                      | |||
| Blue to play 32 | |||
| Position ID: 470PAADjvQ8AAA Match ID: cIkJAAAAAAAA | |||
Positions Where Bearing Off Does Not Yield the Lowest EPC
Without regard to the opponent’s checkers, it uses a one-sided bear-off database to find all positions where the play that results in the lowest EPC is not the play that rips off the most checkers.
The results may be categorized as follows:
| Category | No. of Positions |
|---|---|
| Rip None, on a Roll of Doublets, When You Could Rip 1 | 1,751 |
| Rip None, on a Roll of Doublets, When You Could Rip 2 | 24 |
| Rip 1, on a Roll of Doublets, When You Could Rip 2 | 6,149 |
| Rip 2, on a Roll of Doublets, When You Could Rip 3 | 2,078 |
| Rip 3, on a Roll of Doublets, When You Could Rip 4 | 35 |
| Rip None, on a Roll of Non-doublets, When You Could Rip 1 | 3,825 |
| Rip 1, on a Roll of Non-doublets, When You Could Rip 2 | 1,911 |
| Total | 15,773 |
This may seem like a lot of positions, but remember, the ceiling is quite large. Including the position where all checkers are off the board, there are 54,264 distinct checker arrangements that are possible during a bear off. For each one, there are 21 distinct rolls. Thus, there are 1,139,544 bear off positions in all. 15,773 is only 1.38%.
Even that, however, is a gross exaggeration. Many of the positions—I think well over half— are “junk” positions that never arise during actual play. A common characteristic they share is ridiculous stacks.
One such position, for instance, has 9 checkers on 6pt, 1 checker on the 1pt, 2 on the 3pt, and 3 already off. Talk about junk! If you roll 11, you won’t be surprised to learn that unstacking the 6pt beats ripping 2 off.
Below are XGIDs for a few positions I found interesting. The first of the them is diagrammed above.
XGID=-A--EDE------------ede--a-:0:0:1:32:0:0:3:0:10
XGID=-A--DDF------------fdd--a-:0:0:1:32:0:0:3:0:10
XGID=--D-CDD------------ddc-d--:0:0:1:31:0:0:3:0:10
XGID=--D-CDD------------ddc-d--:0:0:1:31:0:0:3:0:10
XGID=--C-CED------------dec-c--:0:0:1:31:0:0:3:0:10
XGID=--C-CDE------------edc-c--:0:0:1:31:0:0:3:0:10
XGID=--C-CCF------------fcc-c--:0:0:1:31:0:0:3:0:10
XGID=--B-CDF------------fdc-b--:0:0:1:31:0:0:3:0:10
XGID=-A-CBED------------debc-a-:0:0:1:22:0:0:3:0:10
XGID=-A-CBDE------------edbc-a-:0:0:1:22:0:0:3:0:10
XGID=-A-CBCF------------fcbc-a-:0:0:1:22:0:0:3:0:10
XGID=-A-BBFD------------dfbb-a-:0:0:1:22:0:0:3:0:10
XGID=-A-BBEE------------eebb-a-:0:0:1:22:0:0:3:0:10
XGID=-A-BBDF------------fdbb-a-:0:0:1:22:0:0:3:0:10
Mike