Mai 24

3 vs 3 (3 pips behind)

By ace Backgammon, Bearoffs Add comments

Player on roll is 3 pips behind

In this section we take a look at positions where the player on roll is behind 3 pips. This is probably the most difficult chapter. I took two positions for a rollers pipcount of 10, 11, 12, 13, 14 and 15 each. 

+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  ' 1X  ' 1X 1X |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 |  '  ' 1O 2O  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 7, ace 10
Position ID: JQAAwAIAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.529  
  0.765 0.000 0.000 – 0.235 0.000 0.000
Cubeful equities:
1. Double, pass +1.000  
2. Double, take +1.037 +0.037
3. No double +0.639 -0.361
Proper cube action: Redouble, pass

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  ' 1X  ' 1X 1X |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 1O  '  '  ' 2O  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 7, ace 10
Position ID: JQAAYAgAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.423  
  0.712 0.000 0.000 – 0.288 0.000 0.000
Cubeful equities:
1. Double, take +0.791  
2. Double, pass +1.000 +0.209
3. No double +0.520 -0.271
Proper cube action: Redouble, take

 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  ' 1X 1X  ' 1X |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 |  ' 2O  '  '  ' 1O |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 8, ace 11
Position ID: KQAAEAYAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.349  
  0.675 0.000 0.000 – 0.325 0.000 0.000
Cubeful equities:
1. Double, take +0.576  
2. Double, pass +1.000 +0.424
3. No double +0.417 -0.159
Proper cube action: Redouble, take

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  '  ' 2X 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 |  ' 1O 1O  ' 1O  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 8, ace 11
Position ID: GgAAIAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.514  
  0.757 0.000 0.000 – 0.243 0.000 0.000
Cubeful equities:
1. Double, take +0.986  
2. Double, pass +1.000 +0.014
3. No double +0.625 -0.360
Proper cube action: Redouble, take

 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  '  ' 3X  '  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 |  ' 1O 1O 1O  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 9, ace 12
Position ID: HAAAQAUAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.424  
  0.712 0.000 0.000 – 0.288 0.000 0.000
Cubeful equities:
1. Double, take +0.759  
2. Double, pass +1.000 +0.241
3. No double +0.527 -0.231
Proper cube action: Redouble, take

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  ' 1X 1X 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 |  '  ' 3O  '  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 9, ace 12
Position ID: KgAAgAMAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.214  
  0.607 0.000 0.000 – 0.393 0.000 0.000
Cubeful equities:
1. No double +0.325  
2. Double, pass +1.000 +0.675
3. Double, take +0.245 -0.080
Proper cube action: No redouble, take (10.6%)

 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  '  ' 2X  ' 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 1O  ' 1O 1O  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 10, ace 13
Position ID: MgAAQAkAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.317  
  0.659 0.000 0.000 – 0.341 0.000 0.000
Cubeful equities:
1. Double, take +0.473  
2. Double, pass +1.000 +0.527
3. No double +0.416 -0.057
Proper cube action: Redouble, take

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  ' 1X  ' 1X 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 2O  '  '  '  ' 1O |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 10, ace 13
Position ID: SgAAEAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.022  
  0.511 0.000 0.000 – 0.489 0.000 0.000
Cubeful equities:
1. No double +0.080  
2. Double, pass +1.000 +0.920
3. Double, take -0.345 -0.425
Proper cube action: No redouble, beaver (31.6%)

 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  ' 2X  '  '  ' 1X |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 1O 1O  ' 1O  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 11, ace 14
Position ID: YQAAQAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.314  
  0.657 0.000 0.000 – 0.343 0.000 0.000
Cubeful equities:
1. Double, take +0.552  
2. Double, pass +1.000 +0.448
3. No double +0.431 -0.121
Proper cube action: Redouble, take

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   | 1X  '  ' 1X 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 2O  '  '  ' 1O  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 11, ace 14
Position ID: igAAIAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.032  
  0.516 0.000 0.000 – 0.484 0.000 0.000
Cubeful equities:
1. No double +0.127  
2. Double, pass +1.000 +0.873
3. Double, take -0.256 -0.382
Proper cube action: No redouble, beaver (30.5%)

 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  ' 2X  '  ' 1X  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 1O 1O 1O  '  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 12, ace 15
Position ID: YgAAgAoAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.236  
  0.618 0.000 0.000 – 0.382 0.000 0.000
Cubeful equities:
1. No double +0.340  
2. Double, pass +1.000 +0.660
3. Double, take +0.320 -0.020
Proper cube action: No redouble, take (2.9%)

The position above is nonetheless an initial double. 

 


+-13-14-15-16-17-18-+---+-19-20-21-22-23-24-+
|  '  '  '  '  '  ' |   |  ' 1X 1X 1X  '  ' |
|                   |   |                   |
|                   |   |                   |
|  '  '  '  '  '  ' | 2 | 2O  '  ' 1O  '  ' |
+-12-11-10--9--8--7-+---+--6--5--4--3--2--1-+

Pip counts: gnubg 12, ace 15
Position ID: VAAAQAwAAAAAAA Match ID: UQkAAAAAAAAA

• ace doubles

Cube decision
2-ply cubeless equity +0.051  
  0.526 0.000 0.000 – 0.474 0.000 0.000
Cubeful equities:
1. No double +0.141  
2. Double, pass +1.000 +0.859
3. Double, take -0.154 -0.296
Proper cube action: No redouble, beaver (25.6%)

 

Some conclusions:

  • 9 vs 6 pips is always a redouble/pass.
  • 10 vs 7 is usually a redouble/pass. Only if roller has a bd and his opponent has at least ad then it turns to a redouble/take.
  • 11 vs 8 is always a redouble/take.
  • 12 vs 9 is usually a redouble/take. Only if the roller has a bd and his opponent has at least a ad then it turns to a nodouble/take.
  • 13-10 covers everything in the range of redouble/take (gd vs ad) to no double/beaver (bd vs gd).
  • 14-11 covers everything in the range of redouble/take (gd vs ad) to no double/beaver (bd vs gd).
  • 15-12 covers everything in the range of initial double/take (gd vs. bd) to no double/beaver (bd vs gd).
  • 16-13 is always a no double.

 

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