               | |||
| 5/1, 4/2 beats 6/off when you roll 21 next turn. | |||
| Position ID: AAAAkAAAAAAAAA Match ID: cIkKAAAAAAAA | |||
Rip none, when you could rip one.
There are 54,264 distinct checker arrangements that are possible during a bear off. That number is calculated as (7 multichoose 15), which gives the number of ways to position 15 checkers on 7 different points, i.e., on points 0 through 6. Point 0, of course, means off the board.
Since that count includes one position where all 15 checkers are off the board, there are only 54,263 positions that occur during a game. For each one, there are 21 distinct rolls. Thus, there are a total of 1,139,523 bear-off positions.
Out of this total, there are 3825 positions where, on a roll of a non-doublet, it is possible to bear off one checker, but the lowest EPC results when no checkers are borne off.
In this latter group, there is only one position where two checkers remain. It is the one shown in the diagram.
The tally posted here, gives the counts for all the related positions mentioned by Peter. Drop me a line if you would like a list of the XGIDs.
Mike