For the scoring system, the axiom wich could be associated with the "the sum of the angles of a triangle = 180°" axiom is "1 win + 1 loss = 2 draws".

It can also be seen as the scoring system version of dx²+d y² = dy²

So the 1-1/2-0 is our euclidian system, notice that they both came as the most natural and was seen as the only valuable.

The elliptic one would be the scoring wich use the "1 win + 1 loss > 2 draws" axiom as for example, 3-2-0 system (you love solidity, and any lost is seen as a shameful failure).

And the hyperbolic one would be the one wich use the "2 draws > 1 win + 1 loss" (our "beloved" 3-1-0 ;-)).

But there is a point wich i would be more serious:

I don't think it's relevant to say "the 3-1-0 system is bad because with this system, +4;=1;-5 is better than +1;=9".

In fact, "1 win + 1 loss > 2 draws" and "+4;=1;-5 is better than +1;=9" are "equivalent" (the number of losses allowed has to be define).

It's just like saying "this geometry sucks because the pythagorean theorem does not hold in it!".

So i think that the only debate is wether the "1 win + 1 loss > 2 draws" axiom is better than the "1 win + 1 loss > 2 draws" one or than the "1 win + 1 loss = 2 draws".

1. The standings kind of look the same as they would have been if the traditional scoring system was used.>

True, as of now. However, it could be different, and if we continue these tournamnets, inevitably we will get a tournament wherein the 3 - 1 - 0 scoring will yield a standing different than the traditional one.

If the 3 - 1 - 0 scoring is used to determine the apportioning of prize money in traditional scoring system context, then I have no objection.

<2. Ivanchuk gets in to time trouble in every game and plays some of the best chess here. Just goes to show that there are more important things to be considered here, such as consistency, form, preparation etc...>

Right again. However, it's not true with all players. We have already seen Anand playing weakly around move 40 and after.

What I mean is that in general, with the given time control and no increment after move 40, players would tend to commit more errors around move 40 and after.

Game Collection: Vienna 1882

Game Collection: Linares 1993

Game Collection: WCC Index [Zurich 1953] Game Collection: Karlsbad 1929

Game Collection: San Sebastian 1911

Game Collection: Las Palmas 1996

Also

Game Collection: St. Petersburg 1895-96

Game Collection: St Petersburg 1914

Nice joke. Women were Capa's weakness. Capa was also women's weakness. He was like the Rudolf Valentino of chess. My uncle who was a a child in the 30s still remembers stories about Capa, and this chess genius was also monstrously handsome and attractive. When he walked into a roomful of people, everyone would soon be looking at him, even not knowing him. Ladies would swoon over him and flocked to see him playing in tournaments.

I have stated this belief already. Capablanca in 1919 was playing nearly errorless chess (except for one gross oversight, in a game he still won). He won all of his classical games except for one. He had not yet tasted what it felt like to be World Champion and was hungrily trying to win every game he ever played to prove to the world he deserved a Title shot. This 1919 Capa updated in opening theory IMO would have beaten just about anybody in a match, with the possible exception of the 1971 version of Fischer.

I think this was actually money odds: you win $5, I win $1. Nowhere did he specifically mention time odds.>

Thanks for the correction. In any case, Capa all throughout his career was the only player who ALWAYS won all blitz and rapid competitions he entered. Blitz is blitz, but if you play a thousand blitz games, and still win most of them convincingly, the statistics of such s feat would show that you are indeed a very strong chess player. Did Capa ever lose a single blitz game in his life anyway?

Moreover, in blitz opening prep practically becomes useless. The players play largely according to their natural abilities. Even a Capa who was not updated in opening theory but instantaneously saw most possibilities even in complex middlegames and could spot a winning maneuver in almost any endgame where one existed would probably smash everyone in a blitz tournament today.

Personally I regard the finals of St Petersburg 1914 wherein Lasker, Capablanca, Alekhine, Tarrasch, and Marshall played a double round robin as arguably the strongest tournament ever. If Rubinstein instead of Marshall qualified, then you would actually have a dream tournament of Lasker, Capablanca, Alekhine, Tarrasch, and Rubinstein playing a double round robin, and to my mind, there would be no question that this would be the strongest tournament ever.

Where else is there a tournament where you get Lasker, Capa, and Alekhine all at or near their prime playing a double round robin?

My first chessbooks were written by Lasker and Capablanca, (and Nimzovitch), so I have a very healthy appreciation of how monstrously strong these two were. They probably set the gold standard for playing nearly errorless chess in the middlgame and endgame. In the recent super GM tournaments alone, Lasker and Capa would have gotten a few extra points from our present super GMs playing bad endgames.

The only real advantage our present day players have over these guys is the opening. But that would quickly disappear if they got updated in opening theory. Once past the opening minefields and prep, any chess player would have to play the game as Lasker and Capa did in the 1910s, by chess intuition and precise calculations, and in this aspect, few if any could match them.

And if we were to talk about blitz and rapids who could match Capa? He was smashing everyone from Lasker at the beginning of his international career to Reuben Fine at the end of his career (and Fine was the best blitz player in the USA in the 1930s and 40s, aside from being a world contender). I think it was Lasker who remarked, after seeing the young Capa devouring everybody in blitz,

"Young man, it is remarkable that you never seem to commit a mistake."

I am a big fan of Capablanca and Rubinstein, and yes, their endgame skills were legendary.

But to say the endgame theory has not evolved since then is... questionable to say the least.

Please see Dvoretsky's endgame manual or Fundamental Chess Endings and you'll realize how many endgame techniques were discovered after world war II.

I would like to stop here because this is (probably) not a right place to discuss the evolution of endgame theory.

Anyay, my comments are by no means an attempt to degrade old masters such as Capa, Rubinstein. It is beyond doubt their contribution to endgame theory is massive, and they were many years ahead of their time.

It is no shame to be 'inferior' to Lasker and Capablanca in the endgame. IMO, they did play the endgame better than any living player, with Karpov and Kramnik arguably their only equals. Even Kramnik who plays the endgame probably best among the top active GMs sounded a bit embarrassed when an interviewer started to compare his endgame play to Capablanca. I doubt if there is any player today who could go forth and honestly announce he plays the endgame better than Capa.