Five-Count Part 4.3:
Common cancellation patterns in an adjustment

Created by Sho Sengoku, 2001

Five in a row

cancel_01 Checkers lined five in a row cancel all their error counts no mater where they are. This is because any five consecutive points have all different error numbers from -2 to +2 but no duplications.

Check yourself about this, and you will understand that a five point prime in any location cancels all error numbers in it at once.

Weak symmetric patterns

cancel_02a Not exactly symmetric, but you can see they are "balanced" on the group center (the 5 point in this example.) A balanced pattern on a group center always cancel its error numbers.

This pattern is very common and you will often see the same pattern in a real backgammon game.

cancel_02b The same "balanced" pattern, and it cancels all errors at once.
cancel_02c Not balanced as it is, but it would be balanced on the 9 point (the center of Group 2) if the three checkers on the 6 point were the 11 point.

Or you can think that it is a weak symmetric around a group boundary and cancels all error numbers at once.

Diagonal corners in a box

cancel_03a Any pair of checkers on diagonal corners of the left side or the right side of the bar cancels error numbers together.

Distant symmetric patterns

cancel_04a This "distant symmetric" pattern may be a bit harder to catch at a glance. That's partly because they are many pips away, but mainly because the bar cuts off the board in two and change our perception of distance.

If you removed that big bar form the board view, then you could easily see good symmetric patterns.

cancel_04b You can't just erase the bar from a real backgammon board of course.

If you don't like this "fake" board image, then just compare two checkers' locations in the group boxes, and you may find symmetry there.


Continue on to:   Summary of Sho's Pip Count, "Five-Count"


Sho Sengoku's Five Count

Overview:   Summary of Sho's Pip Count, "Five-Count"
Part 1:   Quick View: Introduction to "Five-Count"
Part 2:   Techniques for Easier and Faster Counting
Part 3:   Practice, Practice, Practice
Part 4:   Even Faster!
Part 4.1:   Common patterns for "10s" in group counting
Part 4.2:   To get a "rough count" even faster
Part 4.3:   Common cancellation patterns in an adjustment


See:  Other articles by Sho Sengoku

See:  Other articles on Pip Counting

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