Pip Counting

 Casting out crossovers

 From: Mark Denihan Address: MAR3K@worldnet.att.net Date: 7 October 1996 Subject: Re: Help On Pip Counting Methods Forum: rec.games.backgammon Google: 53bpp4\$t23@mtinsc01-mgt.ops.worldnet.att.net

Back in 1981, while struggling with cumbersome pipcounting methods, I
thought up a method that allows me to get an accurate count quickly and
easily.  Jack Kissane is still a faster counter than me, but most other
none had ever heard of it except Magriel; so I guess I am a co-inventor
with someone.

I call it Casting Out Crossovers.

All you need to learn are a few multiples of six and how to recognize
some patterns of ten.

The fundamental idea is that to move a checker from one quandrant to the
same position in the next quadrant takes six pips.  So if you count all
the crossovers needed to bring all the men into your home board and
multiply this number by 6 you have reduced each quadrant into a home
board position with pip count values of 1-6.  Then you can learn to
recognize patterns of 10; such as 2 men on the 2point and 2 men on the
3point, and just keep adding these tens onto the first number you
obtained when you multiplied by 6.  Then add on the few extra pips that
did not fit conveniently into patterns of ten.  Thats it.  Gone is the
problem of trying to multiply and add or subtract different groups of
numbers or keep mental shifts in your memory.  It's easy for us humans to
increment by tens.

I wrote this explanation off-the-cuff so to speak so if anyone wants a
clearer explanation with examples let me know.  I find that I am faster
and more accurate at counting than most good players even though I have
no natural talent for counting.  It may take you a few days to build up
speed.

Mar3k

### Pip Counting

Casting out crossovers  (Mark Denihan, Oct 1996)
Cluster counting  (camelx+, May 2005)
Counting half rolls  (Bob Hoey, Apr 1998)
Half-crossover method  (Douglas Zare, Mar 2002)
Live play versus online  (Stanley E. Richards+, Apr 2006)
Live play versus online  (Rich+, Mar 2006)
Mental shift  (Stephen Turner, Oct 1996)
Modified direct count  (Daithi, Mar 2011)
Opposing sums and differences  (Donald Kahn, Apr 1998)
Running pip count  (Rodrigo Andrade+, Apr 1998)
Symmetry method, Grouping men  (Brian Sheppard, Jan 1997)
The 51/21 count  (kruidenbuiltje, Mar 2011)