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How we got here, PART 1

Posted By: Nack Ballard
Date: Saturday, 12 December 2015, at 5:18 a.m.

In Response To: What was White's last move? (Nack Ballard)

 White is Player 2 score: 0 pip: 155 Unlimited GameJacoby Beaver pip: 173 score: 0 Blue is Player 1
XGID=----b-E-D---dCa--b-db--AAA:0:0:-1:00:0:0:3:0:10

White, on roll, should cube

The "Part 1" question was:

How can the above position be reached with perfect play from the opening position?
(Any number of rolls is allowed. I believe the fewest is six.)

I found two six-move solutions. The first of these, also found by Mike, is the more satisfying:

 White is Player 2 score: 0 pip: 158 Unlimited GameJacoby Beaver pip: 161 score: 0 Blue is Player 1
XGID=-a--a-E-D---dDa--b-db--AA-:0:0:1:63:0:0:3:0:10

32S-51S-31P-63

White opened with 32S (Split, 24/21 13/11), Blue replied with 51S, and White followed up with 31P, as illustrated above.

From here, Blue plays 63H (Hit, 13/4*), White responds with 43@ (anchor, bar/21* 24/21), and Blue fans. Presto! We have arrived at the target position (the first position of this post).

Mike gave an entertaining and insightful account of how he was able to deduce this solution and the related early game positions he learned in the process.

Here is the other six-mover I found:

 White is Player 2 score: 0 pip: 163 Unlimited GameJacoby Beaver pip: 158 score: 0 Blue is Player 1
XGID=-b----E-DA--eC---b-db---B-:0:0:-1:32:0:0:3:0:10

31P-54D-32 .....(White is on roll)

1.XG Roller++24/21 13/11eq: +0.229
 Player:Opponent: 55.58% (G:16.26% B:0.81%)44.42% (G:12.90% B:0.57%)
2.XG Roller++24/22 13/10eq: +0.226 (-0.003)
 Player:Opponent: 55.43% (G:17.02% B:0.89%)44.57% (G:13.56% B:0.59%)
3.XG Roller++13/11 13/10eq: +0.219 (-0.010)
 Player:Opponent: 55.10% (G:17.46% B:0.89%)44.90% (G:13.59% B:0.83%)
4.XG Roller++13/10 6/4eq: +0.212 (-0.017)
 Player:Opponent: 55.36% (G:17.07% B:0.86%)44.64% (G:13.93% B:0.97%)
5.XG Roller++13/8eq: +0.182 (-0.046)
 Player:Opponent: 54.13% (G:16.58% B:0.81%)45.87% (G:13.16% B:0.65%)

White opened with 31P and Blue replied with 54D, as illustrated above.

Now, White has a 32 to play. According to the XGR++ evaluation indicated, S (Split, 24/21 13/11) is best and the move therefore meets the qualifying conditions (regardless of rollout result). However, the edge over its closest rivals is very slim. If S is not god-best, eventually a stronger, future bot will not evaluate S on top. For that reason, I don't like this solution quite as much as the first (though it's trickier to find). The first is more likely to stand the test of time.

[Update: In a 5k 3-ply/XGR rollout, S (Split, 24/21 13/11) came out 74% best, with D (Down, 13/11 13/10) at ¡V.005, \$ (Slot, 13/10 6/4) at ¡V.006, and Z (reverse-split, 24/22 13/10) at ¡V.017.]

Continuing after White has played 32S...

 White is Player 2 score: 0 pip: 158 Unlimited GameJacoby Beaver pip: 158 score: 0 Blue is Player 1
XGID=-a--a-E-DA--dCa--b-db---B-:0:0:1:51:0:0:3:0:10

31P-54D-32S-51

With his roll of 51, Blue correctly plays X (hit-and-split, 24/23 9/4*). Then White responds with 43@ (anchor, bar/21* 24/21, just as in the other solution), and Blue fans. Again we have reached the target position (first position of this post).

Below is a recap of the two solution sequences. ("C" at the end indicates that White gives an initial Cube).

.....32S-51S-31P-63H-43@-F-C
.....31P-54D-32S-51X-43@-F-C

I'll discuss the nine-move continuation (Part 2) in a separate post.

Nack

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