Backgammon Pip Counting

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. Thanks. 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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