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5pt / 4pt axiom

Posted By: Nack Ballard
Date: Sunday, 25 May 2014, at 7:15 p.m.

In Response To: P U problem (Bob Koca)

I often use the position pair from the openings book of 54S 42P 31 where point is correct by a small amount and 43S 42P 31 where anchor is right by a small amount.

The XG openings book does not seem to have them, so by the "openings book," I guess Bob is referring to Backgammon Openings. On pp. 60–61 (facing pages), the feature position pair is 43S-42P-31 + 43S-64P-31.

In the bottom left corner of each page (with less analysis), a supplemental position is diagrammed (54S-42P-31 on the left, and 54S-64P-31 on the right).

In short, the two-page spread is arranged like this:

----------------------------------------------------------------------------------------------------------------------------------
.....................Page 60........................................Page 61

........43S-42P-31 [@ P43] "<=5............43S-64P-31 [P @68] "<=5

........54S-42P-31 [P @6] "<=31............54S-64P-31 [P @112] "<=5
----------------------------------------------------------------------------------------------------------------------------------

The main concept discussed on this two-page spread is that one has a much greater incentive to anchor when the opponent owns a high point (here, her 4pt) rather than a low point (her 2pt). Comparing horizontally, the P/@ difference is (.043 + .068) = .111 or (.112 – .006) = .106.

To Bob's reference, another useful idea we can learn from the above quadrangle is how much of a difference it makes when there is a second spare on the 8pt (instead of a blot on the 10pt). Comparing vertically, the P/@ difference is .043 + .006 = .049 or .112 - .068 = .044.

The lower-left position denoted above, 54S-42P-31, is also diagrammed below, with the nacbracs representation repeated, showing that P and @ are "tied" (P's edge is within .01).

The second position diagrammed below (displayed on the right, if your window is wide enough) is the same position diagrammed at the bottom of this post and at the top of this post. (In the latter, it is mis-diagrammed -- move Blue's 21pt checker to the 22pt, but there is more analysis in that post). Despite White's three improvements (to 52S-31P-31) of 6/5, 13/8 and 13/11 (the values of which are estimated to sum to .107 in the post just mentioned), P and @ are nonetheless still "tied." The difference between anchoring on the opponent's 4pt versus her 5pt is that big.

I'll reiterate one of my favorite axioms: "Either 5pt is better than either 4pt." (For example, 52S-51S-31 [P @153] vs. 52S-51S-42 [@ P27].) Of course it is not true in every case, but this post helps illustrate the extent of the tweaking required to reach the tipping point.

These are both excellent (tied) P/@ reference positions, one for making Opp's 5pt and one for making Opp's 4pt, each compared to making one's own 5pt.

Nack





White is Player 2

score: 0
pip: 161
Unlimited Game
Jacoby Beaver
pip: 158
score: 0

Blue is Player 1
XGID=-b----E-D---eD---b-dAb--A-:0:0:1:31:0:0:3:0:10

54S-42P-31
[P @6] "<=31
White is Player 2

score: 0
pip: 155
Unlimited Game
Jacoby Beaver
pip: 160
score: 0

Blue is Player 1
XGID=-b----E-D---cDa--c-cc-A-A-:0:0:1:31:0:0:3:0:10

54S-21H-61U-21P-21U-51N-31
[P @7] "<=51


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