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41T-55P-51 and 55P-65

Posted By: Nack Ballard
Date: Monday, 14 April 2014, at 4:28 p.m.

In Response To: 55P-65 and 41T-55P-51 (Nack Ballard)

Tim (while acknowledging that 52S-55P is a bad move) suggested 52S-55P-61 as an instructional variant.

I proposed that Tim's variant (which compares playing U vs D with a 6) could be expanded to include comparisons of additional candidate moves, in one of two ways. The first way is to alter the position one pip, by moving the checker on the roof to the 24pt, and change the roll from 61 to 51.

The second way is to again move the roofed checker forward a pip but also move the second 8pt spare back 5 pips to the midpoint (net change of –4 pips), and change the roll from 61 to 65.

These positions can be represented by 41T-55P-51 and 55P-65, respectively (used in my header, for brevity). However, the first of those sequences includes a poor 41T opener, and the second an illegal opening 55P. My adjusted sequences, which by virtue of being well played, are necessarily longer. They are spelled out below, along with a nacbracs summary of the rollout results.

........62S-41X-43H-61H-51R-65T-55P-51.. [\$ D56 S97 &104 U116] "<=5
........62S-41X-43H-61H-51R-51D-55P-65.. [R D6 S55] "<=20*5

In keeping with the spirit of Tim's original suggestion, we can isolate the D/U comparison by ignoring the rest of the candidates. This reduction yields [D U60] in my first rollout result and [D S49] in my second result. (The U changed to S because 24/18 13/8 moves two checkers, but the 13/8 portion is merely restoring the second 8pt spare I moved back.) It's the identical comparison, so the difference between the .060 and .049 margins is explained by variance. (D was rolled 20k in one of the results, but only 5k in the other, and U was rolled only 5k in both.) Weight averaging, 13/7 beats 24/18 by .052.

Regarding the (D vs U only) variant just mentioned, Mike correctly chose D (Down, 24/18 13/7), which can also be nactated \$ (Slot), among other ways. [In case you're wondering about the 52S-64P-F-64P-61 header in the thread extension there, that was just me lengthening Tim's quick way of nactating it (52S-55P-61) so that the sequence is well-played.]

Mike also responded to my two variants (nacbracked above). In the first, he correctly chose \$ (Slot, 13/8 6/5). In the second position (in his words), he got "bluffed" into D (Down, 13/8 13/7), which according to the rollout is tied with but a hair worse than R (Run, 24/13).

[Mike could have economized his answers by bypassing Tim's variant, as after all he did rank D over S in my second variant. That speaks to the birth of either of my variants as outlined in the second paragraph of this post. Among other things, we discover that even the double-slot 8/3 6/5 is a better use of 6 pips than 24/18.]

Below are the details of the two rollout results that I summarized above in nacbracs.

Nack

 White is Player 2 score: 0 pip: 147 Unlimited GameJacoby Beaver pip: 162 score: 0 Blue is Player 1
XGID=-b----E-D---cD---c-e--b-B-:0:0:1:51:0:0:3:0:10

62S-41X-43H-61H-51R-65T-55P-51
[\$ D56 S97 &104 U116] "<=5

1.Rollout113/8 6/5eq: -0.302
 Player:Opponent: 43.75% (G:11.66% B:0.47%)56.25% (G:18.91% B:1.35%) Conf.: ± 0.008 (-0.310...-0.293) - [100.0%]Duration: 2 hours 10 minutes
2.Rollout113/7eq: -0.358 (-0.056)
 Player:Opponent: 42.42% (G:11.29% B:0.50%)57.58% (G:20.03% B:1.60%) Conf.: ± 0.008 (-0.366...-0.350) - [0.0%]Duration: 2 hours 13 minutes
3.Rollout124/23 13/8eq: -0.399 (-0.097)
 Player:Opponent: 41.39% (G:10.50% B:0.45%)58.61% (G:20.81% B:0.75%) Conf.: ± 0.007 (-0.406...-0.392) - [0.0%]Duration: 2 hours 00 minute
4.Rollout18/3 6/5eq: -0.405 (-0.104)
 Player:Opponent: 42.27% (G:10.53% B:0.43%)57.73% (G:22.21% B:2.18%) Conf.: ± 0.009 (-0.414...-0.396) - [0.0%]Duration: 2 hours 15 minutes
5.Rollout124/18eq: -0.418 (-0.116)
 Player:Opponent: 42.06% (G:9.67% B:0.47%)57.94% (G:23.91% B:0.78%) Conf.: ± 0.007 (-0.425...-0.410) - [0.0%]Duration: 1 hour 55 minutes
1 5184 Games rolled with Variance Reduction.
Dice Seed: 43733867
Moves: 3-ply, cube decisions: XG Roller

 White is Player 2 score: 0 pip: 147 Unlimited GameJacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-b----E-C---cE---c-e--b-B-:0:0:1:56:0:0:3:0:10

62S-41X-43H-61H-51R-51D-55P-65
[R D6 S55] "<=20*5

1.Rollout124/13eq: -0.357
 Player:Opponent: 42.92% (G:8.96% B:0.41%)57.08% (G:20.42% B:0.51%) Conf.: ± 0.004 (-0.361...-0.353) - [97.0%]Duration: 5 hours 04 minutes
2.Rollout113/8 13/7eq: -0.362 (-0.006)
 Player:Opponent: 42.38% (G:11.19% B:0.51%)57.62% (G:19.92% B:1.60%) Conf.: ± 0.004 (-0.367...-0.358) - [3.0%]Duration: 5 hours 20 minutes
3.Rollout224/18 13/8eq: -0.411 (-0.055)
 Player:Opponent: 42.01% (G:9.88% B:0.48%)57.99% (G:23.88% B:0.74%) Conf.: ± 0.008 (-0.419...-0.404) - [0.0%]Duration: 2 hours 11 minutes
1 20736 Games rolled with Variance Reduction.
Dice Seed: 90634172
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 90634172
Moves: 3-ply, cube decisions: XG Roller
These two positions can be viewed side by side, if you widen your window enough.

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