The links from the article are fascinating. I had never heard of Arimaa before, and am quite intrigued.

And from the linked article by Kasparov (http://www.nybooks.com/articles/archives/2010/feb/11/the-che...) comes this gem:

   In what Rasskin-Gutman explains as Moravec’s Paradox, in chess, as in so many 
   things, what computers are good at is where humans are weak, and vice versa. 
   This gave me an idea for an experiment. What if instead of human versus machine
   we played as partners? My brainchild saw the light of day in a match in 1998 
   in León, Spain, and we called it “Advanced Chess.” Each player had a PC at hand 
   running the chess software of his choice during the game. The idea was to 
   create the highest level of chess ever played, a synthesis of the best of man 
   and machine.

   ....

   In 2005, the online chess-playing site Playchess.com hosted what it called a 
   “freestyle” chess tournament in which anyone could compete in teams with other 
   players or computers. Normally, “anti-cheating” algorithms are employed by 
   online sites to prevent, or at least discourage, players from cheating with 
   computer assistance. (I wonder if these detection algorithms, which employ 
   diagnostic analysis of moves and calculate probabilities, are any less 
   “intelligent” than the playing programs they detect.)

   Lured by the substantial prize money, several groups of strong grandmasters 
   working with several computers at the same time entered the competition. At 
   first, the results seemed predictable. The teams of human plus machine 
   dominated even the strongest computers. The chess machine Hydra, which is a 
   chess-specific supercomputer like Deep Blue, was no match for a strong human 
   player using a relatively weak laptop. Human strategic guidance combined with 
   the tactical acuity of a computer was overwhelming.

   The surprise came at the conclusion of the event. The winner was revealed to be 
   not a grandmaster with a state-of-the-art PC but a pair of amateur American 
   chess players using three computers at the same time. Their skill at 
   manipulating and “coaching” their computers to look very deeply into positions
    effectively counteracted the superior chess understanding of their grandmaster 
   opponents and the greater computational power of other participants. Weak human 
   + machine + better process was superior to a strong computer alone and, more 
   remarkably, superior to a strong human + machine + inferior process.

> Indeed, if you start from a closed position where strategy dominates and tactics are of relatively little use, top human players can still trounce computers

I haven't been following computer chess as much as I used to be I suspect this is actually untrue. Computer speed has been increasing as always but there has also been massive gains in chess program strength (e.g. compared to old programs when running on the same hardware). For example, Rybka 4 would absolutely crush programs from 10 years ago.

Those combined gains make computer chess programs so strong that I doubt even top players can hold them off even with the position looks quiet. Rybka can defeat GMs even when they have pawn plus first move odds[1]. In one match Rybka had a tiny opening book so the GM had every opportunity to steer the game in a strategic direction.

1. <http://en.wikipedia.org/wiki/Rybka#Odds_matches_versus_grand...;

If anyone is serious about proving things about chess I would suggest they start by proving things about simpler chess variants.

The variant of chess "wild 5" where your pawns start on the 7th rank and pieces on the 8th (so pawns promote in one move) has far fewer choices than in chess. It's a simpler game. It has a significant advantage for white, much larger than in normal chess. Humans came somewhat near to proving it's a win for white just by learning the (relatively few) openings out to 20 or so moves. At each step there's usually only a couple moves that aren't terrible. For the first six moves there is a single way of playing which is considered best for both sides.

Yet even in this much simpler game which humans are near cracking, I think a pure math type approach would have a very hard time getting anywhere.

If you can't do anything there, you could always try an even simpler game. There is a game called pawns where you start with only your pawns. If you promote you win instantly. Math ought to be able to solve that one. If you crack that, move on to little chess (normal chess but only with pawns and kings). Little chess should no doubt be a draw (you can waste moves with your king unlike in pawns where it's less clear) but proving that would be a good accomplishment I think.

Game researchers don't ignore all Chess-like games that are more difficult for computers. It's just that they've met with very, very limited success in Go. Combined with Go's relative unpopularity outside of southeast Asia, this means you don't hear about it very much.

For example, according to Wikipedia, a computer actually beat a professional Go player for the first time in 2008.

+1 for funding issues.

When I was working on my undergraduate thesis on applying machine learning techniques to board games, I developed the basis of a new method of analyzing board games (using graphs of games and graph isomorphism) but I wasn't able to find anyone who could finance me doing a research masters in it. Although I think part of my issue was that it wasn't obviously Computer Science, nor was it obviously Mathematics.

There is another closely related field that has plenty of real applications: formal verification. Essentially the task is to ensure no reachable state violates some property. The problem is the same as in chess, the reachable state space is enormous. There is probably more funding available for this take on the problem than chess, but it has been studied for decades and there are no easy answers.

> What if we make things easier for the machine? It is obvious to a rank beginner that a perfect game with a rook handicap is a win for the side with the material advantage. No, make it a queen! Surely that must be a provable win?

Hm, I'm sure it must be. Although I don't know how you go about proving it, it's a simple matter to force equal trades; black cannot avoid the exchange of pieces forever, and if white plays a perfect game he will always win, without doubt.

> Not so fast. Even against a crushing asymmetry in material, it is not too hard to avoid mate for a couple of dozen moves, which means that calculating all the way to the end of the game is beyond the reach of search-based algorithms.

Okay, just calculate the moves it would take to force the equal exchange of material from a given position. Generally as the game progresses and the board opens up it becomes inescapable.

After a certain point, when enough material has been removed from the board, looking for mate becomes trivial. Esp if you operate with such a commanding advantage as a queen...assuming you can force the equal exchange of all other material, it is possible to calculate checkmate within a couple of moves.