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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.



Moravec's "Paradox" isn't really paradoxical at all. What makes us say that computers are "strong" in some area? Answer: the fact that they are good there relative to our prior expectations. Where do those expectations come from? From looking at ourselves. Similarly: what determines where we say we're "weak"? Answer: seeing other things being strong relative to us. Computers, for instance.

Now, of course there are other points of reference for deciding where we're "weak". Doesn't that invalidate my argument? Why, no, because actually if we use those other points of reference the paradox rather goes away. For instance: Computers do arithmetic very, very fast. Is that an area where we're weak? Only if we compare ourselves against computers; we do arithmetic much better than chickens or tigers do.


Arimaa is a great game. I've been playing with friends for a couple of months and I'm always amazed by how complex gameplay can emerge from such simple rules.





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