• 54 safe or bold

    From Robert Zimmerman@21:1/5 to All on Mon Feb 27 14:06:41 2023
    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to Robert Zimmerman on Tue Feb 28 09:09:51 2023
    On 2/27/2023 5:06 PM, Robert Zimmerman wrote:

    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

    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

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  • From Robert Zimmerman@21:1/5 to All on Wed Mar 1 10:01:07 2023
    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to Robert Zimmerman on Thu Mar 2 00:08:45 2023
    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Robert Zimmerman@21:1/5 to Timothy Chow on Thu Mar 2 06:23:44 2023
    On Thursday, March 2, 2023 at 12:08:48 AM UTC-5, Timothy Chow wrote:
    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
    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

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  • From MK@21:1/5 to Robert Zimmerman on Thu Mar 2 15:08:44 2023
    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From MK@21:1/5 to Timothy Chow on Sun Mar 5 23:26:56 2023
    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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From MK@21:1/5 to Robert Zimmerman on Mon Mar 6 01:01:46 2023
    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

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  • From MK@21:1/5 to Timothy Chow on Mon Mar 6 01:38:31 2023
    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

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  • From MK@21:1/5 to Robert Zimmerman on Mon Mar 6 02:29:22 2023
    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

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