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December 28, 2013

Urquhart's Pip counting system, adapted

I think I finally found a pip counting system I can use.

I am using a modified version of Urquhart's Absolute Pip Count (UAPC) which was described in Gammon Village in January 2013.

His system is based on the two point and takes four steps to get an exact count.

1: Count # of crossovers times six (This moves all checkers to home board)

2: Count # of semi-crossovers ** times three (This moves all checkers to near half of the home board)

3: Add 30 pips (this assumes all 15 checkers are stacked on the two point)

4: Adjust for Unit crossovers (add one pip for checker at far edge and subtract one pip for checker at leading edge of triad)

** Semi-crossover means moving from the far side of quadrant to near side of quadrant.

Here is my adapted version:

For You:
1: Count # of crossovers

2: Count # of semi-crossovers. Count each as 1/2

For Opponent:

1: Count # of crossovers

2: Count # of semi-crossovers. Count each as 1/2

Difference times six is the approximate pip count difference.

So by omitting the conversion to absolute count I only get the difference.

And also by skipping the last step the difference is not exact. The count may be off be a few pips if checkers are not centered in each triad.

For my purposes, I mainly want to know ...

Is the race about even?
Am I ahead some or a lot?
Am I behind some or a lot?

and this method seems a quick and easy way to determine the status of the race with confidence.

An exact count is usually not needed. If it is, in a race scenario for example, I can use other methods to determine the exact count. Usually I try to get the raw count for each side.


Here is an example using the method:

is tanzsox

score: 0
pip: 129
7 point match
                          pip: 167
score: 0

is Chutzpah
on roll, cube action?

eXtreme Gammon Version: 2.10

I (yellow) have:

crossovers, starting from opponent's home board ... 3,6, plus 5x2 or 16, +2 is 18 crossovers.
Plus semi-crossovers, again starting from opponent's home board ... 18.5, 19, 19.5, 20, none on my outer board, plus 3 more from my home board or 23 Total crossovers.

Opponent (black) has:

crossovers ... 0, 2-4-6-8, plus 5 is 13
semi-crossovers ... 13.5, plus 3 from home board or 16.5 total crossovers.

So I am behind approximately 6.5 crossovers or about 39 pips.

Actual is 38 pips.  Not bad.  And this is actually pretty quick to do in your head.  Much quicker than writing it out long hand.


Here is one more for practice:

is tanzsox

score: 5
pip: 160
7 point match
                          pip: 116
score: 4

is Chutzpah
on roll, cube action?

eXtreme Gammon Version: 2.10

Me / Yellow:

2-4-6, plus 5 is 11 crossovers
plus semis in the home board, 12,13,14,14.5 total crossovers

Opponent / Black:
3-6-9, 11-13-15, plus 4 is 19 crossovers
plus semis 19.5, 20.5-21.5-22 total crossovers

I am up 7.5 crossovers or about 45 pips.   (Actual 44)


  1. If you like the idea of half-crossovers, then be sure to check out Doug Zare's Gammon Village article on the subject:

  2. Hi Tim. Nice to hear fro you as always.

    Zare's Half-crossover is good too. They all are really, it's just a matter of picking one and sticking with it.

    When I want an exact count, like in a race, I actually count the whole race for both sides using various references and shortcuts... but I really like what I wrote and it seems to be working for me. Counting crossovers is super easy and then I only have to count the "long" half-crossovers (which is a bit easier than counting all the half-crossovers). Again, I am just trying to get a sense of am I ahead or behind and by a lot or a little and this method works for me.

  3. Thanks for showing me this. I like it if you only need a quick estimate. I've been using the colorless counting method though because it's exact, where this could be off + or - 30 pips. However, if you were off a lot, the position of the checkers would be obvious. I'll definitely use this for quick estimates. You're right that you just need to find a method that you're comfortable with, and stick with it.

    In your first example though, aren't there only 4.5 semi crossovers for yellow, not 5?

  4. What do you count if you have a man on the bar?