The Game of Chomp

Update: This page is somewhat out of date. In 2013, my results on Chomp were published in the ICGA Journal. See the "Chomp Solver" citation on my Professional Page. This included analysis of all positions up to the 16x16 square. The software is available at SourceForge.

This is a sample graphic representation of some investigations into the game of “Chomp”. Some explanation:

  1. At the moment, I have complete results only for boards up to 9x9, so that's all you will see here. This page shows (some of) the subset consisting of positions that are three rows high. For a theoretical treatment of 3-rowed Chomp, see Brouwer et al, "On Three-Rowed Chomp", INTEGERS: Electronic Journal of Combinatorial Number Theory 5 (2005).
  2. The left column contains possible starting positions; that is, they are rectangles. This means, among other things, that with proper play, the first player wins. In fact, the correct first play in each one is unique, and is shown as a red square with a letter. The pink squares are the ones that are removed by the lettered move.
  3. The other images are the interesting 3-high positions that can arise from the rectangles; each is labelled with a letter A-S. These positions are all "lost"; there are no winning plays. The lower-leftmost is not labelled because taking that square is a loss by definition. The others are labelled with an indication of the correct winning answer to the move at that square. If it's a letter other than C, it's the label of the position that the move and correct answer should arrive at. A C indicates that the losing move has reduced the position to a 1- or 2-row position that is not pictured here, but is easily winnable. A 1 or 2 in a square indicates that the correct response is to take the 0,1 or 0,2 square and reduce the position to a 1- or 2- row position that is easily winnable.
  4. The letters tend to occur in pairs, because in either order, these choices arrive at the given shape. The letter C pairs with a 1 or a 2 in a similar way, but the result is shorter than 3-high and is not pictured here.
  5. Occasionally, a square will be marked with a second possible ending shape. They are both equally good. They are relatively rare in this group, but become increasingly common with larger positions.

This is an experiment in embedding an SVG graphic in a web page. If any browser has trouble with it, I'd like to know; send email to kogorman at pacbell dot net. So far, it has worked as intended in Firefox and Opera. Internet Explorer 8 on Windows Vista needs the Adobe SVG add-in, and even then treats the image as opaque (it is not). Explorer 9 gets it right. Older versions of Safari on Windows Vista clip the image and we lose significant information on the right and bottom edges. Safari 5.5.1 puts scrollbars on that region, so the data is hidden but accessable.

It would be nice to hear from Mac users about how it looks.

Coding help is very welcome.

[SVGPartial Chomp workup, 3-high positions] (Using the link to view the image requires a stand alone SVG viewer and your browser needs to be configured to use this player)