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Stack relevance

Posted By: Nack Ballard
Date: Wednesday, 19 February 2014, at 10:14 p.m.

In Response To: 7men, 8men, 9men in the zone (mochy)

 White is Player 2 score: 0 pip: 153 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=--a--BD-Da--dB---d-e---AB-:0:0:1:00:0:0:3:0:10

Nine in the zone, Blue to play a 2
[U V21] "&e

 White is Player 2 score: 0 pip: 149 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is Player 1
XGID=--a--BD-Da--dB---c-db--AB-:0:0:1:00:0:0:3:0:10

Nine in the zone variant: Blue to play a 2
[V U38] "&e

Your original position (where White has seven checkers in the zone -- two on the 8pt and five on the 6pt) can be reached by the (well-played) sequence 65R-21\$-64K-2-51T-52S-63K-52-52-55H-63R-62.

You're on the right track when you say the number of checkers in the zone is the salient factor for deciding which deuce, but that is not specific enough. I believe it is important to apply that count to STACKS in the zone, rather than just to the zone. The drawback of creating three blots in the back quadrant is that it allows your opponent to unload her stacks with double-hit numbers that might otherwise play poorly.

For example, consider your nine-in-the-zone variant diagrammed above on the left (also the third diagram here). To aid visualization, I've put the obvious 6 on the board (11/5) so that there remains only a deuce for Blue to play. The money evaluation is [U V29] "&e (similar to the –25–25 eval you posted).

Let's alter the situation so that White has made her 5pt with 31. In the right-hand position, White still has nine checkers in the zone and Blue has the same 2 to play. In this case, with the combined number of checkers on her 8pt and 6pt reduced from nine to seven, the money eval has completely reversed to [V U41] "&e (a swing of .070).

In other words, U (Up, 23/21) is clearly best on the left, whereas V (Variant up, 24/22) is clearly best on the right.

While writing the Backgammon Openings book, Paul and I had the opportunity to investigate third roll positions and variants with a roll of 31. In our book, position A231 is 54D-62H-31, diagrammed in the left-hand position below. [For reference, the comparison of bar/21 versus bar/23 24/22 there is the identical decision as Blue to play a lone deuce in the position below it, scroll further down.] Isolating just the two "up" plays (ignoring the option to slot), XG's money evaluation is [V U5] "&e. (The rollout result is [V U11] "<=31, but I'd rather compare apples to apples—evals to evals.)

Both in appearance and V/U eval, this is similar to your eight-in-the-zone decision (which is the upper left position, except with White putting one of her 8pt spares back on the midpoint). There are two differences above: (a) Blue has made her 5pt (with 13/5 6/5), and (b) White's back checker is on the 23pt instead of the 24pt. However, neither of these differences has a significant effect on the V/U comparison.

If you adjust the left-hand position below so that White has pre-made her 5pt with 31, you get the position on its right. White still has eight checkers in the zone, but now the eval soars to [V U65] "&e. As before, the reduction of the stacks makes a big difference. Again, the point is to pay attention to the height of White's STACKS, not just to the number of checkers in the zone. This in an important concept that applies to a range of early game positions.

[U can become best again when White's prime is strong enough and builderless enough, and specific duplications/diversifications (3s vs 2s in particular) is another factor, but that's more than I want to get into in this post.]

Nack

P.S. I was just about to click on "Post Message" when I noticed Daniel's post. His variants are also worthy of study.

 White is Player 2 score: 0 pip: 158 Unlimited GameJacoby Beaver pip: 174 score: 0 Blue is Player 1
XGID=--a---E-Da--eC---c-e----BA:0:0:1:31:0:0:3:0:10

54D-62H-31
[V U5] "&e

 White is Player 2 score: 0 pip: 154 Unlimited GameJacoby Beaver pip: 174 score: 0 Blue is Player 1
XGID=--a---E-Da--eC---b-db---BA:0:0:1:31:0:0:3:0:10

31P-54D-62H-31
[V U65] "&e

 White is Player 2 score: 0 pip: 158 Unlimited GameJacoby Beaver pip: 172 score: 0 Blue is Player 1
XGID=--a---E-Da--eC---c-e---AB-:0:0:1:00:0:0:3:0:10

Blue to play a lone 2 (same U/V decision as above)
[V U5] "&e

 White is Player 2 score: 0 pip: 154 Unlimited GameJacoby Beaver pip: 172 score: 0 Blue is Player 1
XGID=--a---E-Da--eC---b-db--AB-:0:0:1:00:0:0:3:0:10

Blue to play a lone 2 (same U/V decision as above)
[V U65] "&e

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