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Thibault de Vassal    (2006-09-08)
Chess tournament : Zero-sum or not ?

While discussing about Sun Tzu's "The Art of War", and the question "Is the best player always the champion ?" (of course not IMO) , I was argued that any chess tournament "was" (actually could be "reduced to") a zero-sum game :

"In 1944 John von Neumann and Oskar Morgenstern proved that any zero-sum game involving n players is in fact a generalised form of a zero-sum game for two persons, and that any non-zero-sum game for n players can be reduced to a zero-sum game for n + 1 players; the (n + 1) player representing the global profit or loss. This suggests that the zero-sum game for two players forms the essential core of mathematical game theory."

It seems to me that it's out of topic, but I couldn't say exactly why... In my opinion, a tournament is nearer life than game, at least quite far from it. Much more rules, often complex ones, and results that depend on many parameters you couldn't influence...

The word "champion" depends on accurate rules (the best player could finish 2nd, even if he wins all games ie. in an open tournament..), the "best player" depends on general opinion (most commonly through ratings), ie. Topalov vs. Kasparov ...

What do you think ? :-)

Where the discussion started from :

I agree with many points about how to win, but the use of some words seems to be dubious...

I like much this quote :

"I was surprised to see that Capablanca did not initiate any active maneuvers and instead adopted a waiting game. In the end, his opponent made an imprecise move; the Cuban won a second pawn and soon the game. “Why didn’t you try to convert your material advantage straight away?” I ventured to ask the great chess virtuoso. He smiled indulgently. “It was more practical to wait.” "

—Mikhail Botvinnik, 6th World Chess Champion

Thibault de Vassal    (2006-09-12 12:51:56)
Zero-sum games

Ok, the question was obviously a bit hard & unclear :)

Rodrigo Jaroszewski    (2006-09-12 13:19:57)
Math... *sigh*

LOL Thibault, I guess it was.

I'm no mathematician (far from it), but I don't think that this theory will turn out to be true anytime in the near future, even in a "predictable" game like chess. Even chess engines depend on the skill of their programmers to find new ways to make their search algorithms become reliable and faster, and tablebase development is still petabytes away from being complete.

Anyway, I guess the future generations will have to tell us if it worked or not. Only God knows what can get in the way of this "gaming nirvana" as they call, and after I heard that it was proven possible that a computer user can subconciously influenciate the way an idle machine performs, I don't feel like trying to impersonate Baba Vanga on this subject! ;)

Thibault de Vassal    (2006-09-12 13:32:36)
Math... *sigh*

... Well.. I forgot my question :-))





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