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PUZZLE (based on Neil's position) -- SOLUTION

Posted By: Nack Ballard
Date: Friday, 8 January 2016, at 3:53 p.m.

In Response To: PUZZLE (based on Neil's position) (Nack Ballard)





White is Player 2

score: 2
pip: 176
9 point match
pip: 99
score: 5

Blue is Player 1
XGID=--BBbdBCBB-B-----bbca---a-:0:0:1:00:5:2:0:9:10
Blue on roll, loses the game after White makes only one checker play!

Puzzle: Blue is on roll (leading 5 to 2 in a 9-point match). With perfect cube play and checker play from both sides (according to XGR++ evaluation), Blue will get doubled or redoubled out after White has made only one checker play. What is the move sequence?

Congratulations to Carlo, for solving this puzzle. I believe the solution is unique.

The sequence starts with Blue doubling, which XGR++ says is correct by .032, and this is supported by Neil's XG rollout. Then Blue rolls 64 and has nothing better than 11/1, giving the position below.






White is Player 2

score: 2
pip: 176
9 point match
pip: 89
score: 5

Blue is Player 1
XGID=-ABBbdBCBB-A-----bbca---a-:1:-1:-1:61:5:2:0:9:10

White to play 61


With her 61 loker, White makes the obvious move. That puts Blue on roll in the position below.






White is Player 2

score: 2
pip: 169
9 point match
pip: 103
score: 5

Blue is Player 1
XGID=-ABBbcBCBB-a-----bbbb---aA:1:-1:1:51:5:2:0:9:10

Blue to play 51


Here, Blue rolls 51 (his worst) and plays bar/24* 7/2. That puts White on roll in the position below.






White is Player 2

score: 2
pip: 193
9 point match
pip: 97
score: 5

Blue is Player 1
XGID=aACBbcBBBB-a-----bbbb---A-:1:-1:-1:00:5:2:0:9:10

White on roll, redoubles to 4



Analyzed in XG Roller++ No redouble Redouble/Take
  Player Winning Chances: 65.61% (G:16.14% B:0.58%) 65.48% (G:16.12% B:0.60%)
  Opponent Winning Chances: 34.39% (G:18.21% B:0.24%) 34.52% (G:18.41% B:0.25%)
  Cubeless Equities +0.287 +1.156
Cubeful Equities
No redouble:+0.915 (-0.085)
Redouble/Take:+1.156 (+0.156)
Redouble/Pass:+1.000
 
Best Cube action: Redouble / Pass

White redoubles to 4. As the XGR++ evaluation shows (and the rollout agrees, though by 2/3 of the margin), Blue should pass.

A sad story. :)

Nack

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