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Checkers on the bar, and checkers borne off

Posted By: Nack Ballard
Date: Wednesday, 11 January 2017, at 1:13 p.m.

In Response To: COCONUT (Kangaroo on steroids) (Mike Clapsadle)

Are there any adjustments for checkers borne off or on the bar?

I'm glad Mike brought this up. It's a good question. I'll jump straight to the answer first. Then I'll explain why it works that way, with the help of diagrams.

Assume that YOU are the NEAR-side player with the BLUE checkers, and your opponent is the FAR-side player with the WHITE checkers. For counting purposes:

    A Blue checker on the bar (or White checker borne off) is on the 25pt, and does not get counted except as a 2-pip adjustment (or cancellation) in the final step.

    A White checker on the bar (or Blue checker borne off) is on the 0pt, and is counted every step of the way. It is on the near side, it is on the diagonal, and it is on the slants.


[The position below (65R-54S-43K-1) is a simplified selection for demonstration purposes. If it arose in a game and for some unknown reason you wanted a comparison count, admittedly you would just visualize that Blue is ahead by the extra two checkers moved down to his 8pt: Blue leads by 5 x 2 = 10.]






White is Player 2

score: 0
pip: 173
Unlimited Game
Jacoby Beaver
pip: 163
score: 0

Blue is Player 1
XGID=aa----E-D---fD---b-e----AA:0:0:1:00:0:0:3:0:10

When a checker is on the bar, that is the only time you need to pay attention to color in Coconut (or other colorless system), because it tells you in WHICH bear-off tray that checker is located!

In playing backgammon, if we all dutifully put the checkers we hit where they "belong," they would be easier to count! A hit Blue checker would be placed in White's bearoff tray, and a hit White checker would be placed in Blue's bear-off tray. For practical reasons, we don't do that, so it is necessary to visualize (or remember) the real location when we use the faster pip-count systems.

In the next diagram (cleverly created by Mike Clapsadle at my request), the checkers are still on the bar. You just don't see them there! They have been moved over to the 25pt and 0pt where they belong. Now (optimally, I suppose) imagine each of these blots at the base of the 25pt or 0pt, immediately adjacent to the blot on the 24pt or 1pt.

Capture2
Let's count with Coconut, using the (updated) poem:

First you double the near side men
Okay, 17 doubled is 34.

Add the diagonal and double again.
Add 13 makes 47, doubled is 94.

Plus slants, less 105, times 3
Add 15 makes 109, less 105 equals 4, times 3 equals 12.

Thus 12 is your approximate count. If you feel the need to perfect it, add the last step:

Then shift and cancel (for accuracy)
The left half of the board vertically cancels (poof!), both sides' 8pt checkers vanish (already on their middles), and four midpoint checkers on each side vertically cancel. The sole survivors are two 12pt checkers, a pip high from their middle. "High" counts against Blue, so –2. Using that to adjust the approximate count of 12 gives the exact count: Blue leads by 10.

Now let's imagine we did that final step the same way, EXCEPT we leave the 25pt and 0pt checkers on the board. Obviously it comes to the same adjustment of –2, but I'm going to demonstrate something else. [By the way, please ignore XG's stated pipcount in the margin -- it doesn't understand what we're doing!]

Capture3
Okay, try this: Shift the checker on the 0pt TWO pips to the right (to the 2pt), and shift the two 12pt checkers 1 pip each to the left (to the 11pt). This is an equal 2-pip offset, and puts all three checkers on their middles -- poof!

That maneuver left the 25pt checker an orphan, but it is easily counted. It is 2 pips higher than the 23pt middle. High is against Blue, and it therefore counts –2.

That was an alternate (admittedly, longer) way of arriving at the count of –2. It illustrates how you can deal with checkers on the 0pt or 25pt when they don't vertically cancel. Just shift them 2 pips to the right, assuming you see an offsetting 2-pip shift to the left that you like. Otherwise, count such a checker as –2 (if on the 25pt) or +2 (if on the 0pt).

In closing, I'll repeat (reinforce) the answer I gave at the beginning:

Nack

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