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
example:

X
X
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.

Brian
```

### 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)