Hello,

GNU Backgammon Position ID: DwAA4L+jQAAAAA
Match ID : UYlmAYAAMAAE
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| | | O | OOO 8 points
| | | O | OO
| | | O | OO
| | | O | OO
| | | | OO
v| |BAR| | 11 point match
| | | 9 |
| | | X |
| | | X X |
| | | X X | Rolled 51
| X | | X X X X | 6 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: axel (Cube: 2)

an easy one, but I overlooked it over the board in auto-pilot mode. No
rollout needed for the correct solution, but once I saw it after
switching off my reptile brain, it made me smile, because it involves
two counter-intuitive things.

Best regards

Axel

On Saturday, November 19, 2022 at 7:50:16 AM UTC, Axel Reichert wrote:
> Hello,
>
> GNU Backgammon Position ID: DwAA4L+jQAAAAA
> Match ID : UYlmAYAAMAAE
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | | | O | OOO 8 points
> | | | O | OO
> | | | O | OO
> | | | O | OO
> | | | | OO
> v| |BAR| | 11 point match
> | | | 9 |
> | | | X |
> | | | X X |
> | | | X X | Rolled 51
> | X | | X X X X | 6 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: axel (Cube: 2)
>
> an easy one, but I overlooked it over the board in auto-pilot mode. No
> rollout needed for the correct solution, but once I saw it after
> switching off my reptile brain, it made me smile, because it involves
> two counter-intuitive things.

I would call this "straightforward" rather than "easy".
Only basic reasoning is needed, but quite a lot of care and thought is still warranted.
[I'm not sure "warranted" is a great word choice here, but I wanted to avoid repeating
the word "needed" (he says, while repeating the word "needed" twice more!)]

I'm sure I could easily get this wrong OTB, particularly under time pressure.
Note that, even with clockless games, there is often considerable social pressure
to play quickly.
The most obvious play is 12/6. Assuming our opponent rolls non-doubles,
we lose a gammon only with 43.
So we can restrict our search to plays which leave us either with our only anti-joker
being a doubles, or with no anti-jokers at all.
This compels 12/7 so that we cater to small rolls.
So we only have to play the ace now.
We now have our complete candidates list of:
12/6 (hugely expected to be eliminated by QF but for now it's a candidate anyway).
12/7 6/5
12/7 5/4
12/7 2/1

12/6 has been considered.
12/7 6/5 leaves only 33 as an anti-joker so is the best so far.
12/7 5/4 gives a 53 anti-joker (don't care whether there are others) so is eliminated.

12/7 2/1 is the standout QF play because 2/1 does absolutely nothing -- it's the same
as playing 12/7 and just picking up your dice. For a racing position to have the
zugzwang property that it's better to do nothing than to do something would have
a strong paradoxical flavour, which would make Axel's problem quite a good one.
Basically, we should definitely expect 12/7 2/1 to be correct, and are now simply
verifying.
What are the anti-jokers after 12/7 2/1?
Clearly any 1,2,5,6 will work so we only need to consider 33, 44 and 43.
Indeed, they all work.
12/7 2/1 is the uniquely correct play which loses a gammon with a probability of 1/6.
If you play something else, your probability of losing a gammon is larger than 1/6.

BTW, you could pull an April-fool's-type trick where you secretly give the on-roll player 14
checkers, so clearly no play makes any difference. The joke is that readers waste
time, laboriously trying to save a gammon that is already saved.

Paul

On Saturday, November 19, 2022 at 7:50:16 AM UTC, Axel Reichert wrote:
> Hello,
>
> GNU Backgammon Position ID: DwAA4L+jQAAAAA
> Match ID : UYlmAYAAMAAE
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | | | O | OOO 8 points
> | | | O | OO
> | | | O | OO
> | | | O | OO
> | | | | OO
> v| |BAR| | 11 point match
> | | | 9 |
> | | | X |
> | | | X X |
> | | | X X | Rolled 51
> | X | | X X X X | 6 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: axel (Cube: 2)
>
> an easy one, but I overlooked it over the board in auto-pilot mode. No
> rollout needed for the correct solution, but once I saw it after
> switching off my reptile brain, it made me smile, because it involves
> two counter-intuitive things.
>
> Best regards
>
> Axel

If I borrow Tim's Tex IDE, and variantize by transferring two
of X's checkers from the two to the ace, and give X the same roll,
then we get a Funfair position in that we have a pure race where
we would rather play just one of the dice, and lose equity from the rule
demanding that both dice be played.
This raises the question of whether a non-contact position and roll can
be constructed where we'd rather just completely pass on an entire roll
rather than play the roll, if the rules allowed it.
I doubt that this is possible.

Paul Epstein

On 11/19/2022 2:50 AM, Axel Reichert wrote:
> Hello,
>
> GNU Backgammon Position ID: DwAA4L+jQAAAAA
> Match ID : UYlmAYAAMAAE
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | | | O | OOO 8 points
> | | | O | OO
> | | | O | OO
> | | | O | OO
> | | | | OO
> v| |BAR| | 11 point match
> | | | 9 |
> | | | X |
> | | | X X |
> | | | X X | Rolled 51
> | X | | X X X X | 6 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: axel (Cube: 2)
>
> an easy one, but I overlooked it over the board in auto-pilot mode. No
> rollout needed for the correct solution, but once I saw it after
> switching off my reptile brain, it made me smile, because it involves
> two counter-intuitive things.
Very similar to Puzzle 4 here:

https://www.edcollins.com/backgammon/backprobs.htm

That puzzle was created by Bill Davis. I've always assumed that he
created it artificially, but maybe he actually faced it OTB. It's
interesting that you faced such a similar position OTB.

Bill Davis's other puzzles on that page are pretty cool, too. See
also his "Ultimate Backgammon Contest" and "Great Prime Problem" here:

https://www.bkgm.com/articles/authors.html#davis_bill

---
Tim Chow

"peps...@gmail.com" <pepstein5@gmail.com> writes:

> 12/7 2/1 is the uniquely correct play

Yes, and the two counter-intuitive properties are to refrain from
changing the quadrant and instead to pile further checkers onto the
already high ace-point stack.

Best regards

Axel

On November 19, 2022 at 7:06:24 AM UTC-7, Axel Reichert wrote:

> "peps...@gmail.com" <peps...@gmail.com> writes:

>> 12/7 2/1 is the uniquely correct play

> Yes, and the two counter-intuitive properties
> are to refrain from changing the quadrant
> and instead to pile further checkers onto
> the already high ace-point stack.

I mostly skip position discussing threads as
uninteresting but having once had, way back
when, an interest in our "three brains", your
catchy title was irresistible and I'm glad it was.

At my usual playing pace, it would be easy to
see 12/7 takes care of 43, 34 (with 33, 44 not
being problems) but I would play 5/4 not seing
the newly created 53 gap so easily, even after
being tipped off that this is a tricky position.

I (like most people) would only see the 2/1 if
the stakes were high enough to play it slowly
like chess, by considering all possibilities one
by one (as Paul has done and illustrated).

From now on, I think I'll read all threads with
the words "reptilian brain" in the title. :))

MK

On Saturday, November 19, 2022 at 2:50:16 AM UTC-5, Axel Reichert wrote:
> Hello,
>
> GNU Backgammon Position ID: DwAA4L+jQAAAAA
> Match ID : UYlmAYAAMAAE
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | | | O | OOO 8 points
> | | | O | OO
> | | | O | OO
> | | | O | OO
> | | | | OO
> v| |BAR| | 11 point match
> | | | 9 |
> | | | X |
> | | | X X |
> | | | X X | Rolled 51
> | X | | X X X X | 6 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: axel (Cube: 2)
>
> an easy one, but I overlooked it over the board in auto-pilot mode. No
> rollout needed for the correct solution, but once I saw it after
> switching off my reptile brain, it made me smile, because it involves
> two counter-intuitive things.
>
> Best regards
>
> Axel

I always save these straightforward yet don't fall asleep on me save the gammon type plays. I have accumulated quite the collection of naturally occurring positions.

Stick

On Saturday, November 19, 2022 at 11:30:11 PM UTC, MK wrote:
> On November 19, 2022 at 7:06:24 AM UTC-7, Axel Reichert wrote:
>
> > "peps...@gmail.com" <peps...@gmail.com> writes:
>
> >> 12/7 2/1 is the uniquely correct play
>
> > Yes, and the two counter-intuitive properties
> > are to refrain from changing the quadrant
> > and instead to pile further checkers onto
> > the already high ace-point stack.
> I mostly skip position discussing threads as
> uninteresting but having once had, way back
> when, an interest in our "three brains", your
> catchy title was irresistible and I'm glad it was.
>
> At my usual playing pace, it would be easy to
> see 12/7 takes care of 43, 34 (with 33, 44 not
> being problems) but I would play 5/4 not seing
> the newly created 53 gap so easily, even after
> being tipped off that this is a tricky position.
>
> I (like most people) would only see the 2/1 if
> the stakes were high enough to play it slowly
> like chess, by considering all possibilities one
> by one (as Paul has done and illustrated).
>
> From now on, I think I'll read all threads with
> the words "reptilian brain" in the title. :))
>
> MK

Good post.
A small addition is that just as 5/4 makes 53 a problem roll,
6/5 makes 33 a problem roll so we can't do that either, making the solution unique.

Paul

On November 20, 2022 at 4:19:58 AM UTC-7, peps...@gmail.com wrote:

> On Saturday, November 19, 2022 at 11:30:11 PM UTC, MK wrote:

>>> "peps...@gmail.com" <peps...@gmail.com> writes:

>>>> 12/7 2/1 is the uniquely correct play

>> I (like most people) would only see the 2/1 if
>> the stakes were high enough to play it slowly
>> like chess, by considering all possibilities one
>> by one (as Paul has done and illustrated).

> Good post.
> A small addition is that just as 5/4 makes 53 a
> problem roll, 6/5 makes 33 a problem roll so we
> can't do that either, making the solution unique.

Yes, I had quoted that you pointed that out. But I
ignored 6/5 in my comments because "intuitively"
(there must be a better word for this??) I wouldn't
stack checkers in positions like this. I didn't mean
to take away anything from your through process
of elimination analysis.

In fact, now I even value that you dwelled on this
because I'm waiting for Tim's and Axel's replies
to me before I post more one "multiple optimum
strategies", etc. and you made me wonder if the
"uniquely correct plays" should be valued more
than each of the "equally correct plays"...?? (My
reptilian brain says the the answer to this should
be obvious but I'll sleep on it... :)

MK

On 11/20/2022 5:38 AM, Stick Rice wrote:
> I always save these straightforward yet don't fall asleep on me save the gammon type plays. I have accumulated quite the collection of naturally occurring positions.

I have a bunch of these too, although I don't usually save the
ones where the opponent has only two rolls left. Here's one,
chosen more or less at random from my files.

XGID=--BBBBD-A---A-A--------bc-:1:1:1:61:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O |
| | | O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| | | X | +---+
| | | X X X X X | | 2 |
| X X | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 86 O: 7 X-O: 0-0
Cube: 2, X own cube
X to play 61

---
Tim Chow

On November 20, 2022 at 12:55:15 PM UTC-7, Tim Chow wrote:

> On 11/20/2022 5:38 AM, Stick Rice wrote:

>> I always save these straightforward yet
>> don't fall asleep on me save the gammon
>> type plays. I have accumulated quite the
>> collection of naturally occurring positions.

The thread title still has "reptile brain", so I'm
reading on...

"Save the gammon type plays" mostly occur
very late in games, thus are limited enough in
numbers, thus almost all are likely to "occur
naturally", unless you limit yourself to define
naturally as only in "bot vs bot" games.

> I have a bunch of these too, although I don't
> usually save the ones where the opponent
> has only two rolls left.

Why not? There are too many of them? They
don't matter as much as when there are three
rolls left? Four rolls left? Fifteen rolls left?

> Here's one, chosen more or less at random
> from my files.
> XGID=--BBBBD-A---A-A--------bc-:1:1:1:61:0:0:0:0:10

I fail to see any relevance of this position to
Axel's point. Maybe it's there but I can't see it.
Can you explain?

In all levels, your preferred bot XG's first choice
is 12/6 8/7 which is one of the right moves and
thus everything else after that is moot.

The other right move 12/6 2/1 is XG's third best
move.

You may ask what happened to 12/6 14/13 which
is XG's second best move? Well, it's a wrog move
that ranks second in all levels of XG!

Since all moves after XG's first choice of 12/6 8/7
are moot, it shouldn't matter, right? Wrong!

It means a lizard has sneaked into XG's AI brain...

This concerns me because in his original post,
Axel equates auto-pilot brain with reptile brain
and it can have far reaching implications in real
life.

I sure woul hope that when a jumbo jet is flying
on auto-pilot, it's not flown by some lizard/s...

Oh, one last thing, an advice to Axel and all, please
be careful when you ask gamblegammon players
to "switch off their reptile brains".

It may be the only brains they have... ;)

MK

On 11/21/2022 6:28 AM, MK wrote:
> "Save the gammon type plays" mostly occur
> very late in games, thus are limited enough in
> numbers, thus almost all are likely to "occur
> naturally", unless you limit yourself to define
> naturally as only in "bot vs bot" games.

I think Stick meant that one can contrive such positions that
never arose in an actual game. Such a contrived position would
not be "naturally occurring."

>> I have a bunch of these too, although I don't
>> usually save the ones where the opponent
>> has only two rolls left.
>
> Why not? There are too many of them? They
> don't matter as much as when there are three
> rolls left? Four rolls left? Fifteen rolls left?

They're too easy to figure out.

>> Here's one, chosen more or less at random
>> from my files.
>> XGID=--BBBBD-A---A-A--------bc-:1:1:1:61:0:0:0:0:10
>
> I fail to see any relevance of this position to
> Axel's point. Maybe it's there but I can't see it.
> Can you explain?

When I'm on auto-pilot, I usually move the checker in my opponent's
outfield rather than my own outfield, so in this position, my "reptile
brain" would play 12/6 14/13.

> In all levels, your preferred bot XG's first choice
> is 12/6 8/7 which is one of the right moves and
> thus everything else after that is moot.
>
> The other right move 12/6 2/1 is XG's third best
> move.

I don't understand why you describe 12/6 2/1 as "the other right move."

---
Tim Chow

On November 21, 2022 at 7:04:57 AM UTC-7, Tim Chow wrote:

> On 11/21/2022 6:28 AM, MK wrote:

>> "Save the gammon type plays" mostly occur
>> very late in games, thus are limited enough in
>> numbers, thus almost all are likely to "occur
>> naturally", unless you limit yourself to define
>> naturally as only in "bot vs bot" games.

> I think Stick meant that one can contrive such
> positions that never arose in an actual game.
> Such a contrived position would not be
> "naturally occurring."

Yes, I got that. What I mean is that towards the
ends of games, tree branches taper, especially
in bot vs. bot games but in human games more
unusual positions will occur naturally, thus there
won't be much need to "contrive"...

>>> I have a bunch of these too, although I don't
>>> usually save the ones where the opponent
>>> has only two rolls left.

>> Why not? .....

> They're too easy to figure out.

Okay, but I thought Axel's point was that often
they appear deceptively too simple and "reptile
brain" misplays them, right when errors cost the
most (i.e. at the very end of the games). This is
what made it interesting for me.

>>> XGID=--BBBBD-A---A-A--------bc-:1:1:1:61:0:0:0:0:10

>> I fail to see any relevance of this position to
>> Axel's point. Maybe it's there but I can't see it.
>> Can you explain?

> When I'm on auto-pilot, I usually move the
> checker in my opponent's outfield rather than
> my own outfield, so in this position, my "reptile
> brain" would play 12/6 14/13.

I see. I didn't find it interesting because my reptile
brain played 12/6 8/7 (which is one of the right
moves). I guess reptile brains vary...

>> The other right move 12/6 2/1 is XG's third
>> best move.

> I don't understand why you describe 12/6 2/1
> as "the other right move."

Since I didn't find it unusual, I thought that there
may be something hidden deeper. So, I imported
the XGID to see how the bot played. Your move,
which is also the bot's second choice, creates an
additional anti-joker of a 21 followed by a 53 but
the bot's third choice 12/6 2/1 doesn't.

Since the bot's first choice is one of the two right
moves, it doesn't change the outcome but how a
bot can miss what even I could see...? That why I
said a lizard must have sneaked into XG's AI brain. :)

MK

On 11/23/2022 4:40 PM, MK wrote:
>>> The other right move 12/6 2/1 is XG's third
>>> best move.
>
>> I don't understand why you describe 12/6 2/1
>> as "the other right move."
>
> Since I didn't find it unusual, I thought that there
> may be something hidden deeper. So, I imported
> the XGID to see how the bot played. Your move,
> which is also the bot's second choice, creates an
> additional anti-joker of a 21 followed by a 53 but
> the bot's third choice 12/6 2/1 doesn't.
>
> Since the bot's first choice is one of the two right
> moves, it doesn't change the outcome but how a
> bot can miss what even I could see...? That why I
> said a lizard must have sneaked into XG's AI brain. :)

But 12/6 2/1 is certainly a bad move and not right.
If I play 12/6 2/1 (and the opponent doesn't roll doublets)
then on my next turn, if I roll 61 51 41 31 or 21, then I can't
get two crossovers. That forces me to roll doublets after
that to get off the gammon.

---
Tim Chow

On November 24, 2022 at 5:00:41 PM UTC-7, Tim Chow wrote:

> But 12/6 2/1 is certainly a bad move and not right.
> If I play 12/6 2/1 (and the opponent doesn't roll
> doublets) then on my next turn, if I roll 61 51 41 31
> or 21, then I can't get two crossovers. That forces
> me to roll doublets after that to get off the gammon.

It's the same if you roll a lone 1 in the other two cases
also but since I had pointed out the 53 followed by 21,
I first wanted to double check that. Guess what? A 21
followed by 53 plays differently... :o)

I'm not used to analyse and discuss positions at such
detail. So, now where do I/we go from here...?

I think we should let Paul handle this for us... ;)

MK

On 11/24/2022 10:26 PM, MK wrote:
> On November 24, 2022 at 5:00:41 PM UTC-7, Tim Chow wrote:
>
>> But 12/6 2/1 is certainly a bad move and not right.
>> If I play 12/6 2/1 (and the opponent doesn't roll
>> doublets) then on my next turn, if I roll 61 51 41 31
>> or 21, then I can't get two crossovers. That forces
>> me to roll doublets after that to get off the gammon.
>
> It's the same if you roll a lone 1 in the other two cases
> also but since I had pointed out the 53 followed by 21,
> I first wanted to double check that. Guess what? A 21
> followed by 53 plays differently... :o)

I don't quite understand what you're saying here. Are you
now agreeing that the computer is correct when it says that
12/6 2/1 is third best, and that 12/6 2/1 is not a correct
move?

---
Tim Chow

On November 25, 2022 at 10:35:39 AM UTC-7, Tim Chow wrote:

> On 11/24/2022 10:26 PM, MK wrote:

>> It's the same if you roll a lone 1 in the other two cases
>> also but since I had pointed out the 53 followed by 21,
>> I first wanted to double check that. Guess what? A 21
>> followed by 53 plays differently... :o)

> I don't quite understand what you're saying here.
> Are you now agreeing that the computer is correct
> when it says that 12/6 2/1 is third best, and that
> 12/6 2/1 is not a correct move?

No. What I was trying to say is that 12/6 2/1 is still
better than 12/6 14/13 but not as good as 12/6 8/7
because if you roll 21 then 53 instead of 53 then 21,
12/6 2/1 will lose with 22 also on the last roll (which
was a real shocker for me in such a position). If this
is still not clear, here is my analysis a la Paul :)

After playing 12/6 8/7
------------------------
66 55 44 save immediately
If first roll > 7 (i.e. 65 64 63 62 56 54 53 46 45 36 35
33 26 22), all next rolls save including lone 1s
If first roll <= 7 and next roll has a lone 1, it loses

If first roll has a 1 and is 61 16, next roll needs any
doubles (i.e. 11 22 33 44 55 66)
If first roll with a lone 1 is 51 15 41 14 31 13 21 12,
next roll needs doubles => 8 (i.e. 22 33 44 55 66)

After playing 12/6 14/13
---------------------------
66 55 44 save immediately
If first roll > 7 (i.e. 65 64 63 62 56 46 36 26 33 22)
[*except 53 35 54 45*] all next rolls save including lone 1s
If first roll <= 7 and next roll has a lone 1, it loses

If first roll has a 1 and is 61 16, next roll needs any
doubles (i.e. 11 22 33 44 55 66)
If first roll with a lone 1 is 51 15 41 14 31 13 21 12,
next roll needs doubles => 8 (i.e. 22 33 44 55 66)

After playing 12/6 2/1
------------------------
66 55 44 save immediately
If first roll > 7 (i.e. 65 64 63 62 56 54 53 46 45 36 35
33 26 22) all next rolls save including lone 1s

If first roll has a 1 and is 61 16, next roll needs any
doubles (i.e. 11 22 33 44 55 66)
If first roll with a lone 1 is 51 15 41 14 31 13, next
roll needs doubles => 8 (i.e. 22 33 44 55 66)
If first roll with a lone 1 is 21 12, next roll needs
doubles > 8 (i.e. 33 44 55 66) [*22 loses*]

Difference between 12/6 8/7 and 12/6 14/13:
12/6 14/13 loses with 53 35 54 45 (on first roll)

Difference between 12/6 8/7 and 12/6 2/1:
12/6 2/1 loses with 21 12 (on first roll)

Difference between 12/6 14/13 and 12/6 2/1:
12/6 14/13 loses with 4, 12/6 2/1 with 2 rolls

Thus, 12/6 8/7 should be first, 12/6 2/1 second
and 12/6 14/13 third best play.

Phew! I think I overtook Paul. ;) Lots of repeated
copy/paste above but if anyone finds non-typing
errors in my analysis, I may never try this again. :(

MK

On 11/25/2022 4:45 PM, MK wrote:

> After playing 12/6 8/7
> ------------------------
> 66 55 44 save immediately
> If first roll > 7 (i.e. 65 64 63 62 56 54 53 46 45 36 35
> 33 26 22), all next rolls save including lone 1s
> If first roll <= 7 and next roll has a lone 1, it loses
>
> If first roll has a 1 and is 61 16, next roll needs any
> doubles (i.e. 11 22 33 44 55 66)

If I understand you correctly, you're supposing that we first
play 12/6 8/7, and then we roll 61, which I would play 14/8 7/6.
Now what do you mean that the next roll "needs any doubles"?
We have just one checker outside our board, on the 8pt, so all
kinds of non-doubles will get us off the gammon---even 32 will
work.

---
Tim Chow

On November 26, 2022 at 8:54:29 AM UTC-7, Tim Chow wrote:

> On 11/25/2022 4:45 PM, MK wrote:

>> After playing 12/6 8/7
>> .....
>> If first roll <= 7 and next roll has a lone 1, it loses
>> If first roll has a 1 and is 61 16, next roll needs
>> any doubles (i.e. 11 22 33 44 55 66)

> We have just one checker outside our board,
> on the 8pt, so all kinds of non-doubles will
> get us off the gammon---even 32 will work.

Yes, you are right. Actually, that line wasn't
necessary at all since the line above it already
covers 61 16 as <= 7. In fact, the line below it
should have included "all kinds of non-doubles
that save the gammon" as well as doubles also.

I never disputed that 12/6 8/7 is the best play,
which was my reptile play also. I was making
an issue of XG's getting the second and third
best plays backwards.

So, in my post, I first only compared them and
wasn't going to say anything about the 12/6 8/7
but then I thought my analysis would be more
complete with it and I hacked a paragraph for
it from the other two just before I posted.

Let's ignore 12/6 8/7 and concentrate on the
12/6 14/13 and 12/6 2/1. Do you guys agree
with me that XG got them in the wrong order?

This is the critical question and depending on
the answer, there may/will be a lot more to say
about XG...

MK

On 11/26/2022 4:24 PM, MK wrote:
> Let's ignore 12/6 8/7 and concentrate on the
> 12/6 14/13 and 12/6 2/1. Do you guys agree
> with me that XG got them in the wrong order?

No, I don't, and I explained why. 12/6 2/1 is worse because
if X rolls a single 1 on the next roll, then X can't get two
crossovers, and must roll doublets after that to get off the
gammon. If on the other hand X plays 14/13 12/6 and then X
rolls a single 1 on the next roll, then the single 1 can be
played 13/12, and the other die can be used to bring home the
other checker; then 66 65 64 63 62 55 44 33 22 all get off
the gammon.

There are some other differences between the two plays but
this is the main issue.

---
Tim Chow

On November 26, 2022 at 10:22:42 PM UTC-7, Tim Chow wrote:

> On 11/26/2022 4:24 PM, MK wrote:

>> Let's ignore 12/6 8/7 and concentrate on the
>> 12/6 14/13 and 12/6 2/1. Do you guys agree
>> with me that XG got them in the wrong order?

> There are some other differences between
> the two plays but this is the main issue.

Yes, okay, well enough. I thought I had caught
an easy glitch in XG but I just pasted the XGID
to Gnubg which eveluates the position with all
the same exact numbers. I should have done
this as first thing and shouldn't have pursued
it any further, which has been a waste of time
and effort on something that I don't particularly
enjoy doing much anyway. This many reptiles
should be enough to last me for a while... I'll go
on to other threads, especially to one that has
been aging for a while. It's time to pop that cork.

MK