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 nbym 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 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.

David Wolfe presenting Adam and Garrett with their prize

A curious 3x7 position

The following 3x7 position has atomic weight 6, but has a surprisingly complicated canonical form.
The canonical form is shown using a larger clobber position in a file you can dowload in either postscript or pdf.