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.
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| 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