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Handicap Backgammon. One start with cube.

Posted By: Rick Janowski
Date: Wednesday, 21 January 2015, at 12:40 a.m.

In Response To: Handicap Backgammon. One start with cube. (mochy)

Edge in Start Position (XG vs XG)

The edge can be calculated from equation (5) of my paper “Take-Points in Money Games”:

Cube-owned Equity Eo = CL*{p*(W+L+0.5*x)-L}, where:

CL = cube-level, or stake-level

p = cubeless win probability

W = Average value of Win

L = Average value of Loss

x = Cube-Ownership value.

In the opening position, where both sides can start, p = 0.0, and W = L, allowing the equation to simplify to: Eo = CL*x/4

The player holding a theoretical 1-cube is x/4 which equates to about 0.175, assuming x has the typical value of 0.7.

I checked this another way by considering XGR++ evaluated equities for each of the 21 opening rolls with either side starting and averaging for each roll and then averaging overall (these equities assume the player holds a theoretical 1-cube):

Eo = 0.1825 (ranging from 0.1813 to 0.1841)

This equates to an x-value of 0.73, incidentally.

PR-edge required for Fair-settlement

Using Xavier’s equation of Eo (holding 1-cube) = ppg = 0.066*PR-edge,

Fair settlement, PR-edge = 0.1825/0.066 = 2.77

With a PR-edge of 3, the player will be a small equity favourite with an expectation of about 1 point in every 66 games.

Messages In This Thread

• Handicap Backgammon. One start with cube.
  mochy -- Tuesday, 20 January 2015, at 5:30 a.m.
  • Handicap Backgammon. One start with cube.
    Stick -- Tuesday, 20 January 2015, at 5:40 a.m.
    • Handicap Backgammon. One start with cube.
      Bob Koca -- Tuesday, 20 January 2015, at 8:45 a.m.
    • Handicap Backgammon. One start with cube.
      Mochy -- Tuesday, 20 January 2015, at 10:40 a.m.
      • Handicap Backgammon. One start with cube.
        Bob Koca -- Tuesday, 20 January 2015, at 4:47 p.m.
      • Handicap Backgammon. One start with cube.
        mochy -- Wednesday, 21 January 2015, at 12:56 a.m.
  • Handicap Backgammon. One start with cube.
    Casper Van der Tak -- Tuesday, 20 January 2015, at 7:40 a.m.
    • Handicap Backgammon. One start with cube.
      Mochy -- Tuesday, 20 January 2015, at 10:27 a.m.
      • Handicap Backgammon. One start with cube.
        Casper Van der Tak -- Tuesday, 20 January 2015, at 10:38 a.m.
        • Handicap Backgammon. One start with cube.
          Mochy -- Tuesday, 20 January 2015, at 10:53 a.m.
  • Handicap Backgammon. One start with cube.
    AP -- Tuesday, 20 January 2015, at 8:15 a.m.
    • Handicap Backgammon. One start with cube.
      Mochy -- Tuesday, 20 January 2015, at 10:06 a.m.
  • Handicap Backgammon. One start with cube.
    Taper_Mike -- Tuesday, 20 January 2015, at 8:32 a.m.
    • Handicap Backgammon. One start with cube.
      Bob Koca -- Tuesday, 20 January 2015, at 8:39 a.m.
      • Handicap Backgammon. One start with cube.
        Taper_Mike -- Tuesday, 20 January 2015, at 9:54 a.m.
        • Handicap Backgammon. One start with cube.
          Bob Koca -- Tuesday, 20 January 2015, at 9:58 a.m.
          • Handicap Backgammon. One start with cube.
            Taper_Mike -- Tuesday, 20 January 2015, at 10:11 a.m.
      • Handicap Backgammon. One start with cube.
        Mochy -- Tuesday, 20 January 2015, at 9:55 a.m.
  • PR3.0 difference in money game
    Mochy -- Tuesday, 20 January 2015, at 10:03 a.m.
    • PR3.0 difference in money game
      Maik Stiebler -- Tuesday, 20 January 2015, at 2:50 p.m.
      • PR3.0 difference in money game
        Bob Koca -- Tuesday, 20 January 2015, at 3:40 p.m.
        • PR3.0 difference in money game
          Maik Stiebler -- Thursday, 22 January 2015, at 9:08 a.m.
          • PR3.0 difference in money game
            Bob Koca -- Thursday, 22 January 2015, at 1:36 p.m.
            • PR3.0 difference in money game
              Maik Stiebler -- Thursday, 22 January 2015, at 3:19 p.m.
  • Handicap Backgammon. One start with cube.
    eXtreme Gammon -- Tuesday, 20 January 2015, at 2:39 p.m.
    • Handicap Backgammon. One start with cube.
      Bob Koca -- Tuesday, 20 January 2015, at 3:37 p.m.
    • Handicap Backgammon. One start with cube.
      christian munk-christensen -- Tuesday, 20 January 2015, at 3:57 p.m.
      • Handicap Backgammon. One start with cube.
        mochy -- Tuesday, 20 January 2015, at 4:00 p.m.
        • Handicap Backgammon. One start with cube.
          Christian Munk-Christensen -- Tuesday, 20 January 2015, at 5:46 p.m.
    • Handicap Backgammon. One start with cube.
      mochy -- Tuesday, 20 January 2015, at 3:59 p.m.
    • It's not just about what XG says
      Phil Simborg -- Tuesday, 20 January 2015, at 4:32 p.m.
      • It's not just about what XG says
        Bob Koca -- Tuesday, 20 January 2015, at 5:00 p.m.
        • It's not just about what XG says
          Phil Simborg -- Thursday, 22 January 2015, at 4:35 a.m.
    • Handicap Backgammon. One start with cube.
      Rick Janowski -- Tuesday, 20 January 2015, at 11:50 p.m.
    • Am I missing something?
      rambiz -- Thursday, 22 January 2015, at 8:10 p.m.
      • Am I missing something? yes
        eXtreme Gammon -- Thursday, 22 January 2015, at 8:54 p.m.
        • Am I missing something? yes
          rambiz -- Friday, 23 January 2015, at 8:34 a.m.
  • Let's do it! That's the best way to find out
    Phil Simborg -- Tuesday, 20 January 2015, at 4:15 p.m.
    • Let's do it! That's the best way to find out
      Bob Koca -- Tuesday, 20 January 2015, at 4:23 p.m.
      • Let's do it! That's the best way to find out
        Steve Mellen -- Wednesday, 21 January 2015, at 5:40 a.m.
    • Let's do it! That's the best way to find out
      mochy -- Thursday, 22 January 2015, at 5:07 a.m.
      • Let's do it! That's the best way to find out
        Steve Mellen -- Thursday, 22 January 2015, at 6:38 a.m.
      • Let's do it. It's a deal
        Phil simborg -- Thursday, 22 January 2015, at 11:43 a.m.
        • Let's do it. It's a deal
          Bob Koca -- Thursday, 22 January 2015, at 1:38 p.m.
          • Let's do it. It's a deal
            Phil simborg -- Thursday, 22 January 2015, at 3:08 p.m.
  • Handicap Backgammon. One start with cube.
    Rick Janowski -- Wednesday, 21 January 2015, at 12:40 a.m.
    • Handicap Backgammon. One start with cube.
      Taper_Mike -- Wednesday, 21 January 2015, at 1:00 a.m.
      • Handicap Backgammon. One start with cube.
        Rick Janowski -- Wednesday, 21 January 2015, at 1:34 a.m.