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Walter and Hal Heinrich Discovered This

Posted By: Paul Weaver
Date: Wednesday, 7 January 2015, at 11:38 p.m.

In Response To: Optimal non-contact bearoff distribution (Igor)

What is the position with fifteen checkers in the home board with minimal wastage? I believe that Walter and Hal Heinrich independently figured out by 1994 that Blue's 3-5-7 position shown below is the answer to this question.

When Walter showed me this in 1994, I thought it was so cool that I revealed it to the world in an article (my very first backgammon article) on the topic that was published by Bill Davis in The Chicago Point in 1994. I no longer have the article, but I recall writing some BS like this: "How can anyone pretend to know anything at all about backgammon when he doesn't even know to how to play his checkers in a non-contact position?"

Of course, in the actual position shown below, it does Blue no good to have reached the optimal bearoff position because he has already lost the game indeed, he has already lost a gammon with the cube on 32. Be sure to scroll down to check out the rollout data.

White is Player 2

score: 0
pip: 0
Unlimited Game
Jacoby Beaver
pip: 79
score: 0

Blue is Player 1
Blue on roll, cube action?

Analyzed in Rollout No redouble Redouble/Take
Player Winning Chances: 0.00% (G:0.00% B:0.00%) 0.00% (G:0.00% B:0.00%)
Opponent Winning Chances: 100.00% (G:100.00% B:0.00%) 100.00% (G:100.00% B:0.00%)
Cubeless Equities -2.000 -4.000
Cubeful Equities
No redouble:-2.0000.000 (-2.000..-2.000)
Redouble/Take:-4.000 (-2.000)0.000 (-4.000..-4.000)
Redouble/Pass:+1.000 (+3.000)
Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 28.6%
Rollout details
84934656 Games rolled with Variance Reduction.
First 1 moves: 3-ply, cube decisions: XG Roller+
Remaining moves: 3-ply, cube decisions: XG Roller+
Double Decision confidence:100.0%
Take Decision confidence:100.0%
Duration: 3 minutes 37 seconds

eXtreme Gammon Version: 2.10

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