an idea for a new game: Chomp

I propose a new game for this site, Chomp. Has anyone heard of it? will there be people willing to play?

It's a Nim-type game but quite more complex. i think there is no place in the net where it can be played.

Can you point us to a website that describes the game?

I think I found the game you're referring to.

http://markov.math.msu.ru/~pentus/abacus.htm

I'm sure this game has been solved although at this point I'm not sure if the game is a first second player win. But if it has been solved it wouldn't be at all suitable for this site, in my opinion.

So far, playing against the computer applet, I get killed all the time, while going first. However, that doesn't mean a thing... until I figure out the proper way to play, I'd probably lost each time while going second too.

Interesting game, though.

No, the game in general has NOT been solved. The site you mention is probably the only one that chomp can be played.

First, however, you can only play against the applet, not against someone else.

Second, the game can be played in 3 dimensions, (and 4, and 5, ...) and there is surely not solved. The 2-dimensional 5x11 may be solved, yes. Probably the 10x20 too. But the 20x30 is probably not. And the 4x5x6 is surely not. Not to mention 3x3xOmega where Omega stands for the Infinite.

I think a game like 2x5x10 would be fun (although difficult to implement on a web page).

Something else, too. It has been proven that the MxN game where M and N integers >=2 is a first player win, no matter how big M and N are. But nobody knows the correct first move, except only for small numbers.

this is just a 2d version of 'nim'. I don't think that it is an enjoyable game, apart from the mathematical theory around it (it's a nice idea); i wouldn't play it against humans.

Chomp might not have been solved for all initial rectangles, but a specific size would have to be chosen for LG. That size would almost certainly fall into the category of "small," in terms of how easily the game could be solved. The book "Winning Ways for your Mathematical Plays" details a methodology whereby the winning moves have been determined for "small" rectangles, and even shows a table of outcomes for different initial dimensions. For example, if you can leave a symmetric V shape on your move, with all squares removed except the leftmost column and topmost row, and these two are of equal length, your opponent will face a clear loss. This does not look like an interesting game.

I don't think Chomp would be suitable for this server. But there are some other games in "Winning Ways" that could be interesting to have, for instance "Dots and boxes" and "Philosopher's football". What do you think of these?

Dots & Boxes is more fun to play than Chomp, although there too, there may be temptation to use computer assistance. 20x30 Chomp might be too large to completely solve, but a computer could still help a lot. My main complaint about Chomp is that is is opaque. A winning strategy consists of presenting your opponent with a "zugzwang position," a position where the obligation to move is a disadvantage. What do these zugzwang positions look like? The only real way to find out, is to build up a list of them, starting with the smaller ones. This is just the sort of thing a computer does excellently and a human does poorly. I refer you to Mark Thompson's article on abstract games, http://www.flash.net/~markthom/html/game_thoughts.html for an explanation of the term "opaque."

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