Pip Counting

Forum Archive : Pip Counting

Half-crossover method

From:   Douglas Zare
Address:   zare@math.columbia.edu
Date:   22 March 2002
Subject:   Re: Is there a painless way to count pips?
Forum:   rec.games.backgammon
Google:   3C9BD6B2.78285DA5@math.columbia.edu

Ron & Ann Barry wrote:
> If you ever do get to the point of actually counting pips, by far the most
> elegant, easily remembered technique, and the one that requires the fewest
> number of steps, is that which Doug Zare developed some time back. I don't
> have the Web page handy just now, but I'm sure Doug can provide it for
> you.


The basic idea is to count half-crossovers needed to bear your checkers in.
Every checker on your 4-5-6 counts 0 (which is good, since you have a lot
there), every checker on your 7-8-9 counts 1, every checker on you 10-11-12
counts 2, ..., every checker on your 19-20-21 counts 5. The error from
assuming that every checker on the 1-2-3 is on the 2, every checker on the
4-5-6 is on the 5, etc. is remarkably low, particularly in positions which
arise from normal play. Normally, when I play OTB or watch matches on
GamesGrid as I exercise (unable to click the calculator button), I only
perform the count of half-crossovers, and don't bother to make the
adjustments of -1, 0, or +1 for each checker to get an exact count except
in racing doubling decisions. To get an exact count, you multiply the HC's
to bear in by 3 and add to 75, then for each checker on the high point of
its triplet (6 of 4-5-6) add 1, and for each checker on the low point,
subtract 1.

As Sara mentioned, the pip count is extremely important in modern
backgammon, and anyone who does not have an accurate feel for the race will
be eaten alive by any strong player who does. Which system you use is not
very important. What matters is that you choose a system that you will use
when you need to.

Douglas Zare
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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)  [GammOnLine forum]
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) 
Tips  (Patti Beadles, Dec 1994) 
Tips for counting pips  (neilkaz, Sept 2010) 

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