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
|
| |||
| XGID=a---BCC-B---eC---bbcbB----:0:0:1:00:0:0:0:11:10 | ||||
 on roll, cube action? | ||||
is Player 2| 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 © 1999-2013 Ash Dalvi and GammonVillage Inc.
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Feedback about this article:
1.
Subject: Re: Prime vs Blitz: 2 Checkers Behind a 4 Prime
From:
David
Date:
24 Feb 2012 10:40 EST
Do you know how to print this article without the diagrams being split between pages?
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.
3.
Subject: Re: Prime vs Blitz: 2 Checkers Behind a 4 Prime
From:
David
Date:
28 Feb 2012 13:56 EST
It works - thanks!
4.
Subject: Re: Prime vs Blitz: 2 Checkers Behind a 4 Prime
From:
Timothy Chow
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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