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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
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%)
  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
Cubeful Equities
No Double:+0.651 (-0.028)
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 © 1999-2015 Ash Dalvi and GammonVillage Inc.

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Celebrating 15 years in backgammon games