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Contact bearoff is not so easy

Posted By: Taper_Mike
Date: Sunday, 3 June 2012, at 2:26 a.m.

In Response To: Contact bearoff is not so easy (Klaus Evers)





White is Player 2

score: 0
pip: 93
7 point match
pip: 16
score: 4

Blue is Player 1
XGID=-aC--B-a--------a--bbbbbb-:1:1:1:42:4:0:0:7:10
Blue to play 42

In the original position above, you are stuck leaving two blots in any event. One will be on the 1pt, where you are forced to hit with the 4. For the other, you must choose either the 3pt or 5pt. You can bear off one checker, leaving 22 shots, or else bear off nothing, while leaving only 20 shots.

The extra checker off makes a big difference. The reference postions below show your chances when one or two checkers are closed out. (In order to get XG to do the analysis, I had to give White the cube, but no matter. The cubeless winning percentages are what I am interested in.)

One Checker Closed Out

White, the top player, is on roll in the diagrams below. When one checker is closed out, Blue wins an extra 6.5% of the games (cubeless) by taking an extra checker off now.





White is Player 2

score: 0
pip: 57
Unlimited Game
Jacoby Beaver
pip: 32
score: 0

Blue is Player 1
XGID=-AC----------------cccbbbA:1:-1:-1:00:0:0:3:0:10
White on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 38.11% (G:0.00% B:0.00%) 37.85% (G:0.00% B:0.00%)
Opponent Winning Chances: 61.89% (G:0.00% B:0.00%) 62.15% (G:0.00% B:0.00%)
Cubeless Equities -0.238 -0.486
Cubeful Equities
No redouble:-0.112
Redouble/Beaver:-1.703 (-1.591)
Redouble/Pass:+1.000 (+1.112)
Best Cube action: No redouble / Beaver
Percentage of wrong pass needed to make the double decision right: 37.1%

eXtreme Gammon Version: 2.03





White is Player 2

score: 0
pip: 57
Unlimited Game
Jacoby Beaver
pip: 30
score: 0

Blue is Player 1
XGID=-AB----------------cccbbbA:1:-1:-1:00:0:0:3:0:10
White on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 31.59% (G:0.00% B:0.00%) 31.60% (G:0.00% B:0.00%)
Opponent Winning Chances: 68.41% (G:0.00% B:0.00%) 68.40% (G:0.00% B:0.00%)
Cubeless Equities -0.368 -0.736
Cubeful Equities
No redouble:-0.257
Redouble/Beaver:-2.000 (-1.743)
Redouble/Pass:+1.000 (+1.257)
Best Cube action: No redouble / Beaver
Percentage of wrong pass needed to make the double decision right: 36.8%

eXtreme Gammon Version: 2.03

Two Checkers Closed Out

Once again, White, the top player, is on roll in the diagrams below. When two checkers are closed out, Blue wins an extra 5.5% of the games (cubeless) by taking an extra checker off now.





White is Player 2

score: 0
pip: 57
Unlimited Game
Jacoby Beaver
pip: 56
score: 0

Blue is Player 1
XGID=--C----------------cccbbbB:1:-1:-1:00:0:0:3:0:10
White on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 85.86% (G:0.00% B:0.00%) 85.60% (G:0.00% B:0.00%)
Opponent Winning Chances: 14.14% (G:0.00% B:0.00%) 14.40% (G:0.00% B:0.00%)
Cubeless Equities +0.717 +1.424
Cubeful Equities
No redouble:+0.997 (-0.003)
Redouble/Take:+1.330 (+0.330)
Redouble/Pass:+1.000
Best Cube action: Redouble / Pass

eXtreme Gammon Version: 2.03





White is Player 2

score: 0
pip: 57
Unlimited Game
Jacoby Beaver
pip: 54
score: 0

Blue is Player 1
XGID=--B----------------cccbbbB:1:-1:-1:00:0:0:3:0:10
White on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 80.46% (G:0.00% B:0.00%) 80.11% (G:0.00% B:0.00%)
Opponent Winning Chances: 19.54% (G:0.00% B:0.00%) 19.89% (G:0.00% B:0.00%)
Cubeless Equities +0.609 +1.205
Cubeful Equities
No redouble:+0.994 (-0.006)
Redouble/Take:+1.071 (+0.071)
Redouble/Pass:+1.000
Best Cube action: Redouble / Pass

eXtreme Gammon Version: 2.03

Mike

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