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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 GameJacoby Beaver pip: 79 score: 0 Blue is Player 1
XGID=----CEG-------------------:5:1:1:00:0:0:3:0:10
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: -2.000 ±0.000 (-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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