# Clobber research

The goal of this page is to summarize active research in the game
**clobber** (at least for a couple months) and to support
the activity of clobber problem composers competing
in Elwyn Berlekamp's clobber problem composition
contest.
## Rules to clobber

Clobber is a new combinatorial game invented last
summer in Halifax by Richard Nowakowski, J. P. Grossman and Michael
Albert. The first competitive clobber tournament was
held at Dagstuhl, Germany, in February 2002.
Clobber is played by two players, White and Black, on a rectangular
`n``by``m` checkerboard. In the initial
position, all squares are occupied by a stone, with white stones on
the white squares and black stones on the black squares. A player
moves by picking up one of their stones and *clobbering* an
opponent's stone on an adjacent square (horizontally or vertically).
The clobbered stone is removed from the board and replaced by the
stone that was moved. The game ends when one player, on their turn,
is unable to move, and then that player loses.

## Combinatorial game theory values in clobber

You can use my combinatorial game theory toolkit to
calculate values of clobber positions.
Note that all clobber positions are *all
small*: Since White has a legal move if and only if Black does,
non-zero numbers cannot appear as values. Hence, every
clobber positions has a well-defined *atomic
weight.*

It appears that most positions have a far simpler atomic weight than
canonical value. For this reason, we strongly suspect that atomic
weights are the key to understanding most positions which appear in
practice. Using the toolkit, I have searched all positions which can
fit onto a small board for new atomic weights. See this file for the results of this search; a position
is outputed if it has a ``normalized'' atomic weight which has not been
outputed yet.

## LaTeX users

You may wish to use my clobber.sty file to
generate clobber positions.
The file clobber.tex is a sample input file and
clobber.ps is the corresponding output.
## Winning entries to Clobber contest

First prize of $1000 was awarded to Adam Duffy and Garrett Kolpin for
their entry, *By hook or by crook,* available Postscript or PDF.
The second prize of $500 was awarded to J.P. Grossman. His entryand
solution is available in plain text.

## A curious 3x7 position

The following 3x7 position has atomic weight 6, but has a surprisingly
complicated canonical form.
XXXXXXX
XOXXXXX
XXXXXXX

The canonical form is shown using a larger clobber position in a file
you can dowload in either
postscript or pdf.