why chess has small chance of being a black win ?

[Daniel Shawul]

At the risk of sounding so silly and being ridiculed, I ask this question

Apparently had it not been for zugzwangs, chess could almost be weakly proven as either a win or draw for white like tic-tac-toe is. The fact that something subtle like presence of zugzwangs is the whole reason why it can't be solved somewhat shocked me. I always imagined black has some formidable chances.

The game I am working on now Hex can never be win for black due to the strategy stealing argument. Infact for my board size 8x8 is actually proven to be so (shocker ). Maybe I misread something or there could be other factors other than zugzwang that will not make it work for chess...

[PK]

IIRC Fischer used to claim that there are non-zugzwang positions where Black has an advantage. And he thought about something relatively simple, like 1.Nf3 Nf6 2.g3 g6 3.Bg2 Bg7 4. 0-0 0-0 5. d3 d6, where in his opinion Black is already better (!) because he will break the symmetry (6. c4 e5 or 6. e4 c5). This might sound rather extreme, but indeed there are non-zugzwang positions where seeing opponent's plan can be more important than a tempo. Perhaps that's the reason why 1.e4 c5 seems more active than 1.c4 e5. Some moves are made possible only because of the opponnt's developement (have You seen reverse Sveshnikov Sicilian? I bet You haven't!).

The game of shogi can provide us with a few interesting examples supporting this view. there are many move order subtelties, especially in the Yagura opening, where a player tries to wait for certain moves to take advantage of them. And this happens in essentially non-zugzwang game.

[Daniel Shawul]

Hi pawel. Me no good at chess But I can understand what he is saying about breaking symmetry. If black doesn't do so , white would steal his winning strategy by making a random non-loosing (not a zugzwang) first move and pretending to be black. If according to Fischer black wins that position (black has a winning strategy) , then white could steal the win by making a "pass" move (not legal in chess). I read there are some other things that prevent the argument from working in chess but it is hypothesized that the first mover advantage of white is a reminder of what could have been a different story had it not been for zugzwangs.

[Vinvin]

If black is winning by zugzwang that means that at the 1st move white is already in zugzwang, so, in the whole best line the score is constant. Nothing to resolve here or there ...

At the risk of sounding so silly and being ridiculed, I ask this question

Apparently had it not been for zugzwangs, chess could almost be weakly proven as either a win or draw for white like tic-tac-toe is. The fact that something subtle like presence of zugzwangs is the whole reason why it can't be solved somewhat shocked me. I always imagined black has some formidable chances.

The game I am working on now Hex can never be win for black due to the strategy stealing argument. Infact for my board size 8x8 is actually proven to be so (shocker ). Maybe I misread something or there could be other factors other than zugzwang that will not make it work for chess...

[PK]

Black, in all probability, isn't winning by zugzwang. But give White right to make a pass move just once during the game, and automatically chess becomes impossible to lose by White, due to strategy stealing argument.

Really interesting question would be: what is the game-theoretical value of "one black pass chess", i.e. of a chess variant where Black has right to pass once during the game. Would it neutralize White's opening advantage to some extent?

[rjgibert]

Black, in all probability, isn't winning by zugzwang. But give White right to make a pass move just once during the game, and automatically chess becomes impossible to lose by White, due to strategy stealing argument.

Really interesting question would be: what is the game-theoretical value of "one black pass chess", i.e. of a chess variant where Black has right to pass once during the game. Would it neutralize White's opening advantage to some extent?

Being able to pass is a pretty huge advantage in many endgames.

However, one thing you would need to clarify is what happens when Black is stalemated. Is Black compelled to pass or can Black just take the draw? If Black is compelled to pass, then consider:
[D]8/4k3/4P3/4K3/8/8/8/8 w - - 0 1
On the move we are all hard wired to play 1...Ke8? after 2.Kd6 Black is in zugzwang! This despite having the option to pass! If 2...Kd8 3.e7+ Ke8 4. Ke6 pass 5.Kd6 wins. If 2...pass 3.e7 wins. Black would rather not move nor use up his option to pass, hence the zugzwang.

However any other 1st move by Black including passing can draw, but black may not have it so easy in some other endings where being compelled to pass is a greater disadvantage. Overall, passing is an advantage, but there would be exceptions.

[OliverUwira]

At the risk of sounding so silly and being ridiculed, I ask this question

Apparently had it not been for zugzwangs, chess could almost be weakly proven as either a win or draw for white like tic-tac-toe is. The fact that something subtle like presence of zugzwangs is the whole reason why it can't be solved somewhat shocked me. I always imagined black has some formidable chances.

The game I am working on now Hex can never be win for black due to the strategy stealing argument. Infact for my board size 8x8 is actually proven to be so (shocker ). Maybe I misread something or there could be other factors other than zugzwang that will not make it work for chess...

Don't worry, you don't sound silly. Actually there are some very renowned authors who provided pointers into this direction as well.

Initially there were the hypermoderns, most of all Réti, who argued that 1.e4 might be a mistake because it exposes this pawn to black attacks. Réti came to invent and regularly play his namesake opening system for precisely this reason.

About 1990 Mihai Suba published "Dynamic Chess Strategy" and there he provided numerous examples of Hedgehog positions where White had positioned his pieces on absolutely perfect squares but unfortunately he had to move, with Black having a flexible enough position to exploit each and every White move.

The last I want to mention is Jonathan Rowsons "Chess for Zebras". Rowson was clearly influenced by Suba, and in his book he coins the term "Zugzwang Lite" and demonstrates the concept by means of the game Julian Hodgson - Keith Arkell (Newcastle 2001) which began symmetrically as follows: 1. c4 c5 2. g3 g6 3. Bg2 Bg7 4. Nc3 Nc6 5. a3 a6 6. Rb1 Rb8 7. b4 cxb4 8. axb4 b5 9. cxb5 axb5

[D]1rbqk1nr/3pppbp/2n3p1/1p6/1P6/2N3P1/3PPPBP/1RBQK1NR w Kk 0 10

Rowson comments:

Both sides want to push their d-pawn and play Bf4/...Bf5, but White has to go first so Black gets to play ...d5 before White can play d4. This doesn't matter much, but it already points to the challenge that White faces here; his most natural continuations allow Black to play the moves he wants to. I would therefore say that White is in 'Zugzwang Lite' and that he remains in this state for several moves.

The full game can be read with annotation in the Wikipedia article on the first move advantage, in a section on Black's pluses.

http://en.wikipedia.org/wiki/First-move ... advantages

[Daniel Shawul]

Thanks for the link. Black's advantage seem to be mainly psychological . The reason's given are:
- I will copy all your good moves, and as soon as you make a bad move, I won't copy you any more!
- By moving second he gets to see White's move and then decide whether to match it."
It certainly puts some psychological pressure on white but this black's advantage should not exist in computer chess. That black is always 1 step ahead information wise only matters if both can't think till the end of the game. Even for computer games this applies for 'cooked book lines' played by black. White reveals his plan to a certain extent by his first move,then black plays a suitable response. For perfect chess players, the first mover advantage should exist throughout as long as a zugzwang position is not reached that takes it all away.
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cheers

[OliverUwira]

In my opinion the copying aspect is rather negligible in so far as White can at one point force Black to break the symmetry - namely when White eventually threatens something that has to be addressed by Black. An example from established opening theory is the following line from the Four Knight's Game:

1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Bb5 Bb4 5. O-O O-O 6. d3 d6 7. Bg5 Bg4 8. Nd5 Nd4 9. Nxb4 Nxb5 10. Nd5 Nd4 11. Bxf6 Bxf3? 12. Qd2! Qd7??

[D]r4rk1/pppq1ppp/3p1B2/3Np3/3nP3/3P1b2/PPPQ1PPP/R4RK1 w - - 0 13

13. Ne7+ Kh8 14. Bxg7+ Kxg7 15. Qg5+ Kh8 16. Qf6#

So as soon soon as White threatens something with check, Black is forced to break the symmetry. I find it hard to believe that Black could actually have a won game from the beginning just because of the copying technique.

Suba's point, however, is more difficult to assess and also has relevance for computer chess. Directly above the symmetrical example in the Wikipedia article is an example of a Hedgehog position:

1. Nf3 Nf6 2. c4 c5 3. Nc3 e6 4. g3 b6 5. Bg2 Bb7 6. 0-0 Be7 7. d4 cxd4 8. Qxd4 d6 9. Rd1 a6 10. b3 Nbd7 11. e4 Qb8 12. Bb2 0-0

[D]rq3rk1/1b1nbppp/pp1ppn2/8/2PQP3/1PN2NP1/PB3PBP/R2R2K1 w - - 0 13

Suba wrote of a similar Hedgehog position, "White's position looks ideal. That's the naked truth about it, but the 'ideal' has by definition one drawback—it cannot be improved."

This is typical for the Hedgehog. White can of course begin to lay siege on the d6-pawn or launch a kingside attack, but every move White will have to play dislocates pieces from good squares and will eventually enable Black to thrust back with b6-b5 or d6-d5.

The Hedgehog and similar positions, originating e.g. from the Modern Defence, defy the classical strategy of Tarrasch's, which we all implement in our evaluation functions. Suba's keyword here is flexibility: Black is flexible enough to react on all of White's improvement attempts. An evaluation function of a chess engine will not be able to assess flexibility properly.

Yet this flexible approach a serious showcase for an inherent Black advantage. Suba also explained this in game-theoritical vocabulary:

In terms of the mathematical games theory, chess is a game of complete information, and Black's information is always greater—by one move!

In order to not flood this post with too many examples I'll stop here now. I also have an interesting example from the Tarrasch defense where, when played reversed, White's best move is the null move...

[Daniel Shawul]

In order to not flood this post with too many examples I'll stop here now. I also have an interesting example from the Tarrasch defense where, when played reversed, White's best move is the null move...

Thanks. Please post the position with explanation when you can. Some of the GM analysis in wiki are beyond my chess comprehension skills but I have learnt some past few days.
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cheers