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21\$-42H-21X-31U-41-d — An Exception?

Posted By: Nack Ballard
Date: Tuesday, 18 March 2014, at 4:32 a.m.

In Response To: 21\$-42H-21X-31U-41-d — An Exception? (Taper_Mike)

 White is Player 2 score: 0 pip: 162 1 point match pip: 181 score: 0 Blue is Player 1

21\$-42S-21H-31U-41
d [P A8] "&e
d [A P3] "<=62

(Mike's Nactation sequence of 21\$-42H-21X-31U-41-d is also correct; it's a matter of preference.)

Nice catch, Mike, of the A/I typo in the diagram caption of my earlier post. Cutting and pasting nacbracs, then changing the details, is a shortcut, but it is a little more prone to error (forgetting to change something that it supposed to be different).

I cited the value of the first 6pt spare only as a "major factor" in determining whether to (1) point on the 4pt or (2) make the 5pt and hit loose on the 4pt. I wouldn't think "exceptions" are to find, especially at dmp, which lends itself more to the (2) move. They almost exist as early as the second roll: last I knew, even with dmp's tighter B/W error scale categories, 32S-11-d is on the cusp of a "tied" result and 43Z-11-d is definitely tied.

Your example of 21\$-42S-21H-31U-41-d (diagrammed above) favors the loose hit of A (Attack, 8/4* 6/5) in spite of Blue's 11pt builder, which is 6 pips away from his 5pt. Faced with this problem OTB, even with three checkers back, and even at dmp, I believe I would have played P (Point, 8/4* 6/4, which you chose to nactate "a"). In other words, your 62k result of d[A P3] comes as a slight surprise to me.

With Blue having three or more checkers back and no checkers on his 11pt, I imagine you'll find plenty of such positions where hitting loose beats making the 4pt, even with unlimited-play.

Below is the second diagram pair that I posted here. I'm showing it for a few reasons. Firstly, so that you have a unlimited-play "exception" to add to your collection, though it probably should be categorized as tied.

The second reason is to remind us not to blindly trust that close XG evaluations (these are XG2++) tell us the best play; they are often overturned. I had said "For purposes of this analysis, I'm trusting these XG++ evaluations" in part because I suspected the one with 21 might be overturned, and indeed as you will see it has been (though barely).

Thirdly, comparing XG evaluations to each other is an instructive and pretty reliable method to measure the effects of small changes in early game positions. I'm not sure where the "k" breakeven is, but on average it is much worse to use 1k rollouts for such a purpose -- the variance is way too high.

Fourthly, XG++ seems to have a bias for making the 4pt instead of hitting loose in this type of position, based not only on the positions above and below but also consistent with what I've noticed in the past.

According to the unlimited-play evals (summarized immediately below in the "&e rows), the relative value of hitting loose on the 4pt (versus P = Pointing on the 4pt) with the roll of 41 is .069 greater than with the roll of 21. According to the rollout results (summarized immediately below and captioned in the diagrams below), the difference is .071. While the Point-versus-hitloose margin for each position has changed by .016 or .018, the difference of differences is only .002. That is, the rollout results confirm what the evals told us: the size of the 6pt-spare effect (give or take .001) is .07.

........64S-61P-52U-51H-44P-21
................[P I11] "&e
................[I P5] "<=20

........64S-61P-52U-51H-44P-41
................[A P58] "&e
................[A P76] "<=62

Nack

........Nactation tutorial
........Explanation of nacbracs

 White is Player 2 score: 0 pip: 146 Unlimited GameJacoby Beaver pip: 154 score: 0 Blue is Player 1

64S-61P-52U-51H-44P-21
[I P5] "<=20

1.Rollout16/5 6/4* eq: +0.096
 Player:Opponent: 53.21% (G:15.14% B:0.67%)46.79% (G:15.64% B:1.01%) Conf.: ± 0.002 (+0.094...+0.098) - [99.8%]Duration: 10 hours 58 minutes
2.Rollout16/4* 5/4eq: +0.091 (-0.005)
 Player:Opponent: 52.48% (G:15.73% B:0.63%)47.52% (G:14.73% B:0.72%) Conf.: ± 0.002 (+0.089...+0.093) - [0.2%]Duration: 9 hours 39 minutes
1 62208 Games rolled with Variance Reduction.
Dice Seed: 11365963
Moves: 3-ply, cube decisions: XG Roller

 White is Player 2 score: 0 pip: 146 Unlimited GameJacoby Beaver pip: 154 score: 0 Blue is Player 1

64S-61P-52U-51H-44P-41
[A P76] "<=62

1.Rollout18/4* 6/5eq: +0.144
 Player:Opponent: 53.96% (G:16.61% B:0.71%)46.04% (G:15.42% B:1.03%) Conf.: ± 0.004 (+0.140...+0.149) - [100.0%]Duration: 3 hours 27 minutes
2.Rollout18/4* 5/4eq: +0.069 (-0.076)
 Player:Opponent: 51.83% (G:16.01% B:0.62%)48.17% (G:14.94% B:0.72%) Conf.: ± 0.004 (+0.065...+0.072) - [0.0%]Duration: 3 hours 04 minutes
1 20736 Games rolled with Variance Reduction.
Dice Seed: 11365963
Moves: 3-ply, cube decisions: XG Roller

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