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Another PUZZLE (based on Neil's Position) -- SOLUTION

Posted By: Nack Ballard
Date: Thursday, 14 January 2016, at 11:31 p.m.

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





White is Player 2

score: 0
pip: 176
Unlimited Game
pip: 99
score: 0

Blue is Player 1
XGID=--BBbdBCBB-B-----bbca---a-:0:0:1:66:0:0:0:0:10

Blue rolls only 66. .White rolls only 55. ...WHO WINS?


For the rest of the game, Blue rolls only double 6s (repeatedly) and White rolls only double 5s (repeatedly), and both players make the best moves they can given these stated rules. (Blue moves first.)

Who wins (and how)?

Congrats to Bob Koca, who answered: I believe White wins by leaving a blot on 20 point next turn and then hitting from bar a couple turns later.

Here is the solution in detail:

It doesn't matter how Blue plays his first 66, as long as he doesn't leave a blot on the 9pt (which would immediately get hit by a 5). Let's say that he moves the four checkers on his 8pt and 9pt, giving this position:






White is Player 2

score: 0
pip: 176
Unlimited Game
Jacoby Beaver
pip: 75
score: 0

Blue is Player 1
XGID=--DDbdBC---B-----bbca---a-:0:0:-1:55:0:0:3:0:10

White to play 55


Here is where White has to find the winning move. Her only chance is to move three (and only three) checkers off the 20pt. (It otherwise doesn't matter how he plays the fourth 5, but I've chosen 8/3 for the next diagram.)

[If White keeps the 20pt anchor, Blue can only play three 6s (7/1(3)), his high points are even, and it is clearly hopeless for White. Eventually, she'll have to run from the 20pt and Blue will bear in and off without leaving a shot.]






White is Player 2

score: 0
pip: 156
Unlimited Game
Jacoby Beaver
pip: 75
score: 0

Blue is Player 1
XGID=--DDbaBC--cB-----abca-a-a-:0:0:1:66:0:0:3:0:10

Blue to play 66


Obviously, if Blue plays 11/5* 7/1(3), he will instantly hit with a 5. Therefore, he should make his other legal play, which is reflected below. White fans with her double 5s, and then...






White is Player 2

score: 0
pip: 161
Unlimited Game
Jacoby Beaver
pip: 51
score: 0

Blue is Player 1
XGID=aBDDbBBA--c------abca-a-a-:0:0:1:66:0:0:3:0:10

Blue to play 66


Ouch, now Blue is forced to leave a blot with his 66! Well, he does get three checkers off, but is it enough? Let's see.






White is Player 2

score: 0
pip: 161
Unlimited Game
Jacoby Beaver
pip: 28
score: 0

Blue is Player 1
XGID=aCDDbA----c------abca-a-a-:0:0:-1:55:0:0:3:0:10

White to play 55


White rolls 55 from the roof, hitting, and Blue will fan repeatedly, as long as White still owns her 6pt.

White (who continues to roll sets of 5's) has no control where her checkers end up, except for how many checkers she might take off her 6pt prior to bearing off her 5pt. Fast forwarding, White bears in to this position:






White is Player 2

score: 0
pip: 61
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-CDD---------------ed-bbaA:0:0:-1:55:0:0:3:0:10

White to play 55


There are only two wrong plays for White: One is to leave an immediate shot with 6/1(4), and the other is to bear four checkers off, which will force her to leave a 6 shot next turn, and she will lose the game by one roll!

Playing carefully this turn and the next, White bears off only three checkers (which, added to the checker she already bore off, makes four), as shown below:






White is Player 2

score: 0
pip: 21
Unlimited Game
Jacoby Beaver
pip: 48
score: 0

Blue is Player 1
XGID=-CDD----------------a-bbfA:0:0:1:66:0:0:3:0:10

Blue to play 66


Blue, on roll here, needs four rolls to bear off. That's one roll too many. WHITE WINS.

Nack

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