Celebrating 15 years in backgammon games

Prime vs Blitz: 2 Checkers Behind a 4 Prime

by Ash Dalvi
16 February 2012


Ash Dalvi

Positions where the doubler has 2 checkers behind a 4 prime and the taker has a man on the bar occur quite frequently.

In this article, I will show some basic reference positions and a method of calculating variations of these.

My aim is to figure out the value of additional alterations from basic reference positions.

Furthermore, it is important to determine which of these alterations consistently retain their values across different position-types.

Standard Reference Positions



The Count

The counting method is the same as that employed in my previous article, Prime vs Blitz: 1 checker behind a 4 prime.

In Position 1, count 1 for every white checker that has made a board point or is threatening to make a board point and 0.5 for any others in white's outfield. So, the 10 checkers between the 4 and 8 pt count as 1 each, giving a total count of 10 for the first cube. The basic count assumes that white's checkers make up a 3 pt board.

In my previous article, the rollouts indicated that, when white has one checker on the 21 pt, a count of 8.5 is required for first cube. So, the second checker appears to have an additional value of 1.5.

Position 1: First Cube = Count of 10

is Player 2

score: 0
pip: 148
11 point match
pip: 138
score: 0

is Player 1
XGID=a---BCC-B---eC---bbcbB----:0:0:1:00:0:0:0:11:10
on roll, cube action?


Analyzed in Rollout
No Double
  Player Winning Chances: 63.05% (G: 27.49% B: 0.41%)
  Opponent Winning Chances: 36.95% (G: 6.43% B: 0.29%)
Double/Take
  Player Winning Chances: 63.53% (G: 27.40% B: 0.48%)
  Opponent Winning Chances: 36.47% (G: 6.64% B: 0.34%)
 
Cubeless Equities
No Double:+0.477
Double:+0.986
 
Cubeful Equities
No Double:+0.651 (-0.028)
Double/Take:+0.679
Double/Drop:+1.000 (+0.321)
 
Best Cube action: Double / Take
 
Rollout details
1296 Games rolled with Variance Reduction.
Dice Seed: 21637437
Moves: 3 ply, cube decisions: XG Roller
 
Confidence No Double: ± 0.013 (+0.638...+0.664)
Confidence Double: ± 0.017 (+0.662...+0.696)
 
Double Decision confidence: 99.4%
Take Decision confidence: 100.0%
 
Duration: 20 minutes 07 seconds

eXtreme Gammon Version: 1.21, MET: Rockwell-Kazaross


 
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Article text Copyright © 1999-2014 Ash Dalvi and GammonVillage Inc.

 
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Feedback about this article:

2.
Subject: Re: Prime vs Blitz: 2 Checkers Behind a 4 Prime
From: ftw
Date: 28 Feb 2012 13:49 EST

Hi David:

I've modified the article so positions should no longer be cut in half during printing.

Frank Williams GammonVillage Inc.

4.
Subject: Re: Prime vs Blitz: 2 Checkers Behind a 4 Prime
Date: 21 Jul 2012 20:37 EST

As I've said elsewhere, I think this is a great series of articles. If anyone doubts the practical value of these reference positions, here's a cube decision that came up in the 8th game of the 2012 Monte Carlo World Championship final:

XGID=aB--BBBAB---cBa--bbbcBa---:0:0:1:00:8:6:0:25:10

I don't think that Nevzat would have missed this double if he had known Ash Dalvi's reference positions!

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Celebrating 15 years in backgammon games