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  • Escape or close the board?

    From Timothy Chow@21:1/5 to All on Fri Aug 12 07:11:15 2022
    XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

    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 X | +---+
    | O | | O O O O | | 2 |
    | | | O O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X X X |
    | | | X X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 74 O: 121 X-O: 0-0
    Cube: 2, O own cube
    X to play 51

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Fri Aug 12 10:34:39 2022
    On Friday, August 12, 2022 at 12:11:19 PM UTC+1, Tim Chow wrote:
    XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

    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 X | +---+
    | O | | O O O O | | 2 |
    | | | O O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X X X |
    | | | X X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 74 O: 121 X-O: 0-0
    Cube: 2, O own cube

    6/1 2/1 is correct.
    The large number of gammons we get when we escape are a huge factor.
    On a slow day for combinatorial game theory, I could easily imagine Tim
    doing a ton of variantizing by lessening and increasing the gammonability
    to change the play.

    The escape play might seem correct as a gamble on your opponent not rolling a 2.
    But your opponent's 2s will lose some gammons. There's a lot of value in taking away
    all of your opponent's gammons by closing out.
    After closing out, we win immediately with 51 and any 6 except 61.
    This is 11/36. If we don't get such a roll we can hope to escape before the opponent enters.

    Am I confident?

    Recently, I went to spectate a tennis tournament which officially had no spectators. However,
    there was a way of getting in which was to meet a competitor and ask to be on their guest list
    to gain entrance as a competitor's guest.
    I am as confident in my solution, as I was when asking players to sign me in as their guest.

    Paul

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to peps...@gmail.com on Sat Aug 13 09:23:37 2022
    On 8/12/2022 1:34 PM, peps...@gmail.com wrote:
    6/1 2/1 is correct.
    The large number of gammons we get when we escape are a huge factor.
    On a slow day for combinatorial game theory, I could easily imagine Tim doing a ton of variantizing by lessening and increasing the gammonability
    to change the play.

    The escape play might seem correct as a gamble on your opponent not rolling a 2.
    But your opponent's 2s will lose some gammons. There's a lot of value in taking away
    all of your opponent's gammons by closing out.
    After closing out, we win immediately with 51 and any 6 except 61.
    This is 11/36. If we don't get such a roll we can hope to escape before the opponent enters.

    Since you talk about closing out, I assume you meant to say
    "6/1 3/2" and that "6/1 2/1" is a typo?

    By the way, I don't know why you frequently mention combinatorial
    game theory. I haven't ever published anything in combinatorial
    game theory, and I don't even think about it much.

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From ah....Clem@21:1/5 to Timothy Chow on Sat Aug 13 12:41:25 2022
    On 8/12/2022 7:11 AM, Timothy Chow wrote:
    XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

    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     X | +---+
     |             O    |   | O  O  O  O       | | 2 |
     |                  |   | O  O             | +---+
     |                  |   |                  |
     |                  |   |                  |
     |                  |BAR|                  |
     |                  | O |                  |
     |                  |   |                  |
     |                  |   | X        X     X |
     |                  |   | X  X  X  X     X |
     |          O  O    |   | X  X  X  X  X  X |
     +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count  X: 74  O: 121 X-O: 0-0
    Cube: 2, O own cube
    X to play 51

    Sixes don't grow on trees and X is in danger of crunching. Escape!!!


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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Sat Aug 13 12:13:02 2022
    On Saturday, August 13, 2022 at 2:23:41 PM UTC+1, Tim Chow wrote:
    On 8/12/2022 1:34 PM, peps...@gmail.com wrote:
    6/1 2/1 is correct.
    The large number of gammons we get when we escape are a huge factor.
    On a slow day for combinatorial game theory, I could easily imagine Tim doing a ton of variantizing by lessening and increasing the gammonability to change the play.

    The escape play might seem correct as a gamble on your opponent not rolling a 2.
    But your opponent's 2s will lose some gammons. There's a lot of value in taking away
    all of your opponent's gammons by closing out.
    After closing out, we win immediately with 51 and any 6 except 61.
    This is 11/36. If we don't get such a roll we can hope to escape before the opponent enters.
    Since you talk about closing out, I assume you meant to say
    "6/1 3/2" and that "6/1 2/1" is a typo?

    By the way, I don't know why you frequently mention combinatorial
    game theory. I haven't ever published anything in combinatorial
    game theory, and I don't even think about it much.

    Yes, I meant the closeout play.
    Because backgammon isn't sufficiently interesting or stimulating (to me),
    I have to mention stuff outside backgammon so that I don't suffer intensely from extreme boredom.

    I'll try to pick on stuff that I know you have researched, next time.


    Paul

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sun Aug 14 09:31:38 2022
    XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

    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 X | +---+
    | O | | O O O O | | 2 |
    | | | O O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X X X |
    | | | X X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 74 O: 121 X-O: 0-0
    Cube: 2, O own cube
    X to play 51

    Closing the board is in triple-whopper territory.

    1. Rollout¹ 24/18 eq:+0.602
    Player: 67.63% (G:42.86% B:0.55%)
    Opponent: 32.37% (G:8.29% B:0.35%)
    Confidence: ±0.005 (+0.597..+0.607) - [100.0%]

    2. Rollout¹ 6/1 3/2 eq:+0.328 (-0.274)
    Player: 60.95% (G:31.98% B:0.21%)
    Opponent: 39.05% (G:3.06% B:0.08%)
    Confidence: ±0.007 (+0.321..+0.335) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From pepstein5@gmail.com@21:1/5 to Tim Chow on Sun Aug 14 11:41:04 2022
    On Sunday, August 14, 2022 at 2:31:42 PM UTC+1, Tim Chow wrote:
    XGID=aCACBBC-aa-------b-ccbb-A-:1:-1:1:51:0:0:0:0:10

    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 X | +---+
    | O | | O O O O | | 2 |
    | | | O O | +---+
    | | | |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | X X X |
    | | | X X X X X |
    | O O | | X X X X X X |
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 74 O: 121 X-O: 0-0
    Cube: 2, O own cube
    X to play 51

    Closing the board is in triple-whopper territory.

    1. Rollout¹ 24/18 eq:+0.602
    Player: 67.63% (G:42.86% B:0.55%)
    Opponent: 32.37% (G:8.29% B:0.35%)
    Confidence: ±0.005 (+0.597..+0.607) - [100.0%]

    2. Rollout¹ 6/1 3/2 eq:+0.328 (-0.274)
    Player: 60.95% (G:31.98% B:0.21%)
    Opponent: 39.05% (G:3.06% B:0.08%)
    Confidence: ±0.007 (+0.321..+0.335) - [0.0%]

    ¹ 1296 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 3-ply, cube decisions: XG Roller

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow
    Yes, I should have figured that. I like Walt's reasoning, brief though it was.

    Paul

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to peps...@gmail.com on Sun Aug 14 16:27:38 2022
    On 8/14/2022 2:41 PM, peps...@gmail.com wrote:
    Yes, I should have figured that. I like Walt's reasoning, brief though it was.

    Here's another way to think about it. If we close the board,
    what are we hoping for? A 6 or a 51; otherwise we're unhappy.
    Chances of a 6 or a 51 are 13/36. If we run, what are we hoping
    for? A dance; otherwise we're unhappy. Chances of a dance are
    25/36.

    We'd rather be in a situation where 25/36 rolls are good than in
    a situation where 13/36 rolls are good.

    ---
    Tim Chow

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