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How we got here, PART 2

Posted By: Nack Ballard
Date: Monday, 14 December 2015, at 1:43 p.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:1:1:-1:00:0:0:3:0:10

White, having just cubed, is on roll

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 142 score: 0 Blue is Player 1
XGID=----cBCBBC--b-c--bBacA--a-:1:1:1:00:0:0:3:0:10

Final Position (White having played the last move)

The "Part 2" question was:

Assuming perfect play, how can the players get from the first position above to the second position above?
(Any number of rolls is allowed. The sequence I found is nine rolls.)

White starts with a roll of 41 and plays K (Kill, 6/2*/1*). [The alternative of N (Near, 13/9 6/5) evaluates as ¡V.016 but rolls out at ¡V.028.]

Blue, with three checkers on the roof, rolls 11 in response. Obviously, he should play U (Up, bar/24*(3), 24/23).

Following that, White rolls 42 and plays P (Point, bar/21 13/11); i.e., enters and makes the 11pt, which is also clear. White's 41K, Blue's 11U and White's 42P have all been added to the next diagram.

 White is Player 2 score: 0 pip: 168 Unlimited GameJacoby Beaver pip: 172 score: 0 Blue is Player 1
XGID=----c-E-D---cCb--b-cb--AB-:1:1:1:11:0:0:3:0:10

32S-51S-31P-63H-43@-F-C-
41K-11U-42P-11

Blue has rolled another double 1s. The alternative of "e" (each, bar/22 6/5(2)) evaluates as ¡V.035 (and rolls out as ¡V.047). The position after Blue correctly plays N (Near, 8/7(2) 6/5(2)) is shown below.

 White is Player 2 score: 0 pip: 168 Unlimited GameJacoby Beaver pip: 168 score: 0 Blue is Player 1
XGID=----cBCBB---cCb--b-cb--AB-:1:1:-1:21:0:0:3:0:10

32S-51S-31P-63H-43@-F-C
-41K-11U-42P-11N-21...(White is on roll)

1.XG Roller++13/11 6/5eq: -0.119
 Player:Opponent: 51.46% (G:12.93% B:0.62%)48.54% (G:10.66% B:0.38%)
2.XG Roller++13/10eq: -0.120 (-0.002)
 Player:Opponent: 51.58% (G:13.45% B:0.68%)48.42% (G:11.56% B:0.44%)
3.XG Roller++11/8eq: -0.132 (-0.013)
 Player:Opponent: 50.94% (G:12.94% B:0.59%)49.06% (G:10.74% B:0.39%)
4.XG Roller++11/10 11/9eq: -0.182 (-0.063)
 Player:Opponent: 49.74% (G:12.90% B:0.60%)50.26% (G:12.45% B:0.49%)
5.XG Roller++11/9 6/5eq: -0.225 (-0.106)
 Player:Opponent: 48.30% (G:12.55% B:0.58%)51.70% (G:13.00% B:0.52%)

White has a roll of 21, and her choice is even closer than is showed by the above XGR++ evaluation (as that determines which move qualifies for a solution). In a 20k 3-ply/XGR rollout, N (Near, 13/11 6/5) is best, D (Down, 13/10) is ¡V.001, and 8 (8pt, 11/8) is ¡V.010.

Following White's 21N play, Blue rolls 65 and makes the routine bar-point-anchoring play, which brings us to White's next checker-play decision:

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 157 score: 0 Blue is Player 1
XGID=----cBCBB---bCc--bBbc---A-:1:1:-1:54:0:0:3:0:10

32S-51S-31P-63H-43@-F-C
-41K-11U-42P-11N-21N-65@-54...(White is on roll)

White has rolled 54, and has nothing better than X (hit and split, 21/16 5/1*). Second best is A (Attack, 11/6 5/1*) and third best is "2" (2pt, 11/2), which evaluate as ¡V.028 and ¡V.034 (and roll out ¡V.017 and ¡V.030), respectively.

Blue's retort is the powerful double 4s, entering and hitting back on the 9pt (while playing three checkers there), which gives him a five-point prime.

After White's 54X and Blue's 44Z, the position looks like this:

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 142 score: 0 Blue is Player 1
XGID=a---bBCBBC--b-c--bBbbA--a-:1:1:-1:41:0:0:3:0:10

32S-51S-31P-63H-43@-F-C
-41K-11U-42S-11N-21N-65@-54X-44Z-41

In this position, White rolls 41. According to rollout, three plays give her a proper take of the pending redouble: E (Each, bar/21 6/5), B (Both, bar/21 11/10), and E (Each, bar/24 5/1). The latter two are errors of .049 and .052.

After White correctly plays 41E, the target position (second position of this post) is reached.

The full perfectly played 15-roll sequence is recapped below. (The opening 6-move portion illustrated here is in gray typeface. The 9-move continuation covered in this post is in black typeface.)

.....32S-51S-31P-63H-43@-F-C-41K-11U-42P-11N-21N-65@-54K-44Z-41E

[Note: This is not the only (perfectly played) 15-roll sequence that reaches the ultimate target position. For example, from my Part 1 post we already know that the first four rolls can be replaced by 31P-54D-32S-51K. And/or it is possible to replace 43@ with 32H and recoup the 2 pips by also replacing 42P with 22S (though in that case White's seventh-roll doubling position is slightly different).]

Nack

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