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  • Big advantage and high volatility means ND/T

    From [email protected]@21:1/5 to All on Sun May 15 02:02:17 2022
    Here, any 3 that is not answered with a 61 is surely a massive market loser This happens with probability 14/36 * 17/18 = 119/324. This is nearly
    37%. So I'm sure that _considering_ doubling is correct.
    One objection to doubling might be that I don't have a particularly big
    edge. I'm doing great if I get my 3, but I'm an underdog to make it,
    and maybe I'm doing badly enough if I miss to make it a hold.
    I thought this might be the case and that's why my double was by no
    means confident. The mystery (to me) is that the equity figures
    don't make sense. If there's not much to double about, why does D/T
    still give me 0.437??
    As the title says, big advantage + massive volatility = ND/T here.
    What's going on? How can I find my way to a hold in similar positions
    in future?


    XGID=a-BBABBA---------bAbbdBBd-:1:1:1:00:0:0:3:0:10
    X:Daniel O:eXtremeGammon


    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O X | | O O O X X O |
    | O | | O O O X X O |
    | | | O O |
    | | | O O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | | +---+
    | | | X X X X | | 2 |
    | X | | X X X X X | +---+
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 151 O: 83 X-O: 0-0
    Cube: 2, X own cube
    X on roll, cube action

    Analyzed in XG Roller+
    Player Winning Chances: 66.93% (G:15.89% B:0.53%)
    Opponent Winning Chances: 33.07% (G:15.79% B:0.73%)

    Cubeless Equities: No Double=+0.338, Double=+0.678

    Cubeful Equities:
    No redouble: +0.613
    Redouble/Take: +0.437 (-0.176)
    Redouble/Pass: +1.000 (+0.387)

    Best Cube action: No redouble / Take
    Percentage of wrong pass needed to make the double decision right: 23.8%

    eXtreme Gammon Version: 2.10

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to [email protected] on Sun May 15 15:33:06 2022
    On 5/15/2022 5:02 AM, [email protected] wrote:
    Here, any 3 that is not answered with a 61 is surely a massive market loser This happens with probability 14/36 * 17/18 = 119/324. This is nearly
    37%. So I'm sure that _considering_ doubling is correct.

    Well, if X rolls 31 then he might not lose his market, and even if X
    rolls 21 then O can probably take after 11 or 31 as well as 61. But
    that doesn't change your main point.

    One objection to doubling might be that I don't have a particularly big
    edge. I'm doing great if I get my 3, but I'm an underdog to make it,
    and maybe I'm doing badly enough if I miss to make it a hold.

    I believe this reasoning is sound.

    I thought this might be the case and that's why my double was by no
    means confident. The mystery (to me) is that the equity figures
    don't make sense. If there's not much to double about, why does D/T
    still give me 0.437??

    Redoubling as a backgamer is a little different from your typical
    redoubling decision. After a bad exchange, you typically have higher
    chances of getting gammoned than in a "typical" advantageous position.

    More generally, rules of thumb about the relationship between the
    equity and the cube action don't always hold for backgame positions.
    Dirk Schiemann discusses this point briefly in his book "Theory of
    Backgammon," though I think he only explicitly considers cube actions
    in which the backgamee is on roll, rather than post-hit backgamer
    cube actions.

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Timothy Chow@21:1/5 to All on Sun May 15 15:35:30 2022
    Oh, another thing is that if you roll it out, the size of the
    error seems to be smaller than what XGR+ thinks. I didn't feel
    like doing a full rollout, but the short rollout below should
    give you some idea.

    XGID=a-BBABBA---------bAbbdBBd-:1:1:1:00:0:0:3:0:10

    X:Player 1 O:Player 2
    Score is X:0 O:0. Unlimited Game, Jacoby Beaver
    +13-14-15-16-17-18------19-20-21-22-23-24-+
    | O X | | O O O X X O |
    | O | | O O O X X O |
    | | | O O |
    | | | O O |
    | | | |
    | |BAR| |
    | | O | |
    | | | |
    | | | | +---+
    | | | X X X X | | 2 |
    | X | | X X X X X | +---+
    +12-11-10--9--8--7-------6--5--4--3--2--1-+
    Pip count X: 151 O: 83 X-O: 0-0
    Cube: 2, X own cube
    X on roll, cube action

    Analyzed in Rollout
    No redouble
    Player Winning Chances: 67.02% (G:16.14% B:0.55%)
    Opponent Winning Chances: 32.98% (G:15.76% B:0.66%)
    Redouble/Take
    Player Winning Chances: 68.41% (G:17.19% B:0.77%)
    Opponent Winning Chances: 31.59% (G:15.83% B:0.64%)

    Cubeful Equities:
    No redouble: +0.634
    Redouble/Take: +0.555 (-0.080)
    Redouble/Pass: +1.000 (+0.366)

    Best Cube action: No redouble / Take
    Percentage of wrong pass needed to make the double decision right: 15.2%

    Rollout:
    400 Games rolled with Variance Reduction.
    Dice Seed: 271828
    Moves: 4-ply, cube decisions: XG Roller+
    Search interval: Large
    Confidence No Double: ± 0.013 (+0.621..+0.648)
    Confidence Double: ± 0.031 (+0.524..+0.586)

    eXtreme Gammon Version: 2.19.207.pre-release

    ---
    Tim Chow

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From [email protected]@21:1/5 to Tim Chow on Sun May 15 13:41:28 2022
    On Sunday, May 15, 2022 at 8:33:11 PM UTC+1, Tim Chow wrote:
    On 5/15/2022 5:02 AM, [email protected] wrote:
    Here, any 3 that is not answered with a 61 is surely a massive market loser This happens with probability 14/36 * 17/18 = 119/324. This is nearly
    37%. So I'm sure that _considering_ doubling is correct.
    Well, if X rolls 31 then he might not lose his market, and even if X
    rolls 21 then O can probably take after 11 or 31 as well as 61. But
    that doesn't change your main point.
    One objection to doubling might be that I don't have a particularly big edge. I'm doing great if I get my 3, but I'm an underdog to make it,
    and maybe I'm doing badly enough if I miss to make it a hold.
    I believe this reasoning is sound.
    I thought this might be the case and that's why my double was by no
    means confident. The mystery (to me) is that the equity figures
    don't make sense. If there's not much to double about, why does D/T
    still give me 0.437??
    Redoubling as a backgamer is a little different from your typical
    redoubling decision. After a bad exchange, you typically have higher
    chances of getting gammoned than in a "typical" advantageous position.

    More generally, rules of thumb about the relationship between the
    equity and the cube action don't always hold for backgame positions.
    Dirk Schiemann discusses this point briefly in his book "Theory of Backgammon," though I think he only explicitly considers cube actions
    in which the backgamee is on roll, rather than post-hit backgamer
    cube actions.

    I think my 3s aren't quite as good as they seem. I actually rolled a 33 after doubling
    (which is not one of the better 3s admittedly) and XG thought that increased my equity by 0.276 judging it to be below the joker threshold. When I'm stuck so far back,
    XG might have time for the ace and six. 3's are market losers, yes but not by so much
    that I need to double now.
    Thanks for your thoughts on this.

    Paul

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