Pip Counting

Forum Archive : Pip Counting

Symmetry method, Grouping men

From:   Brian Sheppard
Address:   brians@mstone.com
Date:   17 January 1997
Subject:   Re: pips
Forum:   rec.games.backgammon
Google:   01bc0495$b2f88180$3ac032cf@polaris.mstone.com

Robert wrote:
> Peter Schwarzberg wrote:
> > Can anybody tell me about the most easy way to count pips. Is it to
> > count the pips everytime I need the pip count, is it to keep track of
> > the pip counting from the beginning of the game and just substract the
> > number of the dice at every roll, or is it to count the differens
> > between the men of each player, or ...???
> The best way is to keep a difference total from the beginning and
> throughout the game. So if you roll a 3-5 the count is +8 and then your
> opponent rolls a 6-5 the count is -3, etc...  this is just like a
> blackjack count that becomes second nature after you try it for awhile.

This seems excessive. I doubt that you need to know the exact pip
count to make good decisions, so why bother? (You don't have to answer
this question; I know your system works for you :)

I recommend relying on a gut feel for who is ahead or behind until
racing equity is actually required. Then do an exact count using
either the symmetry method or by grouping men.

Symmetry Method
You create a correspondence between each of you men and the opponent's
men that has the closest pip count. Just keep a running total of the
differences between those men.

This system has the disadvantage that you don't know the length of the
race, just the difference.

Grouping Men
Count up each side, taking advantage of the clustering of groups around
central points. An example is helpful:

    X X X X X X
    X X X X X X
1 2 3 4 5 6 7 8

Here we have 12 men, centered around the 5.5 point, so their total pip
count is 12 * 5.5 = 66 pips.

In using this system, when you don't have a clear central grouping,
you can often shift men by a point or two so as to create one. For

    X   X X X X
    X   X X X X
1 2 3 4 5 6 7 8

If two men on the 5-point were moved to the 4-point, we would have
the previous situation, so this situation must be 2 pips more (68 pips).

Pick either the Symmetry Method or the Grouping Men method, depending
on the shape of the board. Sometimes one is easier.

Either is easier than keeping a running total. A running total involves
an addition or subtraction on every turn, and the average game lasts
50 turns (cubeless) apiece, so you have 100 additions and subtractions.
And when a man is hit you have additional work to do.

Both the Symmetry Method and the Grouping Men method yield an accurate
pip count in a handful of additions and multiplications. And since
a pipcount isn't even needed in most games, you have a tremendous
gain in mental efficiency by only computing it when you need it.

Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


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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