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65R-63S-62D-61H-61H-41D-32

Posted By: Nack Ballard
Date: Wednesday, 2 April 2014, at 8:19 p.m.

In Response To: Advanced Backgammon #74 (63S-62D-41D-32) (neilkaz)

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 159 score: 0 Blue is Player 1
XGID=-b----EAC--AcC-aac-e----B-:0:0:1:32:0:0:3:0:10

65R-63S-62D-61H-61H-41D-32

63S-62D-41D-32: Nice retro, Neil.

At the time (late 80s) that the games were played from which Advanced Backgammon probably got its material, opening 62D was still occasionally played. (A championship-division player played it against me in 2006!). Today we know it's a borderline whopper.

Other things being equal, deepening the sequence an extra roll (fourth instead of third) makes the position only 1/18 as likely to have occurred. To compensate, was a player faced with 63S-62, back then, 18 times as likely to have played D than would a player faced with an opening 62? It's unclear to me.

In considering the tradeoff above, it should be noted that 63S-62D itself is iffy. I'm aware of two rollouts: [X D16] "<20, and [X D37] /5. If we shut our eyes to GnuBG and just go with the XG result, 63S-62D is "well played" (within .02), but narrowly.

My subject header (and diagram caption of the position above) shows a perfectly played sequence (zero error). However, if things were otherwise equal, being seventh roll, it is reduced by another factor of 18^3 in probability. In any event, this position can later be searched for using any of the three sequences!

Paul and I wrote some (never organized) material that didn't make it into our book. In three of the positions, we compared the 5pt to the 4pt, the 5pt to the 7pt, and the 4pt to the 7pt. The first of those (5pt vs 4pt) is shown below.

The distribution (of three checkers on the 8pt and four on the 6pt) that results from "4" (making the 4pt), is clearly better than the distribution (of two on the 8pt and five on the 6pt) that results from "5" (making the 5pt). Even so, "5" is .041 better (as reported by the XG rollout result summarized in the caption). This position is a typical case.

There is a key difference in Blue's 11pt builder, which is absent in the (basic) position below but introduced into the (more developed) position above (Advanced Backgammon #74). This builder substantially increases Blue's incentive to make the 4pt. If he makes the 5pt, his 11pt builder will be poorly placed, six pips away from an already-made point.

Is the 11pt factor (+/– the relatively small effect of White's 9pt builder) enough to overcome the (normal) .04 difference? Maybe, I don't know. Gun to head, I guess I'll go with "5" (which, to recap, yields both the inferior distribution and inefficient 11pt builder, but makes the stronger point). When in doubt make the 5pt, though the trick is to know when to be in doubt.

Nack

 White is Player 2 score: 0 pip: 164 Unlimited GameJacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=-b----EAC---dD-a-c-e----B-:0:0:1:32:0:0:3:0:10

63S-42H-F-62
[5 441] "<=5

Key: 5 = 5pt (8/5 7/5), 4 = 4pt (7/4 6/4).

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