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Magriel's Six-Apart Rule Applies Here

Posted By: Paul Weaver
Date: Tuesday, 16 December 2014, at 7:43 p.m.

In Response To: Is this typical? (neilkaz)

 White is Player 2 score: 2 pip: 83 7 point match pip: 98 score: 2 Blue is Player 1
XGID=--ABcBBBBBB-----------cbg-:0:0:1:31:2:2:0:7:10
Blue to play 31

eXtreme Gammon Version: 2.10

Neil's analysis was instructive. I acknowledge that I would not have made the best play (8/5 3/2) over the board.

Magriel made this statement to me in a lesson, "Don't make points six pips apart on your own side of the board." The concept albeit not this exact wording is found in Magriel's book. I call this Magriel's Six-Apart Rule. Your checkers are used more efficiently to form a prime if you do not simultaneously own the 3pt and 9pt or the 2pt and 8pt. Warning: There are literally zillions and Brazilians of counterexamples and one is presented below.

Blue has his sights set on making the six-prime from his 7pt to 2pt (or from his 6pt to 1pt). White, for the time being, occupies the 4pt, but if White is eventually forced to break anchor and leave one checker behind on Blue's 4pt, Blue hopes to attack and complete his prime.

If White had a four-point board, as shown below, getting hit would have more severe consequences and leaving a shot would be wrong. Instead, Blue should focus on blocking White's immediate 6s. Magriel's Rule is superseded here by race considerations.

 White is Player 2 score: 2 pip: 93 7 point match pip: 98 score: 2 Blue is Player 1
XGID=--ABcBBBBBB----------cccc-:1:-1:1:31:2:2:0:7:10
Blue to play 31

1.Rollout15/1eq: +0.538
 Player:Opponent: 76.64% (G:8.37% B:0.28%)23.36% (G:1.32% B:0.01%) Conf.: ± 0.006 (+0.532...+0.544) - [100.0%]Duration: 1 minute 03 seconds
2.Rollout18/7 8/5eq: +0.516 (-0.022)
 Player:Opponent: 76.48% (G:7.01% B:0.16%)23.52% (G:0.66% B:0.00%) Conf.: ± 0.005 (+0.511...+0.521) - [0.0%]Duration: 47.0 seconds
3.Rollout18/5 3/2eq: +0.514 (-0.024)
 Player:Opponent: 75.55% (G:8.87% B:0.24%)24.45% (G:1.56% B:0.00%) Conf.: ± 0.005 (+0.508...+0.519) - [0.0%]Duration: 1 minute 01 second
4.Rollout15/2 3/2eq: +0.503 (-0.035)
 Player:Opponent: 75.85% (G:7.51% B:0.18%)24.15% (G:1.30% B:0.03%) Conf.: ± 0.006 (+0.497...+0.509) - [0.0%]Duration: 59.0 seconds
5.Rollout19/8 9/6eq: +0.481 (-0.057)
 Player:Opponent: 75.96% (G:5.43% B:0.11%)24.04% (G:0.48% B:0.00%) Conf.: ± 0.004 (+0.477...+0.486) - [0.0%]Duration: 45.7 seconds
6.Rollout17/3eq: +0.479 (-0.059)
 Player:Opponent: 74.54% (G:8.07% B:0.23%)25.46% (G:1.65% B:0.01%) Conf.: ± 0.006 (+0.474...+0.485) - [0.0%]Duration: 58.7 seconds
1 1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

This diagram shows the position after Blue makes the best play, 8/5 3/2, in the original position (shown at the very top of this post). Blue owns no two points that are six pips apart. I believe this play is also best at DMP and it wins the most gammons for Blue.

 White is Player 2 score: 2 pip: 83 7 point match pip: 94 score: 2 Blue is Player 1
XGID=--BAcCBBABB-----------cbg-:1:-1:-1:00:2:2:0:7:10
White on roll, cube action?

eXtreme Gammon Version: 2.10

The diagram below shows only each player's checkers in his or her own home board. XG told me the EPCs were 37.6 and 43.6, implying that Blue's wastage is 7.6 and White's is 23.6. This info gives me a crude estimate of the total EPCs of the original position: Blue 98 + 7.6 = 105.6 and White 83 + 23.6 = 106.6. In other words, the race is very close and Blue should therefore take eXtreme measures (i.e., volunteering a shot) to reduce White's racing equity.

 White is Player 2 score: 2 pip: 20 7 point match pip: 30 score: 2 Blue is Player 1
XGID=--AB-BB---------------cbg-:0:0:1:00:2:2:0:7:10
Blue on roll, cube action?

eXtreme Gammon Version: 2.10

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