Why does white exchange knight for a pawn here?

After taking:

8/8/1k6/p6p/3r4/P1R5/6K1/8 w KQ - 49 50

Judith Polgar must have assessed this position to be easily winning for black. I assume black would just win the white pawn and proceed to promote the a-pawn.

Now, while a knight is generally worth much more than a pawn, the endgame King,Rook,Knight vs King,Rook is usually a draw. So Polgar must have hoped to win or blockade the h-pawn and reach a drawn endgame of the K,R,N vs K,R-variety. I guess she knew this wouldn't work out, but the rationale was to set a more difficult technical task to Kasparov than the above rook endgame.

Edit: I looked up the game in her autobiographical best games collection and it turns out, I was half right:

"Following the text move, the rook ending after 50.Nxd4 Rxd4 would be lost for me. Black would advance his pawns to my fourth rank and then activate his king using the rook as shield."

She then proceeds to give 50.Nxa5 an exclamation mark, explaining that it is a study-like way to a draw, because apparently she wins the black pawn by force (which I didn't see).

So, she did assume the rook ending to be lost (erroneously, according to Stephen's comment), but she actually saw that she would win the h-pawn as well, leading to a drawn endgame.


The USCF implemented Elo's suggestions in 1960, and the system quickly gained recognition as being both fairer and more accurate than the Harkness rating system. Elo's system was adopted by the World Chess Federation (FIDE) in 1970. Fide used k=30 factor before July 2014.


"MultiPV" is the UCI option you are looking for.

  setoption name MultiPV value 10


How many unique pawn structures are possible?

To classify pawn formations, a good source is chess master books that explore that topic. The book by Boris Persits comes to mind, for example.
I add that it seems impractical as you have been told, to make an exhaustive index of all the combinations that pawn chains can take.
However, it is useful to connect families of openings (classified by ECO, or by open / closed / flank, positional or tactical) and also by the types of endings that can be found according to the pawn structure.
This information has didactic utility for chess plans. There are books that touch on the subject of pawn structures and chess plans.
The pawn chain structures could be described with the characteristics: doubled or solitary / past / advanced / delayed / blocked pawns, V chain or inverted V chain, castling with / without fiancheto and other descriptors that I cannot imagine.
In this way, the number of pawn formations is much less than combinatorial theory can estimate.


Is my low blitz game drawing rate at www.chess.com an indicator that I am weak in chess?

10% is a high drawing rate for online blitz - I am drawish in classical games and an FM and have 6.6% draw rate on chess.com 3 minutes.
I would suggest you use your rating as the indicator for playing strength - that is it's only purpose and it is fairly objective.

I also wouldn't worry about adjectives like "weak" - it's all very relative.
Chess is fun. Improving is also fun - by all means work hard on your chess just not so that you won't be "weak". I am "weak" to lots of players and I am an FM.


There are plenty of positions that stump engines, and it's not too difficult to find some from engine tournaments. Example, this position stumped Stockfish:

[FEN "1k1r4/pp4pp/4pb2/2Q5/2P5/8/P5PP/6K1 w - - 1 28"]

Stockfish actually reached +2.76 eval later, even though White has no way to break through. In fact Black can afford to give up the e6-pawn and the position is still drawn. Lc0 evaluated the position accurately as a draw, which doesn't mean Lc0 is some kind of goddess at evaluating fortresses, since this position stumped Lc0:

[FEN "5k2/5p2/p3pPp1/3pN2p/b6P/2P5/P5P1/7K w - - 0 35"]

Black plays ...Bb5 and defends along the f1-a6 diagonal, and White will never get anywhere, especially since if the Knight moves too much Black advances the e6-pawn with counterplay. This time Stockfish accurately assessed the position as drawn, while Lc0 was at +1.6 - or about 60% chance to win - or so for quite a while.

If you're wondering about positions with study-like solutions that humans think is pretty - that's a different question.


A few thoughts:

Leaving the king in the centre or long castle are not attractive either with all the open lines and pinned knight on c6
The g file is open but it is not easy for white to make use of it. White has exchanged its bishop which would have had a good square on h6. Also black's pawns on e6 and f6 cover important squares that could be occupied by white knights.
The centre is open and if white concentrates forces on the king side, black will very quickly push through on the queen side and in the centre.
It is an opening and has been analysed by humans and computers and found to be OK.


PythonChess - Get engine to predict a list of the best moves in a position

In the world of chess engines, what you're looking for is called multi-PV (multiple principal variations): telling the engine to look for and return up to n best moves and the associated principal variations for each. ("Up to" because sometimes there's only 1 legal move in a position.)

In python-chess, this is part of the engine protocols, as one of the optional parameters when calling engine.analyse(). From the documentation:

  class chess.engine.EngineProtocol

  coroutine analyse( [...] )

  multipv – Optional. Analyse multiple root moves. Will return a list of at most multipv dictionaries rather than just a single info dictionary.

The .analyse() method tells the engine to analyse the position, returning a dictionary of information, which includes among other things the moves of the principal variation. Specifying for instance .analyse(multipv = 3) will tell the engine to return a list of (up to) 3 such dictionaries -- the first moves in the pv value of each dictionary should be what you are looking for.


What is the best defense against the King's Indian Attack?

I doubt that the King's Indian Attack can be 'broken'.  It's a very solid position that White takes the time to setup, if Black is not careful, White may be able to gain space on the kingside, with moves such as e5, and develop dangerous attacks if Black has castled there.

As for h7 being weak, many things need to happen from Black in order for this to be realized (such as a semi-open h-file, Bg7 has been exchanged, in which case it is h6 that is weaker), so there may not be anything there worth exploring.

I can't comment on what the 'best' defense would be, but there are many good ones, one such is the Botvinnik System.  Black makes use of the extra available tempi to set up a strong and flexible defense.  The typical structure would be pawns at c5, e5, d6, g6 and pieces at Nc6, Nge7, Bg7 and 0-0.  Black has a firm control over the d4 square and can potentially break with either ...b5 or ...f5.


Against Alekhine's defense, can White avoid 2. e5?

A very correct answer to the Alekhine Defense is 2.d3. Strange looking, but after the Nf3,g3,Bg2,Nbd2,O-O, you get a full KIA setup, a favourite of Bobby Fischer, among others.

http://en.wikipedia.org/wiki/King's_Indian_Attack

Not only is this setup easy to learn, but a great answer to almost everything you don't fully know. The transpositions from other openings aren't rare, so it is a good thing to learn. Also, you don't have to learn lines by heart, but rather middlegame plans.

Also one last thing. Since your opponent already has a knight on f6, this makes him go on a mainline in the KIA, so you will find even more examples of games.

Hope this helps.


Shortest sequence of moves to create biggest material imbalance

I got this, which is much shorter.
[FEN ""]

1. a4 a5 2. b4 b5 3. c4 c5 4. d4 d5 5. e4 e5 6. f4 f5 7. g4 g5 8. h4 h5 9. bxa5 Bd6 10. axb5 Be6 11. dxc5 Nf6 12. cxd5 O-O 13. fxe5 Rf7 14. exf5 Ra6 15. gxh5 Rb7 16. hxg5 Rbb6 17. bxa6 Nc6 18. axb6 Qe7 19. dxc6 Kh8 20. cxd6 Ng8 21. a7 Qf6 22. gxf6 Ne7 23. b7 Bd7 24. e6 Ng8 25. c7 Kh7 26. f7 Kg7 27. e7 Kf6 28. h6 Ke5 29. f6 Kf5 30. a8=Q Kg6 31. b8=Q Ba4 32. c8=Q Bb5 33. f8=Q Bc4 34. d7 Bd5 35. d8=Q Be4 36. f7 Bf5 37. e8=Q Bd7 38. h7 Bc6 39. h8=Q Bb7 40. Qcxb7 Kf5 41. fxg8=Q#

It's one move above the lower bound, but I feel that this is optimal.

As @Evargalo suggested, here is @user1583209's proof of optimality from their comments.
"I have a proof now: Start by labeling the columns/files by numbers, i.e. a=1, b=2...h=8. Then for each pawn calculate the sum of the respective files. So in the initial position this sum is 1+2+3...+8=36. Now, if a pawn captures, it changes its file by "1" (either plus or minus 1). In order to achieve a solution in 40 moves, we have to queen the pawns on each of the squares on the 8th rank. This means that in the final position the sum of files (for pawns+promoted pawns now) needs to be 36 again. However we also need to do 15 captures with these pawns.
Each capture changing the file sum by 1, it is impossible to end up with 36 as sum, basically because 15 is an odd number.  (If you have x captures to the left and y captures to the right you end up with equations: x-y=0 and x+y=15 which has no integer solution) That proves that it is impossible to achieve a solution in 40 moves and the solution with 41 moves given by orlp is optimal."


Aggressive Attacking Lines for Black in the French Defence Exchange Variation

Unfortunately, there is nothing you can do. You will have to adapt to White's play and that is it. Only White can sharpen the game, by entering the line with isolated pawn ( by playing c4 at some point ).

The line you chose gives White minimal advantage, according to ECO C ( 2006 ), so I would stay away from it. The position is symmetrical, White is slightly ahead in development, e-file is open, and White has no weaknesses whatsoever. Meanwhile, you are behind in development, you will not castle soon, and now you create isolated pawn without reasonable compensation ( isolated pawn gives you free development, but you are not cramped here so you do not need this! ) which will put you in a long defense.

I hate being "passive" in this line as much as you do, since I play the French and QGD, but reality will not change -> White has a pleasant situation where he can win or draw, if he doesn't blunder, while for Black the only reasonable result is a draw, providing he plays accurately.

You must use your creativity in this line, to outplay the opponent. Set him difficult choices to solve, something along these lines:

Offer him exchanges that are bad for him ( offer your bad piece for his good one );
Offer him to enter into endgame, but try to trick him so the endgame is better for you;
Try to generate mating attack with pieces ( f4 square is very useful for this );

The point is that heavy pieces will be exchanged on the e-file so the only option is endgame. You could exchange only one pair of rooks and try for mate with Qf4 + Ng4 setup, but that requires a lot of maneuvering. Still, it is a thought... The point is to keep trying to invent a plan, don't just fall into stereotypical "exchange all and draw" mindset.

Finally, instead of the line you listed, I would rather go with something like this:

[Title "French defense, Exchange line"]
[fen ""]

1.e4 e6 2.d4 d5 3.exd5 exd5 4.Nf3 Bd6!

This will prevent Bf4 so White will have slightly passive position. This is a thematic idea for both sides ( remember that in symmetric positions everything counts ). If he responds with c4 you have your sharp position ( according to ECO ), but if he goes for the same idea of stopping ...Bf5 then you play ...Nge7! so you can still get ...Bf5. This way you get free development and active position. This is the best you can do in this line. Now is the time to give you the full lines:

[Title "French defense, Exchange line"]
[fen ""]

1.e4 e6 2.d4 d5 3.exd5 exd5 4.Nf3 ( 4.c4 $13 ) 4...Bd6! 5.c4 ( 5.Bd3 Ne7! 6.O-O O-O 7.Bg5 f6! 8.Bh4 Bf5 9.Bg3 Bxg3 10.hxg3 Nbc6 11.Nc3 Qd7 12.Ne2 Bxd3= ) 5...Nf6 6.Nc3 c6 7.c5 Be7 8.Bd3 b6 9.cxb6 axb6 10.O-O Ba6 11.Bxa6 Rxa6 12.Qd3 O-O $13

You can still outplay the opponent in this position... If you need help or you have further questions leave a comment. Best regards.


What are the most popular defences White should be prepared to fight against in the Ruy Lopez?

The mainlines and key ideas are highlighted in wikipedia. The article covers:

Morphy Defence: 3...a6

Exchange Variation: 4.Bxc6
Norwegian Defence: 4.Ba4 b5 5.Bb3 Na5
Variations combining 3...a6 and ...Bc5
Steinitz Defence Deferred: 4.Ba4 d6
Schliemann Defence Deferred: 4.Ba4 f5
Arkhangelsk Defence: 4.Ba4 Nf6 5.0-0 b5 6.Bb3 Bb7
Mackenzie Variation 4. Ba4 Nf6 5.d4
Russian Defence: 4.Ba4 Nf6 5.0-0 d6
Open Defence: 4.Ba4 Nf6 5.0-0 Nxe4

Closed Defence 4.Ba4 Nf6 5.0-0 Be7

Delayed Exchange Variation Deferred: 6.Bxc6
Centre Attack: 6.d4
Worrall Attack: 6.Qe2
Averbakh Variation: 6.Re1 d6
Trajković Variation: 6.Re1 b5 7.Bb3 Bb7
Marshall Attack: 7...0-0 8.c3 d5

Main line: 4.Ba4 Nf6 5.0-0 Be7 6.Re1 b5 7.Bb3 d6 8.c3 0-0

Pilnik Variation: 9.d3
Yates Variation and Bogoljubow Variation: 9.d4
Chigorin Variation: 9.h3 Na5
Breyer Variation: 9.h3 Nb8
Zaitsev Variation: 9.h3 Bb7
Karpov Variation: 9.h3 Nd7
Kholmov Variation: 9.h3 Be6
Smyslov Variation: 9.h3 h6
Smyslov Variation: 9.h3 Qd7

Black defences other than 3...a6

Cozio Defence: 3...Nge7
Smyslov Defence: 3...g6
Bird's Defence: 3...Nd4
Steinitz Defence: 3...d6
Schliemann Defence: 3...f5
Classical Defence: 3...Bc5
Berlin Defence: 3...Nf6


How do I go about learning the Najdorf Sicilian?

Probably(I haven't read it) , other options are a video series eg

https://chess24.com/en/learn/advanced/video/a-complete-najdorf-repertoire/najdorf-introduction

or a more detailed book eg

http://www.qualitychess.co.uk/products/1/49/grandmaster_repertoire_6_-_the_sicilian_defence_by_lubomir_ftacnik/

or

https://www.newinchess.com/The_Sharpest_Sicilian_2012-p-1523.html.

In general I would recommend the Starting Out repertoires for anyone under 2000 FIDE.


latvian, halloween, wing, englund, elephant, freds, colorado, danish gambit, tennison, and budapest gambit of the top of my head. These gambits are unsound and a proper response will have the gambiter in a worse position.
Some gambits I do like are kings gambit, smith morra, evans, queens, scotch, benko, lisitsin, staunton, fried liver(Na5), froms.


Maximum number of non-pawn pieces on the board

@Aschultz is correct that 26 pieces is the maximum number of non-pawn and non-king pieces on the board. Since they said that they have not seen such proof yet, here it is to be seen.
[Title "me, chess.stackexchange.com 6/18/2019, Non-Unique Proof Game In 40.5 Moves"]
[FEN ""]

1. d4 a5 2. b4 c5 3. h4 e5 4. f4 g5 5. dxc5 axb4 6. hxg5 exf4 7. g4 b5 8. a4 h5 9. c4 f5 10. c6 f3 11. c5 f4 12. g6 b3 13. g7 b2 14. Na3 Nh6 15. g5 b4 16. g6 b3 17. g8=B b1=B 18. Bh7 Ba2 19. g7 b2 20. g8=B b1=B 21. e4 d5 22. e5 d4 23. e6 d3 24. Kd2 Ke7 25. Kc3 Kf6 26. e7 d2 27. Qc2 d1=B 28. e8=B f2 29. c7 f3 30. c6 Bb7 31. Bg2 f1=B 32. c8=B Bfe2 33. Bcd7 f2 34. c7 f1=B 35. c8=B h4 36. a5 Ra6 37. Rh3 Rb6 38. Rg3 h3 39. a6 h2 40. a7 h1=B 41. a8=B


Black's tools in the Caro-Kann Advanced Tal Variation

I play the white side of this position often, and have an incredible winrate because to be honest, it feels very hard for black to develop naturally. Here's an example of how things can go wrong:
[FEN ""]

1. e4 c6 2. d4 d5 3. e5 Bf5 4. h4 h5 5. Bd3 Bxd3 6. Qxd3 e6 7. Bg5 Qb6 8. Nd2 c5 9. c4 Qxb2 10. Rd1 Qxd4 11. Qb3 Qxe5+ 12. Ne2 Qc7 13. cxd5 exd5 14. O-O

Black is able to win several pawns, but in order to "punish" white's play has to move their queen many moves in a row. While it appears black has done nothing "wrong," this position just so happens that white gets a huge initiative and is practically winning already because of the open lines against black's king and huge lead in development. Stockfish only thinks this is +0.6 or so, but as you keep playing through the variations, you'll see the evaluation rise and rise, sometimes even with best play from black. Leela loves this position for white.
A more practical alternative for black is to try and trade the queens off instead of pawn grabbing. This is typically done with the maneuver Qa5+->Qa6 (or Qb6->Qa6) so that Qxa6 can be met with Nxa6, supporting a c5 break. Here's the beginning of a game between Nepo and Motylev, 2014 (https://lichess.org/0y7cwwGs) which black won:
[FEN ""]
1. e4 c6 2. d4 d5 3. e5 Bf5 4. h4 h5 5. Bd3 Bxd3 6. Qxd3 e6 7. Bg5 Qb6 8. Nd2 Qa6 9. c4 Bb4 10. b3 c5 11. Nf3 Nc6 12. dxc5 Bxc5 13. O-O Nge7 14. a3 Ng6 15. b4 Ncxe5 16. Nxe5 Nxe5 17. Qc3 Bd6

You can see how pinning the c4 pawn to the d3 queen means that black's center is more secure: the c5 break has the added benefit of not allowing for a later cxd5 exd5, opening up black's central king. White still had some play in the final position, but collapsed after a premature f4, which ultimately opened up the white king rather than opening up the black king. Black's play revolves around the pressure on white's center, which can sometimes collapse (and sometimes should collapse in order to expose black's king) and lead to double-edged positions that black has winning chances in.
To be honest, I think black's best line here is:
[FEN ""]
1. e4 c6 2. d4 d5 3. e5 Bf5 4. h4 h5 5. Bd3 Bxd3 6. Qxd3 Qa5+ 7. Nd2 (7...Qa6?! 8. e6!) e6 8. Nf3 Qa6

so that we get the same sort of play as in the previous game but ensure that white's bishop is stuck still on c1. Vidit won a brilliant game against Andriasian as black in this position in 2018 (https://lichess.org/QAd7qBrk).
Finally, to be complete, but at the risk of giving away some cutting edge opening theory, I think white can improve upon this opening by following a Leela recommendation:
[FEN ""]
1. e4 c6 2. d4 d5 3. e5 Bf5 4. h4 h5 5. Bd3 Bxd3 6. Qxd3 Qa5+ 7. b4!? (7...Qxb4+ 8. Nd2 e6 9. Rb1 Qe7 10. Ne2) Qa6 8. e6! Qxd3 9. cxd3 fxe6

There's a whole world of unexplored territory in this line, but play in it is unlike anything else I've ever seen, so I don't have any amazing recommendations for black except that taking the b pawn seems risky. Currently, this b4 pawn sacrifice seems to have been played only twice in 2018. Time will tell if it catches on in the future! I had a fascinating game from this position recently, where I won the opening battle but ultimately lost on time: https://lichess.org/gUqyAa1u/white.
Enjoy, and good luck in the Caro!


If you are asking why players don't improve despite decades of playing the simple answer is that the more time you spend practicing and reinforcing your mistakes the more ingrained they become and the more likely it becomes that your level will hardly change..

The principle teaching of the Soviet School of chess as described by Dvoretsky and others is that the key to improvement lies in annotating your own games.

Only by critically examining the (bad) moves you make can you identify the kind of mistakes you typically make and only then can you take positive steps to correct them.

This is a very active thing to do. It involves putting your brain into gear. Just putting your game into an engine and seeing where the evaluation changes by a big margin and noting the engine suggestion doesn't count. That is just passive.

EDIT: Analyzing and annotating your own games to identify mistakes with the idea of avoiding those mistakes in the future, something the Soviets practiced in the Botvinnik era, is also one of the centerpieces of Axel Smith's award-winning 2013 book, "Pump up your Rating".

Here is his summary of this technique -

1) Analyse your games with a friend; avoid using an analysis engine
2) Annotate the game in ChessBase, and highlight your mistakes
3) Check the analysis with an engine, and update the annotations
4) Write down the mistakes in a text file
5) Collect all the mistakes in a List of Mistakes, where they are sorted into various categories
6) Make conclusions about typical mistakes, and how they should be avoided in the future

Axel Smith also gives examples of some of his own mistakes and how he used this technique to identify them and correct them in his play.


Why aren't early opening moves generally given exclamation marks?

Wikipedia says the following:

Exclamation points ("!") indicate good moves—especially ones which are surprising or involve particular skill. Hence annotators are usually somewhat conservative with the use of this symbol.

(emphasis mine). 2. c4 is the most played move after 1. d4 d5, therefore it doesn't receive an exclamation mark.


This table can be thought of as a tabular representation of an opening tree of in-theory moves where the rows (y-axis) represent the flow of the game and the columns (x-axis) refer to variations/branches in the tree that can occur.
The author in your quote indicated that 2...exf4 spans a family 24 variations/sub-variations that are noteworthy (and considered theory) for reference.
Here's an example for another such page on these NCO/MCO opening references.

If this is confusing,  let's consider a simpler example with the first few moves (with some early deviations) from the popular Danish Gambit.
Here's what a fragment of the opening tree would look like.

If I wanted to represent/transform this tree into a table, it would look like this.


The Danish gambit isn't very popular these days because of the Schlechter Defense. The idea is to take the gambit pawns but return them quickly.

  e4 e5 2. d4 exd4 3. c3 dxc3 4. Bc4 cxb2 5. Bxb2 d5

5...d5 initiates the Schlechter Defense. The mainline continues 6.Bxd5 (6.exd5 Nf6 closes the position and lets Black develop, still a pawn up) Nf6 7.Bxf7+ Kxf7 8.Qxd8 Bb4+ 9.Qd2 Bxd2+ 10.Nxd2 c5. Black regains the Queen and steers the game to an equal endgame. White has no attack and the position is not even remotely close to tactical, which is psychologically depressing for gambit players.

[FEN ""]

1. e4 e5 2. d4 exd4 3. c3 dxc3 4. Bc4 cxb2 5. Bxb2 d5 6. Bxd5 (6. exd5? Nf6) Nf6 7. Bxf7+ Kxf7 8. Qxd8 Bb4+ 9. Qd2 Bxd2+ 10. Nxd2 c5

The only downside of this defense is, if you keep using it, your friend might not want to play with you anymore.


Can white really not win this rook endgame?

According to the Shredder database (sorry, I can't link directly to a position), the position after Rh7 is won in 32 moves and Ra7 gives the win away.

There are some similar positions with a- and b-pawns which are drawn, but this is not one of them. Actually, playing around with the database, I found that the initial position with the black king on b8, is drawn (and Rh7 is one of the two moves keeping the draw).

Another example is this one, where the white rook is tied to the defense of the b pawn and the white king can't really help.

[White "J. van der Wiel"]
[Black "P. Boersma"]
[Result "1/2"]
[FEN "8/2k5/1R6/PP5r/8/4K3/8/8 w - - 0 1"]

1. Ke4 Rh4+ 2. Kf5 Rh5+ 3. Kg6 Rc5 4. Kf7 Rh5 5. Rc6+ Kd7 6. a6 Rxb5 7. a7 Ra5 8. Re6 Kc7 1/2-1/2

source: Fundamental Chess Endings by Müller and Lamprecht


What are the merits of Anand's exchange sacrifice in game 9 of 1995 World Chess Championship?

Well, the obvious answer is that taking it leaves white with two connected passers (possibly after a future a6). That is incredibly strong since they control so many central squares, and threaten to advance strongly at any moment. This keeps the opponent tied down, and constantly worried about their advance.

I once saw Joel Benjamin sac a whole piece just for connected passers on the 5th. I think it was at the 1985 World open versus Sandeep Joshi, a prodigy at the time. It has been a long time, but they were so strong, i don't think that he never moved them.

Frankly, the other point behind it is that white is going to double rooks. Kasparov was wrong, at least practically, to take. In his notes to the game, Anand give Nxd5 two question marks, and recommends waiting with 27...h5.


For logical reasons the 3...Qd8 Scandinavian is not popular among top grandmasters whatsoever , Stockfish 5 gives it 0.45 after running for around a  5 minutes compared to 0.00 in the French Defense after 3.Nc3 Nf6

For this variation I would recommend looking at the games of Montenegrin Grandmaster Nikola Djukic, who is the only grandmaster who employs the 3...Qd8 variation regurlarly. He also has a plus score with it against an opposition elo average of 2496 which is nice.

The 3...Qd6 Scandinavian is a lot more popular. The very strong Grandmaster Sergei Tiviakov has implemented it regurlarly with a massive plus score against an elo average of 2659.

The 3...Qa5 Scandinavian is the most popular of the 3, the Serbian Grandmaster Miodrag R Savic can be considered a specialist on this since he plays it approximately 71% of the time against 1.e4 with a very positive score against an elo average of 2508.

I've decided to just ignore the 3...Qe5+ variation, which is also called the "Patzer Variation" White scores 71.1% after 4.Be2

Of course this post would not be complete if I didn't answer your question on how to find a plan in the given positions.

FIRST DIAGRAM

Unfortunately the line you are referring to in the first game has only 2 games in Mega Database 2014.

[Event "?"]
[Site "?"]
[Date "?"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "?"]
[Title "Scandinavian defense, with Qd8"]
[fen ""]

1.e4 d5 2.exd5 Qxd5 3.Nc3 Qd8 4.Nf3 c6 5.d4 Bf5!? 6.Bd3!? (6.Bc4) Bxd3 7.Qxd3 e6 8.O-O Nf6 9.Bf4 Nbd7

OK, in the final position black is solid but there is pretty much no way for him/her to win (naturally, with exceptions in human play). White is castled, has 3 pieces and a pawn putting pressure on the center with an added space advantage. White is clearly better, the game has certainly not equalized in blacks favor. Maybe you have avoided theory and complications but unfortunately that is all you have gained.

Another problem with such a position is that black is really lacking in play here. This makes it much harder to formulate a plan of some sort, maybe this is why you are struggling to find a long term plan.

SECOND DIAGRAM

 [Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Black to Move"]
[Black ""]
[Result "*"]
[SetUp "1"]
[FEN "r2q1rk1/pp1nbppp/2p1pn2/8/2PP1B2/2NQ1N2/PP3PPP/R4RK1 b - - 0 1"]
[PlyCount "5"]

1... Nh5 (1... Qb6 2.c5 Qd8  (2. a3 c5)) 2. Bd2 (2. Bg3 $6 Nxg3 3. hxg3
$11) 2... Nhf6 3. Rfe1 Qc7 4.Rad1

In the second diagram your main plan should probably be the elimination of the f5 Bishop, which is severely cramping your position. So therefore Nh5 comes to mind, if the Bishop retreats to g3, simply chop it off and the position is equal, however white can retreat the Bishop and it is not so clear how to proceed for black. I have given some small variations to go by but overall the position seems to be completely devoid of play for black. Black is lacking in any sort of counter-play to put it bluntly.
OK maybe after 3...Qc7 you can centralize the rooks with rook a8 to d8 and rook f8 to e8 and slowly maneuver your pieces, waiting for white, maybe move your d7 Knight to f8 to clear open the d-file and prepare a possible ...Ng6. Black basically just has to sit and wait. The engine recommends ideas involving ...a6 but I find this quite dubious and unnatural, not suited for human play.

White on the other hand has the clear idea of d5, centralizing the rooks, h3 to maintain the powerful dark squared Bishop. The position is rich for white. Better to say the least, because he/she has a clear plan to follow by.

I know that the computer evaluation is a powerful thing, but we are not computers. I highly suggest picking another variation to go by, one which involves "play". For a position with counter-play and imbalances is much more important than a dry one such as this one despite the silicon machine saying 0.36.

I personally think that the 3...Qd8 Scandinavian variation is a very dubious one which should be avoided at all costs by the improving chess player and should only be played for the element of surprise.

All statistics courtesy of Chessbase Mega Database 2014


Determine ELO strength without playing in FIDE tournaments

This is going to sound tautological, but Elo is inherently a measure of how you do in tournaments. Your question is sort of like asking "I don't run, how can I determine how fast I can run a mile?" We could guess from how generally fit you look, but in reality you just have to go run a mile to find out.

There are correlations between various online ratings and a FIDE rating, but they're just correlations; the context of how you play online is very different from playing live (for one thing, online games are usually much faster).

I can tell you that the first time you play in a live tournament you will likely perform 100-200 points worse than you might expect from such a correlation, just because you're not used to the environment of a face-to-face tournament (moving real pieces, using a clock, writing down your moves, having your opponent right there in front of you, being distracted by other games). Luckily it does not take long to settle in.


Stop SF MultiPV from returning an upperbound

You'll need to give the engine more time to think.

Edited

The poster was concern about "upperbound"/"lowerbound" is only returned at the largest depth".

The question makes absolutely no sense. I don't want to get into too much technical details because you need to understand the alpha-beta algorithm. upperbound/lowerbound is NOT something that an end-user ever needs to worry about. It's meant for engine debugging, the information is only and only useful for engine developers. No chess software with a Stockfish engine would tell you anything related to the bounds. Stockfish reports the upperbound/lowerbound information whenever it encounters one for every 3 seconds.

I can't directly answer your question because it is not a valid question. upper and lower bounds are really not something that you should worry.


Is it permitted to stare at a blank chessboard during a tournament game?

FIDE rules 12.3a and 6.14 are relevant to this situation. The former rule is vague, but the latter strongly suggests it is allowed. Let's take a look.

Rule 12.3a

  12.3a    During play the players are forbidden to make use of any notes, sources of information or advice, or analyse on another
  chessboard.

This rule does not define the word analyse, and hence, the verdict would depend on whether "staring at blank chessboard" constitutes analysis.

Rule 6.14

  6.14 Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made,
  and clocks which also show the number of moves, are allowed in the
  playing hall. However, the player may not make a claim relying solely
  on information shown in this manner.

Since a board showing current position is allowed, it is strongly implied (though not explicitly stated) that looking at a blank chessboard is allowed.

Used rulebook on the FIDE website here.


Can a player ever lose her or his rating (voluntarily)?

I found FIDE regulations 7.21 which state:

  Players whose ratings drop below 1000 are listed on the next list as
  ‘delisted’. Thereafter, they are treated in the same manner as any
  other unrated player.

This sounds like a "reset" to me.

Note that this is different to an inactive player which you become after not playing rated games for a year. However in the case of inactive players you retain your rating.

Other than this "delisting" I don't think there is a way to lose your rating.


I don't have Chessbase 2009 software, which is what I think you're showing, but your answer did inspire me to look deeper into the issue.

I did find that with Arena 3.5:

1) right click with the mouse in the engine analysis box area.
2) left click the first option, Configure Rybka (or whatever engine you are using).
3) set MultiPV to 5.


How to exploit the advantage of a bishop over a knight?

Usually you want to open the center up for the bishops so that you can attack on both sides of the board.  Or you can try to exchange bishop for knight in order to obtain a more permanent pawn structure weakness like doubled pawns or isolated pawns to attack later in the game.


What should the penalty be for a player leaving the playing venue?

According to FIDE Handbook (12.9):

  Options available to the arbiter concerning penalties:

  warning
  increasing the remaining time of the opponent
  reducing the remaining time of the offending player
  increasing the points scored in the game by the opponent to the maximum available for that game
  reducing the points scored in the game by the offending person
  declaring the game to be lost by the offending player (the arbiter shall also decide the opponent’s score)
  a fine announced in advance
  expulsion from the competition

I think that the arbiter should penalize the player anyway, the question is which way. For me as an arbiter would be crucial the presence/absence of a mobile phone in player's pocket, bag etc. If the presence of his mobile phone was proven, I would declare the game to be lost for this player. Another problem is that arbiters don't have the right for any inspections without permission, the player has to agree...

If the presence of his mobile phone wasn't proven, reducing the player's time seems most adequate to me.


Endgames: How was "maximum moves required" determined before tablebases?

Nothing was calculated. They arrived at their results by trial and error.

Some guy would start with a seemingly disadvantageous position and tried to find the shortest mate. His result remained valid until the next guy found a more disadvantageous position or a quicker mate.

A long time later, engines became powerful enough to calculate simple endgames like K+Q v K simply by exhausting all possibilities, but by that time technology was also advanced enough to create the first tablebases.


Rd6 followed up with 3. c5 looks strong for White, unless I am missing some obvious tactics.


How does the chess24 rating compare to other server ratings?

From my own experience chess24 ratings are quite inflated. I can get a 2200 rating easy on chess24 but struggle to maintain a 1900+ rating on chess.com.


Returning scores for all possible moves from a chess engine

Of course there's a way: I'm going to show you one way of doing it on your own, using only free software. We'll write a small script in Python (I'm using v2.7) and only use the wonderful python-chess library (licensed under GPL3, note that I'm using the version 0.14.0).

In short, the script will first load up the engine, we will stick to free and open source software so we'll use the amazing Stockfish engine [*], then create a board instance of the position you want analyzed (using the FEN notation), generate all legal moves, and finally ask the engine to evaluate each move for a predefined amount of time (in this example it is set to 1 second ponder time). Here's a working sample:

import chess
import chess.uci

#Let's try our code with the starting position of chess:
fen = 'rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1'
board = chess.Board(fen)
handler = chess.uci.InfoHandler()

#Now make sure you give the correct location for your stockfish engine file
#...in the line that follows: e.g., /home/.../stockfish_6_x64
engine = chess.uci.popen_engine('stockfish_6_x64')

engine.info_handlers.append(handler)
engine.position(board)
if board.turn: print 'White to move'
else: print 'black to move'

for el in board.legal_moves:
    engine.go(searchmoves=[el],movetime=1000)
    print str(board.san(el)), 'eval = ', round(handler.info["score"][1].cp/100.0,2)

Note that this is not necessarily the best/most efficient way of doing it, I wrote this in 5 minutes just to showcase it at a basic level without using any advanced features of the engine, I'm sure you will do much better on your own. Anyhow here's the output once you run it (assuming you have python installed on whatever OS you're using, same goes for the python-chess library):

White to move
Na3 eval =  -0.39
Nc3 eval =  0.15
Nf3 eval =  0.15
Nh3 eval =  -0.37
a3 eval =  0.01
b3 eval =  -0.15
c3 eval =  -0.03
d3 eval =  -0.06
e3 eval =  0.12
f3 eval =  -0.49
g3 eval =  -0.33
h3 eval =  0.0
a4 eval =  -0.12
b4 eval =  -0.67
c4 eval =  0.07
d4 eval =  0.17
e4 eval =  0.17
f4 eval =  -0.15
g4 eval =  -0.74
h4 eval =  -0.15

There you go! The beauty of all this is of course the fact that you have now your own software to work with, modify and extend it as you wish...no limitations. All very easy to do, just acquaint yourself with the workings of the library we're using by following its documentation, and knock yourself out ;)

Don't hesitate to ask if you have any questions about the code, or adding potential functionalities.

[*]: which also happens to be one of the strongest current chess engines.

Edit to address the common request:

Here's the updated version of the same code using the latest version:

python-chess 0.30.0 and using the latest Stockfish

import chess
import chess.engine
import os

#here we assume the engine file is in same folder as our python script
path = os.getcwd()
#Let's try our code with the starting position of chess:
fen = 'rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1'
board = chess.Board(fen)
#Now make sure you give the correct location for your stockfish engine file
#...in the line that follows by correctly defining path
engine = chess.engine.SimpleEngine.popen_uci(path+'/'+'stockfish-10-64')

if board.turn: print('White to move')
else: print('black to move')

for el in board.legal_moves:
    info = engine.analyse(board, chess.engine.Limit(time=1), root_moves=[el])
    t = str(info["score"])
    if t.startswith('#'):
            print(str(board.san(el))," eval = mate in ", t)
    else: print(str(board.san(el))," eval = ", round(int(t)/100.,2))
engine.quit()

The output for ponder time set to 1 second per found move chess.engine.Limit(time=1):

White to move
Nh3  eval =  -0.43
Nf3  eval =  0.69
Nc3  eval =  0.29
Na3  eval =  -0.35
h3  eval =  0.41
g3  eval =  -0.2
f3  eval =  -0.62
e3  eval =  0.45
d3  eval =  0.03
c3  eval =  0.19
b3  eval =  0.1
a3  eval =  0.46
h4  eval =  -0.42
g4  eval =  -1.22
f4  eval =  -0.07
e4  eval =  0.82
d4  eval =  0.63
c4  eval =  0.57
b4  eval =  -0.26
a4  eval =  -0.02


I realised as I finished typing up my question that if White wants to trade off the knight for a Bishop (thus retaining the bishop pair, which is good for reasons, probably) White can't just play 3.Ne5 immediately, because after 3...Bxe5 4. Bxe5 Black can play 4...c4!, and now threatens to fork the king and the bishop. For example, you could continue 5. Qxc4 Rc8 6.Qa6 Qc5+, after which White is still better, but then Black has counterplay and active pieces (e.g. Black can play ...R8d8 and have pressure along the d-file, and apparently ...Ng4 is playable as well, but I don't understand that line).


How you should use the book is really a matter of opinion, but I very much believe in immersion learning, so rather than do a few every day for a longer period, I believe that doing as many as you can in a shorter period of time is more beneficial. I have seen this play out in practice in both my progress, and in the progress of those, whom I have taught.

Therefore, I always say, that try and do at least 50 per day, spending no more than two minutes per move on each problem.

The whole point of pattern recognition is that you do not have to try to remember the specific positions you see in the book as you will likely never get those exact positions in your lifetime. What you will get in your games is certain elements of those games, the patterns", and by doing enough of these tactics exercises, you will start to remember them.

I just looked at the table of contents of the Polgar book, and it is well-organized. You want to stay within a certain type of tactic when you are studying, like doing pins for a while, and maybe later, forks, etc.

You should, and shouldn't, have to consciously identify the patterns. I think it will come naturally as you read that book, and MANY more tactics books after. Even if you become an "ordinary" Master, even then, your tactics will still always be helped by continued tactical practice.

I am not sure how number three relates, or really what you are asking, but in general, when doing tactics problems, I would not set up a board as it takes too long, and you want to start calculating in your head anyway.

A tactic can lead to either a material advantage, which I think is more common, or a positional advantage. You always need to be mindful of the evaluation at the end of a tactic, and ask if you are really better, and is there any trap at the end that you may have missed. If you have a tactic that can lead to either type of advantage, you have to weigh the pros and cons of each final position. I would say that, in general, material is more likely to be preferred, but there are definitely cases where I would not want the material, and would take the position.

For example, I recently answered a question here where the OP took the exchange. I would not have played the move 35...Ne3+ winning an exchange, and would have preferred to maintain the pressure. The short "tactical exchange" winning the exchange allowed white to use e4 as a blockading square for quite a while, whereas keeping the attacker would have probably led to more. The positional pressure was worth more, in my opinion. So this is an example of having a choice between material and position, and having to make a decision.


What are some free chess software for showing the best moves in the final output analysis?

You can download Stockfish for free. It has a great UI. You can also use the engine with scripting languages such as python which we do for our app Chess Puzzle Blitz.
Stockfish: https://stockfishchess.org/
Both Lichess and Chess.com have analysis tools (you can load a PGN or FEN, or manually set a board).
Chess.com: https://www.chess.com/analysis
Lichess.org: https://lichess.org/analysis


Yes there is a Python wrapper to the Chess.com API. Here's the package: https://pypi.org/project/chess.com/


How can I speed up my check detection in Javascript?

It looks like your engine is using very simple for loop and arrays. Your code simply loop over again and again, possibly repeat each search iteration.

That’s obviously not good. Chess engine can’t run fast if it has to loop like that. If the position had no check surely all CPU time wasted?

My recommendation is change your data structure to a bitboard. Bitboard will allow you run check detection quickly, just do a AND the pieces your opponent can attack and your king position.


Is this the quickest way to clearing the board to two kings?

Samuel Loyd found faster in 1895.

[FEN ""]
1. c4 d5 2. cxd5 Qxd5 3. Qc2 Qxg2 4. Qxc7 Qxg1 5. Qxb7 Qxh2 6. Qxb8 Qe5 7. Qxc8+ Rxc8 8. Rxh7 Qxb2 9. Rxh8 Qxa2 10. Rxg8 Qxd2+ 11. Kxd2 Rxc1 12. Rxg7 Rxb1 13. Rxf7 Rxf1 14. Rxf8+ Kxf8 15. Rxa7 Rxf2 16. Rxe7 Rxe2+ 17. Kxe2 Kxe7

https://pdb.dieschwalbe.de/search.jsp?expression=PROBID=%27P0001931%27

This is 17.0 moves.

It is also possible to do it in 16.5 moves but I can't find it yet. See François Labelle's page.


What is the current theoretical state for the Chinese Dragon?

When black plays the Dragon, recently, the top players tend to choose 9.0-0-0 and 9.g4, instead of 9.Bc4. For example, Topalov-Lu Shanglei, Wei Yi-Lu Shanglei, Caruana-Nakamura and Karjakin-Nakamura.

According to the Game Database of ChessTempo, after 9.Bc4 Bd7 10.0-0-0, 10....Rc8 is the most popular choice. A couple of months ago, two books about the Dragon have been published, written by GM Jones. In Volume 1 he recommends 10....Rc8 and a couple of days ago, he used this move to beat GM Yu Yangyi.

However, according to the Game Database of ChessTempo, 10....Rb8 scores close to 50% with a performance of 2410, for players with an average rating of 2407. This indicates that 10....Rb8 is a good alternative for 10....Rc8.

White usually continues with 11.Bb3. After 11....Na5 12.Bh6 Bxh6 13.Qxh6 b5 14.g4, white does seem to be slightly better. Recent games of strong players are: Mamedov-Can, Ledger-Jones, Saric-Cvitan, Demchenko-Kanter and Georgiadis-Cvitan.
The same position can arise after 12.g4 b5 13.Bh6 Bxh6 14.Qxh6.

      [FEN ""]
      [StartPly "20"]

      1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.f3 O-O 8.Qd2 Nc6 9.Bc4 (9.O-O-O)(9.g4) Bd7 10.O-O-O Rb8 (10...Rc8) 11.Bb3 Na5 12.Bh6 (12.g4 b5 13.Bh6 Bxh6 14.Qxh6) Bxh6 13.Qxh6 b5 14.g4


No, the Black king is not checkmated in the photo, but it will be on the next move if you move your queen to either of the squares indicated by the arrows (i.e. to c8 or f7).  Qd8# would also work.  This is because all of the black king's potential escape squares are covered by your men in the case of Qc8# or Qd8#, and of course there are no potential escape squares after Qf7#. The opposing king doesn't have to be in check before you make your move for it to be a potential checkmate.


A lot of questions with many different answers depending on the type of competition. Leagues can be either Swiss or round robin. I suspect most leagues are round robins but by no means all are.

Perhaps the most interesting league from the viewpoint of pairings is the the UK's 4NCL (originally 4 Nations Chess League). There 4 main divisions with subdivisions and both Swiss and round robin pairings are used according to numbers. If you are genuinely interested then the examples from this league are worth investigating. The rules are here - http://www.4ncl.co.uk/1718_rules.htm

  Is there some fixed rule how teams for leagues are paired?

No. There is no one fixed rule. If there are roughly the same number of rounds as teams then a round robin (all-play-all) pairing system would be used which does have fixed rules. If there are many more teams than rounds then some form of Swiss is used. Sometimes the league might be split into two time-wise with several subdivisions paired with one system (rr or Swiss) for the first half and then rejoined depending on results into separate sections which may again be paired in different ways. Again there are rules but some are fixed and some mutable.

More information on Swiss rules are available on the FIDE website here

For round robin tournaments Berger tables are used. The only reference I have for these is the FIDE Arbiters Manual These start on page 66.

  Is it deterministic once team gets its starting number?

For round robin, yes. For Swiss, no.

  If for example two teams must play in early rounds (e.g. A, B from
  same club), is it always done by giving them appropriate starting
  numbers or are some leagues where rounds are done manually?

It depends entirely on the circumstances. For a round robin it is easier to do this by assigning start numbers appropriately but it is not essential.

  Do some leagues have an odd number of teams and would it change
  something?

Of course some leagues have an odd number of teams. For round robins, where the Berger tables are used, one team has a zero-point bye each round. For Swiss systems triangular matches are used.

As I said at the beginning the UK 4NCL is interesting and complex with a full range of pairing and worthy of study if you are really interested in this sort of thing.

You might find Division 3 North of particular interest because it has a relatively large number of teams. The discussion on this (2017-18) season on the English Chess Forum is here . The arbiter's job was complex. This post shows one of the interested parties posting the ingenious pairing rules that were decided on by the arbiter to solve the problems posed.


Study endgame first before studying opening? Is it true?

I'm only a 1600 so take my advice at face value

I hear a lot of people saying all the time not to waste their time on openings, just focus on tactics and endgame. That advice is nice and everything but if you never make it out of the opening the endgame is worthless. I had a game in a tournament where I fell for Lasker's trap in the Albin-Counter Gambit. If I had spent just 5 minutes studying that line I could have avoided that and survived to use the lessons I have studied in the endgame.

I guess what I am trying to say is that instead of thinking of it as "should I do one or the other" you are going to have to do both. If you want to get good you can't avoid any one area you are going to have to give them all attention. Studying openings leads to a strong positional understanding and leads to understandings in similar openings. For instance understanding the sveshnikov sicilian  helps with understanding the themes in the kalashnikov.

Study a lot of tactics because every 2000+ I have heard has said tactics are what you need to know. Hope this helps


These were the rules for the 2006 Amber blindfold tournament with many super-GMs participating:

  Rules of play

  Rules for the blindfold games

  Play will be governed by the FIDE Laws of Chess, except where they are overridden by the following rules.
  Players are not allowed to record the moves.
  At the start of the game each player has twenty-five minutes on his clock. Before a player makes his move twenty seconds will be added to
  his remaining time.
  The computer clock marks the end of the time-control period.
  The monitor will show the players when the same position has appeared on the board three times or that the "50 moves rule" can be
  applied. In this case either player has the right to claim a draw.
  If a player makes an illegal move, the monitor will display the message: "Illegal move, make another move". In this case there is no
  need for additional action by the player.
  If a player needs the assistance of the arbiter, he may call the arbiter. The arbiter will in this case interrupt the game;
  interrupting of the game takes about 5 seconds. In this situation the
  players may not leave the playing area of the playing hall and may not
  watch the position on the monitors.
  Players, who leave the playing area without permission of the arbiter, will lose the game immediately.

  Regulations in case of computer breakdown

  After a computer breakdown, it is forbidden to speak to anybody except the arbiter.
  The games will be continued on empty boards in the two playing halls and, if three games are in progress, also in a room of the
  hotel.
  The time will be controlled using the Fischer clock; the time will be transferred as accurately as possible from the computer system to
  the Fischer clock. 25 seconds extra will be added for each move
  (instead of 20 seconds).
  Two persons will control the game; the arbiter will write the moves down on a scoresheet, which is hidden from the players, and operate
  the clock. The assistant will play the moves on a pocket set, which is
  hidden from the players. The arbiter will check the intended move for
  legality, and if it is legal he will operate the clock and then write
  the move on the scoresheet. Note: it is possible that it takes a few
  seconds for the arbiter to check the move and press the clock, but in
  any case the time taken is not more than for the player to enter the
  move on the computer.
  The players shall show their moves on the empty board by pointing to the start and destination square of the move they intend to make;
  at the same time, they will speak the move aloud. If the move spoken
  differs from the move indicated on the board, then the arbiter shall
  say, "What do you mean?"
  If a player makes an illegal move, then the arbiter will say "Illegal move" and he will not push the clock. For example, if a
  player says "Rook takes d6" and the move is not a capture, then the
  arbiter will say "Illegal move", or if the player shows d1-d6 on the
  board and says "Queen d6", but the piece on d1 is actually a rook,
  then the arbiter will again say "Illegal move".

SOURCE: ChessBase News, 2006


For Android you have the 7-piece chess endgame training App, with sets of exercises against Lomonosov tablebases and classified by remaining material per side.


For white

The Danish Gambit.

For black

A variation of the four knights with 4. Bc4 will lead to an opening of the game for black by the means of 4...Nxe4 5. Nxe4 d5.

Alternatively, 5. Bxf7+ Kxf7 6. Nxe4 may also occur with sharp play (although you do give up the bishop pair, Black also gave up his right to castle).

Related: Very Aggressive Openings


What is the rationale behind Black playing e6 in so many openings?

In the French Defense, the modest pawn advance in e6 simply plans to challenge the e4-pawn by d5, without having to recapture with the Queen after a possible capture in d5. The idea is thus similar to the Caro-Kann. The differences are that the Caro-Kann takes away the best square for the b8-Knight, while the French blocks the natural diagonal for developing the c8-bishop. So there is a trade-off but both openings are safe and solid methods against 1.e4.

The idea of e6 in the Semi-Slav is also to reinforce the control in d5 and take back with a pawn if White plays cxd5. It's true that the c8-bishop is blocked but Black can solve this by either taking in c4, followed by b5 and Bb7, or by playing b6.


I have tried using MCTS before for a chess engine and the results were not very good. The problem was that the results when playing out a game with only random moves were basically just that: random. Most of the results would only be reached after over 100 plies so the initial position had little to do with the result.
I had better results when I cutoff the tree after x plies where x would be somewhere between 20 and 50 and using a simple evaluation function for that position. But then you would be relying on a evaluation function again.


I'm answering without an engine to back me up, but I do have some knowledge of French positions and can answer on that account:

The move b5-b4 is not necessarily a bad move.  What Black always should worry about in the French is placing all his pawns on white squares and then exchanging his dark squared bishop.  It is a common theme in the Winawer variation of the French.

Here it is Bxa3 which is the most strategically dubious move.  In the French, do not exchange this bishop unless you get something for it. Look at your remaining bishop, all closed in by the pawns.  Your bishop at f8 was stronger than the white knight at a3.

Besides, the move bxa3 is not so strong either. It opens the a-file for Ra1 and the principle for pawn exchanges is to capture towards the center, not away for it. That put aside, Bxa3 is strategically much worse as you give up the fight on the dark squares and your bishop pair for a knight in the rim.


Which openings give a winning pawn-structure in the endgame?

Here's a somewhat cheap answer: the Nimzowitsch Variation of the Caro-Kann Defense, given by 1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Nf6 5. Nxf6+ exf6. In the resulting position,

if we were to remove all the pieces and leave a pure king-and-pawns endgame, then White would have a winning advantage, because he has a healthy pawn majority on the queenside which can create a passer, while the doubled pawns of Black's kingside majority make it so that White can prevent her from creating a passer. So this is an accurate answer to your question. The only reason I call it "cheap" is because the pawn structure here is just a mirror-image of the Ruy Lopez Exchange structure your question already mentions, but I guess that doesn't make it any less of an example.

I think one reason your question hasn't gotten any answers until now, though, is that for the resulting pawn endgame to really be a winning one structurally, it seems you need this feature that one side can forcibly make a passer while the other side can't, and that means having a workable majority for one side and a "broken" one for the other. That basically requires there to be (1) some doubled pawns for one player, and (2) two distinct sides of the board, in terms of the pawn islands remaining. (E.g. if the white e-pawn and black d-pawn hadn't been exchanged in my example, then the pawn endgame wouldn't yet be a winning one.) And there's actually not so many (truly distinct) ways for that to happen, at least not in realistic ways.

Another common sort of opening that would at least feature a very favorable pawn endgame for one side is those in which one side has an isolated queen pawn. The side that has the isolani could find his king being so tied down to its defense that the other side can force a win. But this won't always be the case, so I wouldn't give that as an answer in and of itself. If you want to find some further openings that at least get part of the way toward what you're after, ones with an isolated queen pawn would be a promising place to look.

All in all, for the reasons I've spelled out, I'm not too optimistic that you'll find all that many (essentially different) examples of what you're after, but I hope this helps.

That said, there is an entire class of openings that provide truly cheap answers to your question: gambit openings. Since these would feature pawn endgames with a pawn deficit (at least), these will generally be lost for the gambiteer's side. I sure wouldn't want the pawn endgame from the Danish Gambit line 1. e4 e5 2. d4 exd4 3. c3 dxc3 4. Bc4 cxb2 5. Bxb2, for instance :)


EDIT: Final calculation matches actual proof game exactly.
That’s a nice new chess-math question, which deserves wider circulation.
Begin by promoting a White pawn as quickly as possible, because until that happens, White is just haemorrhaging pawn moves. Now can promote a second pawn more slowly. This promoted piece is captured by Black pawn to open a file, and the first file's promotions can happen.
Scheme: axb to let all wPs from the a-file promote, then bxa+bxa to let all remaining wPs from the b-file promote, then cxb to let all wPs from the c-file promote, and so on.
One player is the active one, moving pawns. This player can also capture spare officers with officers. But pawns can never be captured before they promote (hugely expensive) and there are only 2 captures by wPs and 9 captures by bPs.
There are in principle 188+36+48+15=287 marks (captures & pawn moves). However, we lose 9 for Black pawn captures, 2 for White pawn captures, and 5 for pawn moves leading to the first White promotion. So there are really just 271 marks. So if the count begins after 4. a8=?, we have a total length of 20328.5 moves minus 0.5 for each parity switch.
So how many parity switches must there be? White is the first active player, then need two switches to promote the pawns from any file. So that's 16 switches, and White has promoted all his h-file pawns. A 17th switch is required for Black to capture these.
What impact does dead position have? If it applies literally, then Black cannot win if he has lost all his units, because he can't capture the last White unit. So let's suppose that Black winning "counts" as checkmate for DP purposes. That gives a total of 20320.0 moves.
The final proposed total is hence: 20320.0 moves.
An actual animated proof game has been constructed which achieves this total: https://pdb.dieschwalbe.de/P1370701


Is my solution to this puzzle wrong or a transposition of the official one?

They're not equivalent, but your solution is just as good. In fact, it's more easy to find because Nf2+ is a 'forcing' move.


What's the point of the Two Knights French?

Another idea of the two knights variation is to provoke 3...d4 and get some kind of reversed Old Indian. Some players like these pawn structures, and it also may not be blacks taste to be the one with the space advantage.
For example:
[FEN ""]
[Title "Analysis"]
[StartPly "99"]

1.e4 e6 2.Nf3 d5 3.Nc3 d4
    ( 3...Nf6 )
4.Ne2 c5 5.c3 $1 Nf6
    ( 5...d3 $6 6.Nf4 c4 $2 7.Qa4+ $18 )
6.cxd4 cxd4
    ( 6...Nxe4 $5 )
7.Ng3
    ( 7.e5 Nfd7 8.Nexd4 Nxe5 $10 )
7...a6 $1
    ( 7...Nc6 8.Bb5 $14 )
8.d3
    ( 8.Bc4 $6 b5 9.Bb3 $2 d3 $1 $17 )
8...Nc6 9.Be2 e5 $13

Objectively black is minimal better due to his space advantage, but white operates with the vacuum which d5-d4 has created in blacks position. He will sooner or later play f2-f4 and attack the pawn chain e5/d4, for example by playing h3 and Nh2. If black takes on f4 this will isolate the d4 pawn, and white may be able to win it. Of course that will not work if black plays it sensible, for example by protecting the pawn with Qb6 and Rd8. The stronger player will win.
But as you already said, Black can play 3...Nf6 and this transposes to the main lines.


This page contains a lot of information about DGT boards, including the patent, detailed description of technologies and algorithms used. Many additional references are provided, too. It is definitely an interesting read!


What was the longest World Championship game?


What is the Elo rating of Stockfish version that played AlphaZero?

The Stockfish version that played agaist AlphaZero was significantly compromised in several different aspects:

There was no opening book available
Time control was 1 minute/move, which throws out of the window various optimizations re: using more time thinking about difficult moves
Stockfish had threads=64 set, but the actual hardware had only 8 CPU cores, that effectively slowed things down quite a lot
The hardware was quite different -- an average $1k PC (Stockfish) against a bunch of specialized hardware that might cost millions and is not accessible to anyone
There are more, but these are main points.

Answering your question, there's no way to measure how much rating Stockfish had in a very handicapped conditions it had to run.

Nonetheless, winning over Stockfish is quite an achievement, no matter how handicapped it was and how much was the difference in hardware cost.

UPDATE: in the recent article "AlphaZero: Shedding new light on the grand games of chess, shogi and Go" the rating for Stockfish was drawn as a line at 3500. Besides that, the article provides the new games played with a reasonable time control for SF as well as opening books.


Useful solving composed mate-in-2 problems?

I am going to re-post my exact answer to the question "Improving the observation skill & making less blunders" with this preamble, because if you use them in this manner, you can cut down on mistakes early in calculation. Of course, this can be very helpful. If you learn to do this effectively, and as a matter of course in tournament games, you should see improvement.

In addition, you will see common patterns repeated, even if finding the first "key move" is difficult. I think scanning all possible moves, and not necessarily calculating deeply, depending on your current skill level, can lead to your solving these more quickly.

Here is that answer:

I will go back to what Artur Yusupov, three-time World Championship Candidate, former top-10 player,  and one of the greatest living trainers recommends in the first book of his 10-volume series. In volume one, "Boost Your Chess - Build Up Your Chess", chapter 9, which is two-move mates, including composed problems:

  The aim of this lesson is to improve your calculation of short
  variations. It is more important to find a lot of options in the
  first few moves than to calculate moves long variations. Most mistakes occur in the early moves in variations. What
  is the use of calculating a long and correct variation if your
  opponent has a much better reply on move one?

  You must develop your skill at calculating short variations, while at the same time taking into account the possibilities available to
  your opponent. This skill should reduce blunders.

  Exercises with mate in two moves are very well suited for training in
  the art of calculating short variations with great accuracy.
  Emphasis as written, not mine.

I will take this one step further with my own suggestion. Try to train yourself that before you make every move, look at EVERY move your opponent has. I am not saying that you are calculating anything. You are simply looking at it so you consider it. It will do two things: If you are hanging a piece, just looking at it will usually "hit you in the face like a brick", and second, I have done many combination problems over the last 40 years, and sometimes, when I cannot figure it out, and look at the answer, I realize immediately that had I just LOOKED at the move, I would have seen the combination.

So, again, you are not trying to calculate, just consider every move. You will be amazed at what you register immediately.


Is there any free software to automatically analyze and annotate games?

Chessbase will do what you're describing (enter the game, then tell it to annotate), but it is not free.

Scid is a free alternative database program, but it will not automatically annotate your game.

See here for more discussion: http://www.chess.com/forum/view/general/is-there-any-free-software-to-analyse-the-completed-game


Interactive tutorials, for example presenting a game with commentary and periodically asking you to provide input, e.g. what you think is the best move, how to exploit a mistake etc.

Passive tutorials where you just look at the screen. Youtube is best placed for this.

Set up a position and play against the computer is great for setting up endgames and taking resigned positions from master games and playing them against the engine. After all, the hardest thing to do in chess is to win a won game.

Online arena for playing against real opponents under various time controls.

Mini games such as knight's tour, pawn wars etc. to practice key skills such as visualisation and endgame technique.


A more practical form of your question relates to the Exchange Lopez and Tartakover Caro-Kann.
Euwe did a complete analysis of how White wins the Exchange Lopez pawn ending if you set up the pawn structure with no pieces on the board:
4k3/1pp2ppp/p1p5/8/4P3/8/PPP2PPP/4K3 w - - 0 1

While the Tartakover Caro=Kann is the same thing on the other wing.
In this impractical 8-vs.-7 thing you envision, the side with the extra pawn would surely begin with the unopposed pawn two squares, as the first step toward creating a passed pawn.


The position is roughly equal. The problem for both sides, but it is a little worse for white, is king safety. That is the overwhelming positional factor here.

Kg2 and Qd4 is the best plan for white here to counter the threat on f2. It is positionally mutually difficult to do anything since both queens and rooks must keep defending soft spots. Trying to do more, and you likely get mated.

Here is a short sample line with notes.

 [FEN "5r2/5q1k/6pp/1p2P3/1P2p2P/6RK/3Q1P2/8 w - - 0 1"]

 1. Kg2 {to defend f2} Qf5 {activating the queen a little} 2. Qd4 {also activating the queen a little, but keeping an eye on f2 at the same time} Rf7 3. Qb6 {keeping black thinking about the white queen taking on g6 and then mate} Kg7 {pass} 4. Kg1 {pass, and not much progress can be made.}


A suggestion I have is to start playing gambits, and high-risk-high-reward openings. For example, playing the King's Gambit as White forces you to utilize any initiative you are given. Playing the KID as Black will force you to sacrifice pieces now and then to win istead of losing.

Basically what you need to do is to start appreciating initiative by experiencing it for yourself. Otherwise it becomes very difficult to dare making risky decisions based on tempo and piece activity, if you've never done it successfully before.

Based on what you wrote, I guess you tend to play mainly rather slow and positional setups in the opening. Then you have to expect it to be rather difficult to learn about this style of play, as you are probably not very familiar with it.

Other things you can do is to look for inspiration in games by e.g. Kasparov. He was excellent at utilizing the initiative, and just crushing his opponents with daring attacks. Just look at the notable games at his personal page on chessgames.com, some of them are rather amazing examples of this.


On the feasibility of a KBN-K mate within 50 moves using a particular method

Is this satisfied for ALL legal KBNK positions using that particular stratagem only?

Absolutely not! Please don't try to prove something that's impossible. Consider this position.
[startflipped ""]
[FEN "3kB3/4N3/8/8/8/8/8/3K4 b - - 0 1"]


Why do miniature games happen at the grandmaster level?

Your statement, Grandmasters think of next many moves ... is a bit misleading for your question.

Grandmaster are able to calculate many moves ahead, but this is not something they do at each and every move. Basically, as for the start of the game, the first 10 or 20 moves are played from memory (known opening repertoire + home preparation) and not found over the board.

Even when the home preparation ends, players usually do not start calculating  like crazy all possible moves to depth 20. They would rather (also see here):

evaluate/analyze the position based on general principles and experience
depending on this analysis develop a general plan (Should I improve piece activity? Should I play against an opponent's weakness?....)
come up with concrete (candidate) moves
calculate the consequences of the candidate moves: Depending on the position at hand this can be many moves ahead (e.g. in tactical or forced lines) or it can just be a single move, basically just checking whether you don't blunder something (e.g. in less tactical, more positional games where it is just practically impossible to calculate all possible lines)

So how can grandmasters lose in less than 25 moves?

They are humans so not perfect and might make mistakes. In this case they can go wrong at basically each part of the thought process:

They might mix up memorized opening theory, confusing lines and thereby making a bad move. Occasionally they might run into a strong opening novelty prepared by the opponent in which case even playing the commonly accepted opening line can bring them into trouble. Also there is the funny story around the Zapata-Anand miniature where Anand apparently blindly followed published opening theory (informator) of a Miles-Christiansen game which was a prearranged draw but in fact included a huge blunder.
They might evaluate the position wrongly, e.g. underestimate a threat.
They might come up with a plan that is impossible to push through or pick the wrong plan out of a choice of plans.
They might miss a possible candidate move
They might  make a mistake in calculation.

In addition any combination of the above is possible.


Is this 2B vs. N endgame won for the bishops?

Try Syzygy tablebase: https://syzygy-tables.info/?fen=8/8/5b2/8/K7/8/k7/1b1N4_w_-_-_0_1

Please ignore DTZ if you don't know what it is, look at DTM. It's checkmate in 139 piles with perfect play.

No, the position is drawn under the FIDE 50-move rule.


According to Wikipedia:

"A pure mate is a checkmating position in chess in which the mated king
and all vacant squares in its field are attacked only once, and
squares in the king's field occupied by friendly units are not also
attacked by the mating side (unless such a unit is necessarily pinned
to the king to avoid it interposing to block the check or capturing of
mating unit."

Essentially, a pure mate is a position in which each square around the opposing king is attacked only once by the mating side, so your first example is indeed a pure mate. However, your second example is not. While kings can be blocked off by their own units, they cannot be attacked unless they are pinned, which they aren't.
To summarize, the Black king can be surrounded by its pawns and pieces so long as they are not attacked, and if they are, they must be pinned. Furthermore, the pin must prevent the pinned piece from interfering with the mate.
As far as I can tell, multiple pieces may be on the board so long as the stipulations of a pure mate are met. The enemy pieces surrounding the king’s squares can be attacked, so long so as the mating piece is actually capable of mating, i.e. it cannot be captured or blocked.
Wikipedia gives an example from the final position from the famous Evergreen Game (link the chessgames.com).
 [Title "”The Evergreen Game,” Adolf Anderssen-Jean Dufresne. Berlin GER, 1852"]
[FEN "1r3kr1/pbpBBp1p/1b3P2/8/8/2P2q2/P4PPP/3R2K1 b - - 0 1"]

In this position, each of the Black king's available squares that it could move to are attacked exactly once by the White pieces, and the black blocking pieces are not attacked by white pieces at all. Although the White pawn that blocks off the g7 square for the black king is attacked, this is a real pure mate from high-level play nonetheless.
If you wish to see a constructed position for a pure mate, @DM has a great position in his answer to a related question on this site.


What do D and +-- mean in chess annotation?

"D" means see diagram. "+/-" means white is better, but not much better.


Yes, you can.

Fide rules of chess 3.7.e):

When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival.
This is called the square of ‘promotion’. The player's choice is not restricted to pieces that have been captured previously. This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate.

(bold by me)


Is there a good program to play chess online in ubuntu?

On ubuntu, you can download Firefox, Chrome, or any other browser of your choice. From within that browser, go to lichess.org, chess.com, or chess24.com, create a free account, and play against others online.


Queenside vs Kingside pawn majority: Looking for comprehensive resources

The main idea can be summarized as follows

  The deciding factor is the control over the open d-file

Thus, you should play this position with one, two or three heavy pieces each still on the board and make sure you will control the d-file. As usual, invade the seventh rank, bring your king to the center (as long as the king is safe when doing so) and cramp the opponent.

EDIT (2014-03-14):

If you want to win this position, you should exchange down to a rook endgame where you control the d-file. If you want to prevent a loss, you should avoid a position where your opponent exchanges down to a rook endgame where the opponent controls the d-file. The middlegame (more pieces on the board) adds more complexity. Learn the clean cut case and that will guide you in more complex situations.


Outcome of a game in case of an illegal checkmate

The mate stands and white wins. Although the position both before and after the mating move is illegal the mating move itself is legal therefore article 5.1.a is satisfied.

If an arbiter observes black playing 1...Qc5 then they declare the game lost for black for playing an illegal move. If they do not see the move but they observe the position after 1...Qc5 they will wait for white's move. Since white played 2.Rxc5 both kings are no longer in check hence article A.4.d does not trigger. In fact the purpose of the arbiter having to wait one move is to give the player a chance to correct the position. As it happens in this example the final position is still illegal but for a reason not covered by article A.4.d.


Openings that Black has success with statistically?

It depends very much on what you intend by the word "advantage": if you are asking

  Are there any openings that give Black advantage at correct play?

the answer is obviously no, as well as there are no openings that give White advantage, at correct play. If otherwise there will just be no openings, rather only that one line that always gives advantage to White (or Black, respectively) without any need to play anything else. At correct play all standard opening variations are equal, if only there might be a tiny slight advantage for White in the sense that it is enforced to play the next move and as such the next-to-come threat.

If instead you are asking

  What are the major defenses that statistically have seen the most success by Black?

that is another matter completely. You might want to have a look at any of the large chess databases present on the internet where openings are sorted by winning percentages according to the variation (for the games contained in the database, obviously); an example is this page from ChessTempo showing winning percentages for the Sicilian Najdorf variation, for instance, that is well-known to be among the most played defenses versus 1.e4. Other examples for 1.d4 are the Slav defense or the Indian defenses, as standard sound counterplay for Black.


Is this position with KRP against KBP a draw?

This endgame is indeed a draw. You can check positions with 7 or fewer pieces in the Sygyzy tablebases to see if they are a win, a loss, or a draw. If you want the depth to mate for 6 pieces or fewer, use the Shredder database
Given the context, I suppose you would like to know why this is a draw. If White was trying to win, the best option is to take Black’s pawn. Black’s bishop is stuck defending it. If the pawn falls, Black falls with it. White can and will win the pawn.
[FEN "6R1/8/3k4/pK6/Pb6/8/8/8 w - - 0 1"]

1. Ra8 Kd5 2. Rxa5 Bxa5 3. Kxa5 Kc5

The clutch is doing soh leaves White with a major problem. The pawn endgame is a draw! Due to having a rook pawn, White will either be stalemated by the Black king, or Black will get in front of the pawn and be stalemated by White.

[Title "White is stalemated"]
[FEN "8/8/8/K1k5/P7/8/8/8 w - - 0 1"]

1. Ka6 Kc6 2. a5 Kc7 3. Ka7 Kc8 4. a6 Kc7 5. Ka8 Kc8 6. a7 Kc7

[Title "Black is stalemated"]
[FEN "8/8/8/K1k5/P7/8/8/8 w - - 0 1"]

1. Ka6 Kc6 2. Ka5 Kb7 3. Kb5 Ka7 4. a5 Kb7 5. a6+ Ka7 6. Ka5 Kb8 7. Kb6 Ka8 8. a7

If White does not target g the Black pawn, BBlack will merely wait it out. They will just shuffle their bishop around to keep protecting their pawn. The Black king will move around such that the pawn endgame will remain drawn. Eventually, there will be a draw via the 50-move rule or threefold repetition.
For all situations with head-to-head pawns, it seems that most will be won. Moving your position one file over move creates gives a win for White. Therefore, it seems to me that the only drawn positions are ones with rook pawns and a close enough Black king. In other words, there are very few of them.
[FEN "7R/8/4k3/1pK5/1Pb5/8/8/8 w - - 0 1"]

1. Rb8 Bb3 2. Rxb5 Kd7 3. Rb7+ Kc8 4. Re7 Bd1 5. b5 Bf3 6. Rf7 Be4 7. Kb6 Bg6 8. Re7 Kd8 9. Re5 Bc2 10. Kc6 Bb3 11. b6 Ba4+ 12. Kd6 Kc8 13. Re7 Kb8 14. b7 Be8 15. Kc5 Ka7 16. Rxe8 Kxb7 17. Re7+ Kc8 18. Kc6 Kb8 19. Rf7 Ka8 20. Kb6 Kb8 21. Rf8#


Stalemate is a draw in classical chess yet there are other chess variants both historical and modern where stalemate is not a draw.

Very early versions of Chess, such as Shatranj Chess (props to Andrew Latham) declare the player causing stalemate the winner and even today there are callings to return to that rule.

for example:

Larry Kaufman Chess Life Sept. 2009 writes:

  "calling stalemate a draw is totally illogical, since it represents
  the ultimate zugzwang, where any move would get your king taken"

A typical counter to this point is that Chess tradition dictates that a stalemate cannot result in a win for the stalemating player because it would require a suicidal move from the stalemated player (moving your king into check is, in most forms of chess, an illegal move). If there are no moves on the board that you are able to make (other then resigning) then in making the stalemating move your opponent has effectively ended the game without a definitive result (capture of the king) and is judged to have not won the game.

So.. "In Classical Chess what is the probable origin of stalemate being considered a draw?"

The earliest reference I can find to Stalemate being a draw in formalised chess rules is 13th century Italy where the version of Chess played declared that a game could only be won by checkmate or resignation. Stalemate, under those terms, describes a state where a player cannot make a legal move. In effect the game has stalled in a state where neither player can achieve Checkmate and is drawn.

Stalemate as a draw then spread to Germany (1400s), Spain (1600s) and throughout Europe by 19th Century when the formal rules of what we know as classical chess were put in place.

England was one of the final adopters of Stalemate as a draw in the 1800s (up until that point the stalemated player had actually been declared the winner).

Opinion:

Yes tradition does favors the player in stalemate but it has been that way for a very long time. The flipping of that advantage to the stalemating player would greatly change the nature of the endgame (and thus the game of chess and a huge amount of chess theory), which is probably why such arguments have not recieved too much traction.


If the opponents are known (e.g. in a round robin tournament) you can prepare specifically for these opponents, i.e. find openings or positions which your opponents don't like or in which they perform badly, etc.Professional players would do this even during the tournament (in-between rounds).

If the opponents are not known (e.g. in a large open tournament) there is not much you can do other than what you should always do: practice tactics, learn/study endgames, strategy, refreshing your openings, doing some sports (not chess)...

Overall at your level I would not worry too much about all this. Arriving relaxed to a match will be more important than trying to prepare specifically for one opponent.


Did Indian systems really have fianchettos?

The page you linked to mentions that "Mohishunder originally played traditional Indian chess, in which pawns did not have the option of moving two squares from the starting row." I think that reference to traditional Indian chess refers not all the way back to shatranj/chaturanga, but rather to this 18th and 19th century variant, which has some significant differences from chess as we know it today, but seemingly does not in any way preclude a fianchetto. And since those rules do preclude any advance of a pawn by two squares, it seems reasonable that systems combining g6/d6 or b6/e6 would naturally arise as methods to develop the bishops in that variant.

Updated References: As the OP noted in a comment, the wikipedia entry I linked to doesn't indicate any source material. I found another page which describes this variant under the name Hindustani Chess, and it includes a helpful pointer to the 1913 book A History of Chess, a 900-page tome written by H.J.R. Murray, which details this particular chess variant in its Chapter IV. As it turns out, it appears that Skyhorse Publishing will be reissuing the book later this year. From their blurb:

  An epic work that took over a decade to complete, A History of Chess, originally published in 1913, was a historic undertaking that shattered preconceptions about the game upon its release. Over a century later, Murray’s research, in which he argues that chess originated in India, is still widely accepted by most chess historians.


Is checkmate possible in knight vs knight pawnless endgame?

Yes, it is indeed possible :)  I'll give you the coordinates for the pieces in a possible mating position, and you can set it up on your chessboard.

Place the White King on g6.

Place a White Knight on f7.

Place the Black King on h8.

Place a Black Knight on g8.

6nk/5N2/6K1/8/8/8/8/8 w - - 1 1

In that position, Black's King is checkmated.  Although, I doubt even the biggest beginner would ever let that happen to them :)  You would only be able to checkmate in that endgame if your opponent literally played the worst moves multiple times in a row.


Please help me understand the f6 break in the French defense

The f6 break is a key idea in the French defense, and the point is mainly to add more pressure to White's center. In the French, one basic line of thought is the following:

Let White occupy the center
Destroy White's center
Occupy the center yourself
Win the game, as White now will be totally helpless!

If black manages to complete steps 1-3 outlined above, without significant material losses or a serious weakening of the king's position, step 4 will indeed often be possible to accomplish.

Let us examine the move f6 in view of the steps above. If White has a pawn on e5 and black plays ...f6, it's possible to

a) take on f6
b) defend the e5 pawn
c) ignore it

a) If Black hasn't castled, it most likely means that Black will have to respond to this with ...gxf6. Black now typically has pawns on e6 and on f6. It is not hard to see that Black can have plans to push ...e5 in the near future, and if the pawn capture on f6 hasn't left Black's king open to direct attack, it's possible that Black will achieve steps 2-3 outlined above shortly.

If Black has castled, on the other hand, more options than ...gxf6 will be available. Often either a knight, bishop or a rook could also take on f6 in this case. In case of rook capture, Black has a semi-open f-file for his/her rook. Taking with a bishop adds more pressure on the a1-h8 diagonal. Taking with a knight adds possibilities to play ...e5 to free the black bishop on c8 in some cases. It is clear that the ...f6 break by Black has given many possibilities for future plans.

One more note: If White takes the pawn on f6, the h2-b8 diagonal will be ripe for the black bishop to occupy, often coupled with a queen on c7. This is sometimes very unpleasant for White.

b) If White protects the pawn, Black has some other options with ...f6 played. If White has played f4, Black could sometimes take on e5, and if White recaptures with the f-pawn, it can in some cases be possible to play ...Qh4+ for some concrete tactical purpose. Other times Black can be perfectly happy with just trying to take over the f-file and pressure White's position that way. If White recaptures with the d4 pawn instead of the f-pawn, Black has the option to open the diagonal a7-g1 with ...c4, or play ...d4 and just try to break once again in the center, to activate his/her pieces.

If White has played f4, and it's not good for Black to take on e5, Black can wait, and try to maneouver the c8 bishop to g6 via Bc8-d7-e8-g6. This is a standard plan in the French defense to activate that light squared bishop. Or Black can lock the center with ...f5 in some cases, to stop White from attacking the black king. In rare cases, after White has played f4, Black can even try to play ...g5, to again just try to break up White's center. This can be very risky, so it's not often the first idea Black thinks of, but it should never be forgotten, as it can recieve a great pay-off if well executed.

If White guards the e5 pawn with Bf4, the g5 break is more natural, and Black can even try to go for a kingside pawn storm in some cases. Again, it has to be well executed, as it can easily expose Black's king. Otherwise it's more typical for black to keep the tension in the center, and let White make the big decision to alter the status quo. However, at every move, White has to be wary of possible alterations of the center. The same is usually true if White defends e5 with another piece.

c) This option is very rare, and can only be considered if White manages to create an enormous treat elsewhere on the board that black needs to deal with immediately. If this is the case, the ...f6 break may be a bad idea. Otherwise, if White ignores the ...f6 break, Black can usually just take on e5, and normally having a knight on c6 and a queen on c7 (and maybe even a knight on d7 in some cases), this can mean that black simply wins a pawn.

This reply got much longer than I originally had intended it to be, but I feel like most of the reasons why Black may consider playing ...f6 in the French defense are in here. Remember that I have not included any concrete examples here, and that it all depends on the position. If ...f6 is an obvious blunder, for some reason I failed to mention here, it should of course not be played.

TL;DR: ...f6 is about challenging White's control over the center, and trying to open up the position for Black's pieces.


Do grandmasters practice blindfold chess or does it come naturally with practice?

Your question is quite interesting. If you are new to blindfold, I think this thread will help you: Can playing blindfold chess be learned or is it a natural skill?
Now, back to your query. I have discussed this topic with a GM, who is one year senior at my college. According to him, playing blindfold is "NOT impossible", but it's fairly difficult. As they participate in lots of classical tournaments where they have to write the scoresheet by hand, it is easy for them to quickly visualize the board. Also, their training process helps them to calculate from certain positions without playing the moves. But, on the other hand, it is fairly difficult to keep up every possible move, visualize every possible position and that needs intense focus and concentration. But, since they are calculating and visualizing chess more often than normal people, it is comparatively easy for them to play blindfold chess after practising for some time.
In a nutshell: it doesn't come naturally over time without practice, even if you are a GM.


What is the Elo of a player who is half as good as another player?

This answer addresses one concrete portion of the OP; namely, for an arbitrary N > 0, what rating difference between Player A and Player B corresponds to Player A's expected score against Player B being N times the expected score for Player B? I'll speak in terms of the USCF's Elo rating system, since I'm most familiar with it.

If Player A's expected score is N times that of Player B when they face each other, then Player A's expected score is N / (N + 1) while Player B's expected score is 1 / (N + 1) (since the two expected scores must sum to 1). Let A be Player A's rating and let B be Player B's rating. According to the USCF rating system, these ratings are intended to indicate that Player A's expected score is then

1 / (1 + 10^((B - A) / 400))

Thus if we solve the equation

1 / (1 + 10^((B - A) / 400)) = N / (N + 1)

for A - B, we will have an answer as to what rating difference corresponds to Player A's expected score being N times greater than Player B's when they match up. What we get is that

A - B = -400 * ln(1 / N) / ln(10)

So we have the following approximate rating differences corresponding to certain values of N:

N     A - B
-     -----
1     0
1.5   70
2     120
3     191
4     241
5     280


What is the main purpose of the Evans gambit?

Black's choice of where to put the Bishop on move 5 is awkward, and any choice will give White some compensation:

5... Ba5 would give White the possibility of Ba3 at some point to cut off the King from castling and the Bishop won't be very useful after White castles out of the pin on c3.
5... Bc5 allows 6. d4, taking control of the center with tempo after which White can develop quickly and try to attack.
5... Be7 is rather passive and blocks a square for the g8-Knight, and White can develop very naturally and aggressively.

The reason White is better off than before move 4 is that the c3-pawn supports d4. d4 is very strong especially when White can gain a tempo on the Bishop.

Declining it with 4... Bb6 is not unheard of, but 4... Bxb4 is generally considered more challenging.


What is the best defense for White against the Traxler Counter Attack?

6. Kf1 is the best response.

It looks like this:

[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 Bc5 5. Nxf7 Bxf2+ 6. Kf1 Qe7 7. Nxh8 Bb6 8. Bf7+ Kd8 9. Nc3 *


When a GM, or even lesser strong players reach a position that is totally unfamiliar, they have to break it down into components. They evaluate the following for BOTH sides. In general, a lot of this is done subconsciously by strong players.

Material, and what pieces are better. Sometimes a well-placed knight can be better than a rook, for example.
Can any of the pieces be shut out of play?
King safety.
Are there any direct threats?
Pawn structure and any corresponding weaknesses. (like doubled pawns, but not all doubled pawns are weak or bad as sometimes they provide great protection...more in the endgame can they really be a big problem, but you have to judge this carefully.)
How many pawn islands does each side have? (less is usually better)
Where are the pawn majorities? (Usually a q-side pawn majority is easier to mobilize)
Passed pawns.
Who has more space?
Who better controls the center?
Are there open lines, and who can control them?
Are there half-open files that you can put pressure down?
Strong outposts like being able to put a knight on d6, or a bishop on h6. This can disrupt communication between the two sides of the board, and make defense moving from one side to the other very difficult.
Any colored square weaknesses, like being weak on the light or dark squares.
Any lead in development for either side.
Which trades are good for me, and bad for him? (exchanges are one of the least written about subjects in chess, but they are one of the most important factors in chess as you get stronger. Too bad it has not been translated, but there is a book in Russian called "The Encyclopedia of Exchanges".)
Related to number 16, and that is who has the better endgame if certain trades happen?

Finally, based on these factors, players weigh them based on experience and importance, and then they come up with a list of candidate moves, and they calculate likely continuations.

I might have missed a point, but that is a pretty complete list.