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SOLUTIONS

Posted By: Nack Ballard
Date: Friday, 4 December 2015, at 7:49 p.m.

In Response To: Retro Pair, and Blue to Play 51 (Nack Ballard)

Congratulations to Maik for solving both (unique-solution) retro-problems!

Mike is too modest to mention it, but I e-mailed him the problems before posting, and he solved them both expediently. So, he equally deserves kudos. Maik and Mike are the geniuses this time around.

Detailed solutions follow.






White is Player 2

score: 0
pip: 148
Unlimited Game
Jacoby Beaver
pip: 152
score: 0

Blue is Player 1
XGID=-a--B-D-CA--dC-a-d-e----B-:0:0:1:00:0:0:3:0:10

Problem 1
Reach in Four Moves...(Blue, White, Blue, White)


Problem 1 (above): The position above was reached in FOUR moves (two by each player), that were perfectly played according to XGR++ evaluation. Blue moved first. (Blue, White, Blue, White.) What is the move sequence?

There is only one solution. It goes like this:

Blue rolls an opening 43 and plays D (Down, 13/10 13/9). XGR++ evaluates D as slightly better than Z (reverse split, 24/21 13/9) and S (Split, 24/20 13/10), with U (Up, 24/21 24/20) also close. By nacbrac: [D S4 Z5 U17] "&e. The result of combined rollouts changes the order of Z and S but essentially agrees: [D Z2 S10 U23] "+149*12 7.

In reply, White rolls 64 and plays R (Run, 24/14). XGR++ evaluates R as .003 better than S (Split, 24/18 13/9). Best rollouts suggest it is even closer¡Xa margin of .002 or .001.

So, 43D-64R is perfect so far. The (midway) diagram below shows these two moves played on the board. Okay, STOP. I recommend looking at the diagram only and covering up the details beneath, before scrolling further. Quiz yourself: How would you play Blue's (next) roll of 62?





White is Player 2

score: 0
pip: 157
Unlimited Game
Jacoby Beaver
pip: 160
score: 0

Blue is Player 1
XGID=-a----E-CAAaeC---c-e----B-:0:0:1:62:0:0:3:0:10

43D-64R-62


1.XG Roller++10/4 6/4eq: +0.130
Player:
Opponent:		51.87% (G:16.61% B:0.51%)
48.13% (G:10.88% B:0.55%)
2.XG Roller++24/18 13/11* eq: +0.086 (-0.045)
Player:
Opponent:		52.02% (G:15.05% B:0.76%)
47.98% (G:13.40% B:0.78%)
3.XG Roller++13/7 9/7eq: +0.030 (-0.100)
Player:
Opponent:		49.84% (G:14.85% B:0.48%)
50.16% (G:12.04% B:0.62%)

If you chose X (hit and split, 24/18 13/11*), as would many players OTB, then good, this post has helped improve your game. If you are surprised by the size of the .045 margin, that has helped too. Carefully study Blue's distribution after each play.

Here is the position after Blue plays his 62 correctly:





White is Player 2

score: 0
pip: 157
Unlimited Game
Jacoby Beaver
pip: 152
score: 0

Blue is Player 1
XGID=-a--B-D-CA-aeC---c-e----B-:0:0:-1:63:0:0:3:0:10

43D-64R-62A-63...(White to play 63)


Finishing up the sequence, White rolls 63 and makes the obvious play of d (down, 14/8 13/10), thereby reaching the target position for Problem 1 (see the first diagram of this post).

The recap of the Problem 1 solution sequence is 43D-64R-62A-63d. [Blue's 62A move might also be nactated "p" or "4" but not capital P (as that would indicate 13/7 9/7)].)

-------------------------------------------------------------------------------------------------





White is Player 2

score: 0
pip: 148
Unlimited Game
Jacoby Beaver
pip: 154
score: 0

Blue is Player 1
XGID=-a--B-D-C--AdC-a-d-e----B-:0:0:1:00:0:0:3:0:10

Problem 2
Reach in Four Moves...(Blue, White, Blue, White)


Problem 2 (above): The position above was reached in FOUR moves (two by each player), that were perfectly played according to XGR++ evaluation. Blue moved first. (Blue, White, Blue, White.) What is the move sequence?

Again, there is only one solution. It goes like this:

Blue rolls an opening 42 and makes his 4pt. In reply, White rolls 64, the XGR++ evaluation for which is shown below:





White is Player 2

score: 0
pip: 167
Unlimited Game
Jacoby Beaver
pip: 161
score: 0

Blue is Player 1
XGID=-b--B-D-B---eE---c-e----B-:0:0:-1:64:0:0:3:0:10

42P-64...(White to play 64)


1.XG Roller++24/14eq: -0.299
Player:
Opponent:		43.67% (G:9.36% B:0.38%)
56.33% (G:17.87% B:0.61%)
2.XG Roller++8/2 6/2eq: -0.301 (-0.002)
Player:
Opponent:		42.81% (G:12.81% B:0.65%)
57.19% (G:18.55% B:0.95%)
3.XG Roller++24/18 13/9eq: -0.319 (-0.020)
Player:
Opponent:		43.39% (G:10.96% B:0.57%)
56.61% (G:19.79% B:0.95%)

Some of you opening experts might know that current rollouts support P (Point, 8/2 6/2), though the margin is a mere handful of millipoints, and (given the difference in type of move) it wouldn't surprise me if future-bot rollouts eventually swing back in favor of R. Be that as it may, for reasons of convenience, XGR++ evaluation determines "perfect play." For puzzle purposes, therefore, 42P-64R is the legitimate two-move sequence.

After White plays (runs with) 64R above, Blue rolls 52 and plays the obvious D (Down, Instead, K (Kill, 13/11* 6/1*) would be a blunder (evaluates as ¡V.089). That gets us to the position diagrammed below:





White is Player 2

score: 0
pip: 168
Unlimited Game
Jacoby Beaver
pip: 154
score: 0

Blue is Player 1
XGID=aa--B-D-C--AeC---c-e----B-:0:0:-1:55:0:0:3:0:10

42P-64R-52D-55...(White to play 55)


Finally, White rolls 55 and plays B (Both, bar/15 15/10 13/8), thereby reaching the target position of Problem 2 (which you can verify by scrolling back a couple of diagrams). Making the 3pt with P (bar/20 13/3 8/3) evaluates as ¡V.100 (a whopper).

The recap of the Problem 2 solution sequence is 42P-64R-52D-55B. [Blue's 52D move might also be nactated H (Hit, with down clause).]

Nack

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