54 safe or bold

[Robert Zimmerman]

XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O X O O | | O O O |
| O O X O O | | O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X X | | |
| X O X X X | | X |
| X X O X X X | | X |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 104 O: 118 X-O: 0-0
Cube: 1
X to play 54

Bob

[Timothy Chow]

I'd break anchor here. If we don't break anchor then 6/1 is the 5
and then the 4 is either 8/4 or 5/1, and either way, our position
has deteriorated and will likely continue to deteriorate. So 21/16,
and then I would cover the blot with 5/1 rather than continue with
16/12; the blot on the 1pt is a liability and O's 3's are duplicated.
We could get attacked, of course, but we have the stronger board and
have decent chances of survival. And we gain a lot if we are not hit.

---
Tim Chow

[Robert Zimmerman]

XG agrees, Tim, that the blot on the ace point is a liability. It prefers covering to moving the runner past O's outfield blot (Question for you: how do you know that XG just doesn't want to risk an indirect shot from O's anchor, which escapes and hits at once, and chooses the covering 5 for that reason?). But ultimately, it's willing to kill the spare on the 5 point rather than break the anchor at all. Below is a variant that kills O's outfield blot and makes it a closer call between breaking anchor and killing a checker. It's an unsubtle change to the position, not surprising given the differences in equities in the original.

Bob

XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O X O O | | O O O |
| O O X O O | | O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X X | | |
| X O X X X | | X |
| X X O X X X | | X |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 104 O: 118 X-O: 0-0
Cube: 1
X to play 54

1. Rollout¹ 6/1 5/1 eq:-0.065
Player: 48.55% (G:9.75% B:0.23%)
Opponent: 51.45% (G:11.22% B:0.39%)
Confidence: ±0.009 (-0.074..-0.056) - [100.0%]
Duration: 2 minutes 00 second

2. Rollout¹ 21/16 5/1 eq:-0.214 (-0.149)
Player: 43.10% (G:11.48% B:0.37%)
Opponent: 56.90% (G:14.72% B:0.37%)
Confidence: ±0.010 (-0.224..-0.205) - [0.0%]
Duration: 1 minute 03 seconds

3. Rollout¹ 21/12 eq:-0.288 (-0.223)
Player: 41.20% (G:11.68% B:0.42%)
Opponent: 58.80% (G:15.41% B:0.51%)
Confidence: ±0.009 (-0.297..-0.279) - [0.0%]
Duration: 55.1 seconds

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

eXtreme Gammon Version: 2.10


VARIANT
======================
XGID=-ABbBCC-B--------bbbbBcb--:0:0:1:54:0:0:3:0:10

Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O X O O | | O O |
| O O X O O | | O O |
| O | | |
| | | |
| | | |

| |BAR| |
| | | |
| | | |
| X X | | |
| X O X X X | | X |
| X X O X X X | | X |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+

Pip count X: 104 O: 109 X-O: 0-0

Cube: 1
X to play 54

1. Rollout¹ 21/16 5/1 eq:+0.186
Player: 55.46% (G:14.89% B:0.72%)
Opponent: 44.54% (G:11.24% B:0.29%)
Confidence: ±0.011 (+0.176..+0.197) - [100.0%]
Duration: 1 minute 32 seconds

2. Rollout¹ 6/1 5/1 eq:+0.139 (-0.047)
Player: 53.77% (G:12.00% B:0.24%)
Opponent: 46.23% (G:9.47% B:0.42%)
Confidence: ±0.010 (+0.129..+0.148) - [0.0%]
Duration: 2 minutes 18 seconds

3. Rollout¹ 21/12 eq:-0.089 (-0.275)
Player: 48.41% (G:11.96% B:0.47%)
Opponent: 51.59% (G:14.26% B:0.47%)
Confidence: ±0.008 (-0.097..-0.081) - [0.0%]
Duration: 1 minute 22 seconds

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

eXtreme Gammon Version: 2.10

[Timothy Chow]

On 3/1/2023 1:01 PM, Robert Zimmerman wrote:
> XG agrees, Tim, that the blot on the ace point is a liability. It prefers covering to moving the runner past O's outfield blot (Question for you: how do you know that XG just doesn't want to risk an indirect shot from O's anchor, which escapes and hits at once, and chooses the covering 5 for that reason?).

I'm not sure I understand the question. You're asking why,
if 21/16 is my 5, I chose 5/1 for the 4 instead of 16/12?
That maybe my reasoning is wrong and that avoiding shots is
the main point? But if avoiding shots were the main point
then surely one would play 16/12, to avoid the direct shot
from O's outfield blot.

Here are two variants that may yield further insight. In
Variant 1, I think that O's duplicated 4s may be the reason
why the equity difference between the two plays is smaller
than in your original position. In Variant 2, I have made
a further change by pushing O's anchor back a pip, and this
is enough to swing the play.

---------
Variant 1
---------

XGID=-ABbCBC-B---a----bbbbBbb--:0:0:1:53:0:0:0:0:10

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 X O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| X | | X X X O X |
| O X | | X X X O X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 103 O: 119 X-O: 0-0
Cube: 1
X to play 53

1. Rollout¹ 6/1 4/1 eq:-0.097
Player: 47.72% (G:10.03% B:0.22%)
Opponent: 52.28% (G:11.94% B:0.44%)
Confidence: ±0.011 (-0.108..-0.086) - [100.0%]

2. Rollout¹ 21/16 4/1 eq:-0.135 (-0.038)
Player: 45.95% (G:12.28% B:0.40%)
Opponent: 54.05% (G:14.91% B:0.41%)
Confidence: ±0.010 (-0.145..-0.125) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.

Dice Seed: 271828

Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

---------
Variant 2
---------

XGID=-AbBCBC-B---a----bbbbBbb--:0:0:1:53:0:0:0:0:10

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 X O O |
| | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |

| X | | X X X X O |

| O X | | X X X X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 105 O: 121 X-O: 0-0
Cube: 1
X to play 53

1. Rollout¹ 21/16 4/1 eq:+0.305
Player: 57.64% (G:15.98% B:1.15%)
Opponent: 42.36% (G:10.42% B:0.29%)
Confidence: ±0.006 (+0.299..+0.311) - [99.9%]

2. Rollout¹ 6/1 4/1 eq:+0.291 (-0.014)
Player: 58.12% (G:14.54% B:0.47%)
Opponent: 41.88% (G:8.86% B:0.31%)
Confidence: ±0.006 (+0.285..+0.297) - [0.1%]

¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 271828

Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

[Robert Zimmerman]

I was definitely unclear. For one, I made a typo "covering 5" should be "covering 4". But I'll try to clarify.

Running play 21/16 5/1 leaves O with 13 hits. O will still need to free her back checkers.
Running play 21/12 leaves O with 4 indirect shots that free a back checker at the same time, a much less desirable hit to X.
My question was: Is X accepting those extra 9 hits for the sake of covering the ace point blot, or is X more motivated by the avoidance of the hit and run by O. With more time to consider it, it's pretty apparent that X is accepting the extra shots to cover the ace point and really for no other reason. The reason you were confused, most likely, is that my alternative explanation is so tortured and wrong you couldn't fathom it. I do sometimes overcomplicate the straight forward.
I will say that I did not understand how much of a liability that ace point blot is, so this has been instructive. Thanks!

Bob

[MK]

On February 27, 2023 at 3:06:43 PM UTC-7, Robert Zimmerman wrote:

> XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10

As I developed an interest in the possibility of bots
making "this or that", "such vs. such" checker play
decisions (specifically based on but not limited to
score), I have been reading at least the first posts
in threads with related titles and had marked this
one as possibly interesting to keep an eye on.

Too bad that thus far only two people participated
but even so it became quite a spectacle beyond my
expectations. :)

I will give it a little more time to see if anyone else
will join the circus (bozo costume optional). Then,
posts will be answered in the order received... ;)

MK

[MK]

On February 28, 2023 at 7:09:53 AM UTC-7, Timothy Chow wrote:

> On 2/27/2023 5:06 PM, Robert Zimmerman wrote:

>> XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10

>> X to play 54

> I'd break anchor here ... And we gain a lot if we are not hit.

I'm surprised that more people haven't participated in
this thread which I thought would be very interesting.

It looks like all the bozos of RGB have they gone Walt
on me but I won't retaliate... ;)

As I have pointed out countless times over the years
that by their nature, even the gamblegammon playing
bots don't gamble.

It may be interesting for humans to discuss "pay now
or later", "safe or bold", etc. it's totally idiotic to consult
bot rollouts because of the plain fact that bots always
pay later, always play safe, etc.

The correct play here is 6/1 5/1 and it's also the play
referred to as the "safe" one here. Thus, any/all other
moves can then be said to be the "bold" one/s.

I'm not necessarily saying that Tim or other humans
who wouldn't play 6/1 5/1 here are all wrong. In fact,
it may very well be the opposite and that the bot may
be wrong because of its inability adjust its play to the
score (let alone to the skill level of its opponent).

Here are some examples to show how the bot/s will
play 6/1 5/1 regardless of the cube value in a money
game. (I will post separately on match games.)

All hints from analysis level set to XGR++.

Position in initial post with jacoby on:
6/1 5/1 eq:-0.0472 [49.1% 8.5% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.2177 (-0.1705) [43.7% 12.0% 0.5% - 56.3% 15.0% 0.4%]

With jacoby off:
6/1 5/1 eq:-0.0488 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.2174 (-0.1686) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

I don't know why "game winning chances" are different
even if by very little but jacoby doesn't make difference
enough in this position to not play safe. Once the cube
is turned, all "game winning chances" remain the same
regardless of the cube value.

With X owning cube at 2:
6/1 5/1 eq:+0.2766 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.0388 (-0.3153) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

With X owning cube at 32:
6/1 5/1 eq:+4.4254 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.6201 (-5.0456) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

With O owning cube at 2:
6/1 5/1 eq:-0.4250 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.6973 (-0.2723) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

With O owning cube at 32:
6/1 5/1 eq:-6.7996 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-11.1564 (-4.3568) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Setting cube limits don't make any difference either.
Playing a 1-point match, i.e. without risking to lose a
gammon or backgammon, doesn't make a difference.
1-away/2-away/crawford combinations don't matter.

Do you think bots are capable of making "bold" plays
depending on score and/or cube value in matches..?
We will see in my next post...

MK

[MK]

On March 1, 2023 at 11:01:09 AM UTC-7, Robert Zimmerman wrote:

> XG agrees, Tim, that the blot on the ace point is a liability.

Ha ha ha! This is beyond funny. :) Did Ex-Gee tell you
that or did you read Ex-Gee's mind...?

Our new puppy with etiquette, fresh out of obedience
school, kissing up to Tim, trying to find his existence
among the RBG's pack of sick dogs... (One thing I've
never figured out is "Who is the alpha female? Tim?")

Anyways, let's get serious and get back to our topic.

> Below is a variant that kills O's outfield blot and makes

> It's an unsubtle change to the position, ....
> VARIANT

> XGID=-ABbBCC-B--------bbbbBcb--:0:0:1:54:0:0:3:0:10

> X to play 54
> 1. Rollout¹ 21/16 5/1 eq:+0.186

What is accomplished by creating a variant position to
make 21/16 5/1 the top play unless 21/16 5/1 is still a
the "bold" play in the variant position also, as it was one
in the original position..?

The question "54 safe or bold" applies differently to it!

But there are different ways of looking at variants of a
position where the "position itself" is not the variant.

Let's look at the same position at varying scores within
a cubeless 5-point match play, for example:

Score X=0, O=0:
6/1 5/1 eq:-0.0502 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 eq:-0.2290 (-0.1788) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Since this is a match, let's switch from equity to mwc.
6/1 5/1 mwc: 49.634% [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 mwc: 48.328 (-1.305) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Bot starts out playing safe.

Score X=0, O=4:
6/1 5/1 mwc: 16.993% [49.4% 7.8% 0.1% - 50.6% 9.7% 0.3%]
21/16 5/1 mwc: 15.682 (-1.311) [43.3% 10.6% 0.2% - 56.% 14.4% 0.4%]

I don't know why "game winning chances" are different,
even if by little but the bot plays safe when way behind.

Score X=4, O=0:
6/1 5/1 mwc: 82.050% [49.0% 8.4% 0.1% - 51.0% 9.7% 0.3%]
8/4 6/1 mwc: 79.370 (-2.680) [40.3% 7.5% 0.1% - 59.7% 9.6% 0.2%]
21/16 5/1 mwc: 79.369 (-2.681) [44.0% 11.9% 0.4% - 56.6% 14.9% 0.6%]

Wow! What an accuracy! 8/4 6/1 replaces 21/16 5/1 as
the second choice by 0.0001 :) But what matters is that
the bot plays safe when way ahead also.

Score X=4, O=4:
6/1 5/1 mwc: 49.101% [49.1% 8.5% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 mwc: 43.694 (-5.407) [43.7% 12.0% 0.5% - 56.3% 15.0% 0.4%]

No reason to play other than the best move. Well enough.

Score X=3, O=0:
6/1 5/1 mwc: 74.453% [49.0% 8.7% 0.1% - 51.0% 9.9% 0.3%]
21/16 5/1 mwc: 72.839 (-1.613) [43.7% 11.9% 0.5% - 56.3% 14.9% 0.4%]

The bot is quite ahead and a gammon can win the match
but it still plays safe.

Maybe this is why Philippe Michel had said, in this thread:

https://groups.google.com/g/rec.games.backgammon/c/9ICaJyXz1B0/m/w9q7cVUVEQAJ

"As far as play decisions go, this is irrelevant.
"Whatever the set score, your goal is to win
"the match you are playing.

Perhaps gamblegammon bots are just not good at playing
cubeless classic backgammon...

But can they adjust their checker play to the score and the
cube value in cubeful gamblegammon matches?

We'll take a look at that in my next post...

MK

[MK]

On March 1, 2023 at 10:08:48 PM UTC-7, Timothy Chow wrote:

> I'm not sure I understand the question.....

> Here are two variants that may yield further insight.

"Insight" to what...!?

> In Variant 1, I think that O's duplicated 4s may be the
> reason why the equity difference between the two
> plays is smaller than in your original position.

One reason is that in your variant jacoby is turned off.

> Variant 1

> XGID=-ABbCBC-B---a----bbbbBbb--:0:0:1:53:0:0:0:0:10

> X to play 53

With jacoby off:
6/1 4/1 eq:-0.0603 [48.3% 8.4% 0.1% - 51.7% 10.3% 0.3%]
21/16 4/1 eq:-0.1157 (-0.0554) [46.0% 11.2% 0.3% - 54.0% 14.0% 0.4%]

With jacoby on:
6/1 4/1 eq:-0.0784 [48.1% 9.3% 0.1% - 51.9% 10.4% 0.4%]
21/16 4/1 eq:-0.1740 (-0.0956) [45.4% 11.6% 0.3% - 54.6% 10.4% 0.4%]

Zimmer's example with jacoby on:
6/1 5/1 eq:-0.0472 [49.1% 8.5% 0.1% - 50.9% 9.9% 0.3%]
21/16 5/1 eq:-0.2177 (-0.1705) [43.7% 12.0% 0.5% - 56.3% 15.0% 0.4%]

Zimmer's example with jacoby off:

6/1 5/1 eq:-0.0488 [49.1% 8.6% 0.1% - 50.9% 9.9% 0.3%]

21/16 5/1 eq:-0.2174 (-0.1686) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Even with jacoby off for both positions, you made 21/16 5/1
"less bold". So what? Should the thread title be changed now
to say "53 safe or boldish"...?

> In Variant 2, I have made a further change by pushing O's
> anchor back a pip, and this is enough to swing the play.

As I had commented to Zimmer, what do you think you are
accomplishing by concocting such a different position that
the original question "54 safe or bold" doesn't apply...? The
ideas of "safe or bold" are totally different in your variant,
in which you left jacoby turned off again, that makes some
difference in the opposite direction.

> Variant 2

> XGID=-AbBCBC-B---a----bbbbBbb--:0:0:1:53:0:0:0:0:10

> X to play 53

Variant with jacoby off:
21/16 4/1 eq:+0.2941 [57.5% 16.1% 1.2% - 42.5% 10.5% 0.3%]
6/1 4/1 eq:+0.2814 (-0.0127) [58.1% 14.7% 0.5% - 41.9% 8.9% 0.3%]

Variant with jacoby on:
21/16 4/1 eq:+0.2976 [57.6% 16.2% 1.2% - 42.4% 10.4% 0.3%]
6/1 4/1 eq:+0.2965 (-0.0010) [58.2% 13.4% 0.5% - 44.6% 8.9% 0.3%]

Variant with X owning the cube at 2:
21/16 4/1 eq:+0.8367 [57.4% 16.1% 1.2% - 42.6% 10.5% 0.3%]
6/1 4/1 eq:+0.8215 (-0.0152) [58.1% 14.2% 0.5% - 41.9% 8.8% 0.3%]

Variant with X owning the cube at 32:
21/16 4/1 eq:+13.3878 [57.4% 16.1% 1.2% - 42.6% 10.5% 0.3%]
6/1 4/1 eq:+13.1444 (-0.2433) [58.1% 14.2% 0.5% - 41.9% 8.8% 0.3%]

Variant with O owning the cube at 2:
6/1 4/1 eq:+0.0861 [58.7% 13.7% 0.5% - 41.3% 8.7% 0.3%]
21/16 4/1 eq:+0.0539 (-0.0322) [57.8% 16.1% 1.2% - 42.2% 10.4% 0.3%]

Lo and behold! Ownership of cube makes a difference in your
variant while it didn't in Zimmer's original position.

Variant with O owning the cube at 32:
6/1 4/1 eq:+0.0861 [58.7% 13.7% 0.5% - 41.3% 8.7% 0.3%]
21/16 4/1 eq:+0.0539 (-0.0322) [57.8% 16.1% 1.2% - 42.2% 10.4% 0.3%]

Lo and behold! When O is owning the cube, the value of the
cube doesn't affect X's equity...

Is this a bug or a beetle...? ;)

MK

[MK]

On March 2, 2023 at 7:23:45 AM UTC-7, Robert Zimmerman wrote:

> I was definitely unclear. For one, I made a typo
> covering 5" should be "covering 4". But I'll try to clarify.

Yes, please do because correcting your typo still doesn't
make clear what do you mean by covering the already
covered 5 (or 4). Do you mean putting another layer of
tarp over them...?

> The reason you were confused, most likely, is that my
> alternative explanation is so tortured and wrong you
> couldn't fathom it.

When you said you play backgammon because of your
masochistic tendencies, I didn't think you were going to
pee all over yourself in RGB... :( But enough of blotting
Bob, lets go back to our "54 safe or bold" discussion.

> XGID=-ABbBCC-B----a---bbbbBbb--:0:0:1:54:0:0:3:0:10

> X to play 54

I spent over half hour trying all kinds of combinations of
match lengths and match scores and cube values to see
if Ex-Gee would make a move other than 6/1 5/1. Here
are some examples based on an 11-point match:

Score X=0, O=0:
6/1 5/1 eq:-0.0493 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 eq:-0.21795 (-0.1702) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Score X=9, O=0:
6/1 5/1 eq:-0.2112 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/12 eq:-0.3942 (-0.1830) [43.4% 10.9% 0.3% - 56.6% 14.8% 0.6%]
21/16 5/1 eq:-0.4322 (-0.2210) [44.0% 11.9% 0.4% - 56.0% 14.9% 0.6%]

Interestingly/unexpectedly 21/12 takes second place but
the bot plays 6/1 5/1 as expected.

Score X=0, O=9:
6/1 5/1 eq:+0.1160 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 eq:-0.0361 (-0.1521) [43.7% 11.0% 0.2% - 56.3% 14.8% 0.4%]

Score X=8, O=8 cube owned by X at 2:
6/1 5/1 eq:+0.1579 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 eq:-0.0130 (-0.1709) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

Score X=8, O=8 cube owned by X at 4:
6/1 5/1 eq:-0.180 [49.1% 8.6% 0.1% - 50.9% 9.8% 0.3%]
21/16 5/1 eq:-0.1261 (-0.1081) [43.8% 10.6% 0.2% - 56.2% 14.6% 0.4%]

And so on.... In all that time, I came accross only a few match
lengths and match scores and cube values combinations that
Ex-Gee actually played 21/16 5/1.

As you may have guesses, I was clueless as to what caused
Ex-Gee to play anything other than 6/1 5/1 in those situations.

For now, I won't share those situations with you here in order
to see if anyone of you can come up with similar examples
and/or if any of the AI-bot developers here can directly give
any explanations based on their having programmed some
algorithms into their gamblegammon bots.

If I don't hear a yip, yap, yelp, yowl, howl, bark, grunt, etc. for
a while, I will post my examples and let you chew on them... ;)

MK