 11/2/2021 7:49 AM, peps...@gmail.com wrote:

There are some bearoff plays where, given the choice between playing a single
die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie.
So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?

Yes, I have a couple of these. Here's maybe the best example (there is
a similar example in "Backgammon Funfair" I think):

XGID=-CCAD-B-------------cdbba-:1:-1:1:63:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 42 X-O: 0-0
Cube: 2, O own cube
X to play 63

1. Rollout¹ 6/3 6/Off eq:+0.057
Player: 58.29% (G:0.00% B:0.00%)
Opponent: 41.71% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.056..+0.058) - [100.0%]

2. Rollout¹ 6/Off 3/Off eq:+0.019 (-0.038)
Player: 56.97% (G:0.00% B:0.00%)
Opponent: 43.03% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.018..+0.020) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
It's important here that X has an odd number of checkers, so that
his voluntary miss with 6/3 doesn't hurt much, whereas playing 3/off
risks missing *twice* later on, if he rolls a 5 and then a 3, or
even three 3's before clearing the 4pt.

Here's another example.

XGID=-CAFA---------------dbccb-:1:-1:1:52:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O O | +---+
| | | O |
| | | |
| |BAR| |
| | | 6 |
| | | X |
| | | X X |
| | | X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 45 X-O: 0-0
Cube: 2, O own cube
X to play 52

1. Rollout¹ 4/2 3/Off eq:+0.888
Player: 94.84% (G:0.00% B:0.00%)
Opponent: 5.16% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.887..+0.889) - [100.0%]

2. Rollout¹ 4/Off 2/Off eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

3. Rollout¹ 4/Off 3/1 eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
Again, X has an odd number of checkers so his voluntary miss 4/2 doesn't hurt much, and if he doesn't miss now then his chances of missing twice later on are fairly high.

Thanks, I'll look at these.
Here, I think you can actually quantify "best" among the examples.
I think a good metric is that the strength of an example is measured by how much equity the greedy play loses (the more the better the example). So, since 0.047 > 0.038, your second example
is actually stronger than your first.
I don't know where my copy of Backgammon Funfair is right now (although I did buy it). But my guess is that
they would use the same metric I did.
So what is your metric to make the first example best? Instructional value perhaps?

Oh, ok, I get it now. If you play 6/2 (in the original position), you must take one off the two point.
[You shouldn't actually play 6/2, but that's besides the point.]
With my play, you're preserving an extra 2 but also sacrificing a 2 -- senseless.
In your examples, you don't have the option of removing a checker from the point you just moved to -- which
is why they work, but my play doesn't.

Paul

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

On Thursday, November 4, 2021 at 9:02:11 AM UTC, peps...@gmail.com wrote:

On Thursday, November 4, 2021 at 8:52:09 AM UTC, peps...@gmail.com wrote:

On Thursday, November 4, 2021 at 4:12:17 AM UTC, Tim Chow wrote:

On 11/2/2021 7:49 AM, peps...@gmail.com wrote:

There are some bearoff plays where, given the choice between playing a single
die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie. So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?

Yes, I have a couple of these. Here's maybe the best example (there is
a similar example in "Backgammon Funfair" I think):

XGID=-CCAD-B-------------cdbba-:1:-1:1:63:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 42 X-O: 0-0
Cube: 2, O own cube
X to play 63

1. Rollout¹ 6/3 6/Off eq:+0.057
Player: 58.29% (G:0.00% B:0.00%)
Opponent: 41.71% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.056..+0.058) - [100.0%]

2. Rollout¹ 6/Off 3/Off eq:+0.019 (-0.038)
Player: 56.97% (G:0.00% B:0.00%)
Opponent: 43.03% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.018..+0.020) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
It's important here that X has an odd number of checkers, so that
his voluntary miss with 6/3 doesn't hurt much, whereas playing 3/off risks missing *twice* later on, if he rolls a 5 and then a 3, or
even three 3's before clearing the 4pt.

Here's another example.

XGID=-CAFA---------------dbccb-:1:-1:1:52:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O O | +---+
| | | O |
| | | |
| |BAR| |
| | | 6 |
| | | X |
| | | X X |
| | | X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 45 X-O: 0-0
Cube: 2, O own cube
X to play 52

1. Rollout¹ 4/2 3/Off eq:+0.888
Player: 94.84% (G:0.00% B:0.00%)
Opponent: 5.16% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.887..+0.889) - [100.0%]

2. Rollout¹ 4/Off 2/Off eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

3. Rollout¹ 4/Off 3/1 eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
Again, X has an odd number of checkers so his voluntary miss 4/2 doesn't hurt much, and if he doesn't miss now then his chances of missing twice later on are fairly high.

Thanks, I'll look at these.
Here, I think you can actually quantify "best" among the examples.
I think a good metric is that the strength of an example is measured by how
much equity the greedy play loses (the more the better the example). So, since 0.047 > 0.038, your second example
is actually stronger than your first.
I don't know where my copy of Backgammon Funfair is right now (although I did buy it). But my guess is that
they would use the same metric I did.
So what is your metric to make the first example best? Instructional value perhaps?

Oh, ok, I get it now. If you play 6/2 (in the original position), you must take one off the two point.
[You shouldn't actually play 6/2, but that's besides the point.]
With my play, you're preserving an extra 2 but also sacrificing a 2 -- senseless.
In your examples, you don't have the option of removing a checker from the point you just moved to -- which
is why they work, but my play doesn't.

Paul

My Backgammon Funfair reports many variations where it is correct to bear off no checkers instead of one; no checkers instead of two; one checker instead of two; two checkers instead of three; three checkers instead of four. All these are from the
late Walter Trice.

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

On Thursday, November 4, 2021 at 5:10:13 PM UTC, ra...@clara.co.uk wrote:

On Thursday, November 4, 2021 at 9:02:11 AM UTC, peps...@gmail.com wrote:

On Thursday, November 4, 2021 at 8:52:09 AM UTC, peps...@gmail.com wrote:

On Thursday, November 4, 2021 at 4:12:17 AM UTC, Tim Chow wrote:

On 11/2/2021 7:49 AM, peps...@gmail.com wrote:

There are some bearoff plays where, given the choice between playing a single
die by moving N places or removing a checker from position N, the move of N places is
better. I think this is mentioned in Advanced Backgammon by Robertie.
So you do sometimes voluntarily miss now to avoid missing lately even though it's not the right idea here.

Do you know any of these paradoxical bearoff plays?

Yes, I have a couple of these. Here's maybe the best example (there is a similar example in "Backgammon Funfair" I think):

XGID=-CCAD-B-------------cdbba-:1:-1:1:63:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | O |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X |
| | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 40 O: 42 X-O: 0-0
Cube: 2, O own cube
X to play 63

1. Rollout¹ 6/3 6/Off eq:+0.057
Player: 58.29% (G:0.00% B:0.00%)
Opponent: 41.71% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.056..+0.058) - [100.0%]

2. Rollout¹ 6/Off 3/Off eq:+0.019 (-0.038)
Player: 56.97% (G:0.00% B:0.00%)
Opponent: 43.03% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.018..+0.020) - [0.0%]

¹ 2592 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller+
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
It's important here that X has an odd number of checkers, so that
his voluntary miss with 6/3 doesn't hurt much, whereas playing 3/off risks missing *twice* later on, if he rolls a 5 and then a 3, or
even three 3's before clearing the 4pt.

Here's another example.

XGID=-CAFA---------------dbccb-:1:-1:1:52:0:0:0:0:10
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-+
| | | O O O O O | +---+
| | | O O O O O | | 2 |
| | | O O O | +---+
| | | O |
| | | |
| |BAR| |
| | | 6 |
| | | X |
| | | X X |
| | | X X |
| | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 27 O: 45 X-O: 0-0
Cube: 2, O own cube
X to play 52

1. Rollout¹ 4/2 3/Off eq:+0.888
Player: 94.84% (G:0.00% B:0.00%)
Opponent: 5.16% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.887..+0.889) - [100.0%]

2. Rollout¹ 4/Off 2/Off eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]

3. Rollout¹ 4/Off 3/1 eq:+0.841 (-0.047)
Player: 92.92% (G:0.00% B:0.00%)
Opponent: 7.08% (G:0.00% B:0.00%)
Confidence: ±0.001 (+0.840..+0.842) - [0.0%]
¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: XG Roller++
Search interval: Gigantic

eXtreme Gammon Version: 2.19.207.pre-release
Again, X has an odd number of checkers so his voluntary miss 4/2 doesn't
hurt much, and if he doesn't miss now then his chances of missing twice
later on are fairly high.

Thanks, I'll look at these.
Here, I think you can actually quantify "best" among the examples.
I think a good metric is that the strength of an example is measured by how
much equity the greedy play loses (the more the better the example). So, since 0.047 > 0.038, your second example
is actually stronger than your first.
I don't know where my copy of Backgammon Funfair is right now (although I did buy it). But my guess is that
they would use the same metric I did.
So what is your metric to make the first example best? Instructional value perhaps?

Oh, ok, I get it now. If you play 6/2 (in the original position), you must take one off the two point.
[You shouldn't actually play 6/2, but that's besides the point.]
With my play, you're preserving an extra 2 but also sacrificing a 2 -- senseless.
In your examples, you don't have the option of removing a checker from the point you just moved to -- which
is why they work, but my play doesn't.

Paul

My Backgammon Funfair reports many variations where it is correct to bear off no checkers instead of one; no checkers instead of two; one checker instead of two; two checkers instead of three; three checkers instead of four. All these are from the late

Walter Trice.

I might buy another copy if you publish a variation where it is correct (and uniquely optimal), in a no-contact position, to bear off no checkers instead of four.

Paul

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

On 11/4/2021 4:52 AM, peps...@gmail.com wrote:

So what is your metric to make the first example best? Instructional value perhaps?

I felt that the second one had a slight aesthetic flaw
because one of the plays required bearing off the checkers
in a certain order and wasting an extra pip. I suppose
that some people might actually consider this to be a
feature and not a bug, since wasting an extra pip might
seem like an additional argument against the top play.

---
Tim Chow

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

On 11/4/2021 5:02 AM, peps...@gmail.com wrote:

Oh, ok, I get it now. If you play 6/2 (in the original position), you must take one off the two point.
[You shouldn't actually play 6/2, but that's besides the point.]
With my play, you're preserving an extra 2 but also sacrificing a 2 -- senseless.
In your examples, you don't have the option of removing a checker from the point you just moved to -- which
is why they work, but my play doesn't.

The way I think about it, if you voluntarily miss now, it's because
otherwise you run a high risk of missing *twice* later, which
would be worse.

So here, if we're comparing your play of 6/2 4/2 with the bot play of
4/off 4/2, we play 4/2 first and then think about whether 4/off leads
to a high risk of missing twice later. It could happen; you could
roll a 5 and then two 2's, or you could roll a 4 and then *three* 2's.
But these are not particularly likely parlays, and if you roll a 4
and then three 2's, you're going to miss even after 6/2 4/2. So it's
not going to be worth voluntarily missing now.

---
Tim Chow

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