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Puzzle (based on this position)

Posted By: Taper_Mike
Date: Tuesday, 10 November 2015, at 7:31 p.m.

In Response To: Puzzle (based on this position) (Nack Ballard)

I have one sequence that works by sleight of hand. It is based on a common misplay that occurs on the second roll. How should one play 63 after the opponent opens 54S = 24/20 13/8?

In the XGR++ eval below, White, the player on top, is on roll

 White is Player 2 score: 0 pip: 167 Unlimited GameJacoby Beaver pip: 158 score: 0 Blue is Player 1
XGID=-b----E-D---eD---c-eA---A-:0:0:-1:63:0:0:3:0:10
White to play 63

1.XG Roller++13/7 8/5* eq: -0.207
 Player:Opponent: 45.29% (G:11.96% B:0.44%)54.71% (G:16.58% B:1.18%)
2.XG Roller++24/18 8/5* eq: -0.227 (-0.020)
 Player:Opponent: 45.10% (G:10.39% B:0.40%)54.90% (G:16.82% B:0.79%)

eXtreme Gammon Version: 2.10

Slot the bar! It avoids giving your opponent a good ace, which 24/18 would do. In this XGR++ eval, X = 24/18 8/5* is right on the cusp. It is a 0.02 error, so it fits the definition of "well played" that is used for this puzzle.

The rest is pretty easy.

 White is Player 2 score: 0 pip: 158 Unlimited GameJacoby Beaver pip: 163 score: 0 Blue is Player 1
Blue to play 64

Blue will enter and hit with 64, and afterwards, White will enter and cover with 53.

 White is Player 2 score: 0 pip: 165 Unlimited GameJacoby Beaver pip: 153 score: 0 Blue is Player 1
White to play 53

The final sequence is 54S-63X-64H-53C.

So, what about the sleight of hand? Well, look what happens when you display 4 decimal places on the XGR++ eval of 54S-63.

 White is Player 2 score: 0 pip: 167 Unlimited GameJacoby Beaver pip: 158 score: 0 Blue is Player 1
XGID=-b----E-D---eD---c-eA---A-:0:0:-1:63:0:0:3:0:10
White to play 63

1.XG Roller++13/7 8/5* eq: -0.2069
 Player:Opponent: 45.29% (G:11.96% B:0.44%)54.71% (G:16.58% B:1.18%)
2.XG Roller++24/18 8/5* eq: -0.2270 (-0.0201)
 Player:Opponent: 45.10% (G:10.39% B:0.40%)54.90% (G:16.82% B:0.79%)

eXtreme Gammon Version: 2.10

Whoops! X = 24/18 8/5* no longer qualifies as well played.

Mike

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