Computer detection of dead positions is much trickier than people think. It is unlikely that an algorithm exists that runs in reasonable time and is 100% accurate.

It is easy to check for a simple condition like insufficient material (K+B v K, K+N v K). It is less easy to check for cases with blocked pawns, for instance:

2b1k3/8/8/1p1p1p1p/1P1P1P1P/8/8/2B1K3 w - - 0 1

since there are a lot of legal moves to check. Computers aren't based on intuition like humans: you'd have to enumerate every single possible continuation for up to 150 ply without pawn moves/captures (those reset the counter) and check that none of them end up in checkmate for either side.

You could try other tricks, like trying to store the positions reached in a tree and checked that none of the reachable positions are mate. That's only 76176 positions for the example I gave, but you'd need to check that the tree is indeed exhaustive - i.e. every legal move in every position must be tried. That's not going to be efficient.

You could also try to invent some arbitrary heuristics to help your algorithm, like checking for blocked pawns and same coloured bishops. The problem with this approach is that sometimes the heuristics are wrong, or they aren't general enough. (Brian Tower's answer is an example of an attempted heuristic, but in the comments user17439 shows it fails to flag some dead positions and I show it incorrectly flags a non-dead position.)

And I would love to see any heuristic or algorithm that can distinguish between the following positions (problem by Andrew Buchanan, StrateGems 2002)

Dead:

Bb1k1b2/bKp1p1p1/1pP1P1P1/1P6/p5P1/P7/8/8 w - - 0 1

Alive:

Bb1k1b2/bKp1p1p1/1pP1P1P1/pP6/6P1/P7/8/8 w - - 0 1

The second position is alive since mate is possible after

1.Ka6 Ke8 2.Bb7 Kd8 3.Bc8 Ke8 4.Bd7+ Kd8 5.Be8 Kc8 6.Bf7 Kd8 7.Bg8 Ke8 8.Kb7 Kd8 9.g5 Ke8 10.Kc8 a4 11.Bf7#

In sum, I do not believe you can have an algorithm that is 100% accurate in distinguishing between dead and alive positions that runs in reasonable time. Brute force is the only 100% reliable method, but it is definitely not efficient. You can get a decent success rate for "practical" positions with heuristics, but it will not be 100% accurate, even for real game positions.


What are the main strategic concepts in the Grunfeld?

Very often Black will end up with a poor pawn structure in return for piece activity for example after the pawn moves d5 e6 dxe6 and fxe6 (not necessarily right after another).

As for other concepts, you need to accept that you need to study a lot of concrete lines. White has many options against your defence of choice such as:

The crazy sharp anti-Grünfeld 3.f3.
The positional 5.Bd2 line.
The crazy tactical lines with an early h4.
The system with Nf3 + an early Qb3.
etc. etc.

Tactics abound in this opening and trying to work it all out over the board against a prepared opponent is suicide.

As for endgames, you can get absolutely any kind of material distribution due to the tactical nature of the opening. In general Black will get a queen side pawn majority, but whether it'll be relevant is an entirely different matter. First of all there's the matter of surviving the middlegame, and then there's the question of how many concessions Black had to make in order to neutralise the white centre in order to get there. For a great example of this going completely wrong for Black, see this game.


No, Player A cannot do this. FIDE rules of chess article 9.1.1:

  A player wishing to offer a draw shall do so after having made a move on the
  chessboard and before stopping his clock and starting the opponent’s clock.
  An offer at any other time during play is still valid but Article 12.6 must be
  considered. No conditions can be attached to the offer. In both cases the offer
  cannot be withdrawn and remains valid until the opponent accepts it, rejects
  it orally, rejects it by touching a piece with the intention of moving or
  capturing it, or the game is concluded in some other way.

Key parts highlighted. Player A made the draw offer at one of these "other times", so it's still valid and cannot be withdrawn. Player B asking player A to make a move, and player A actually making a move, are not one of the four actions that can terminate the draw offer, so the offer remains valid.


Are there any Chess960 positions where Black has the advantage?

It happens that someone tried to evaluate all 960 positions with an engine. Several positions got a score of 0.00, but none of them offered any advantage for black.

Of course, those conclusions are only the evaluations of Stockfish at 40 plies depth. It is a strong hint, but no definite proof, that Black is fine  in the huge majority of 960-chess starting positions, but not better in any of them.

This result matches with the intuition that in a symmetric, non-developed position, with all pawns on the 2d and 7th rank, there is always something useful to do if you are on move: in other words, there cannot be mutual zugzwang.


Similar opening positions and structures

There are two paths you can choose and they both depend on the current pawn structure you play.

You see, I understand exactly what you face here, as I have the same problem. When you work or have other reasons not to devote yourself to studying chess, you need to learn the least amount of openings possible in order to focus on more important stuff such as tactics/endgames/middlegame.

Therefore you need openings that are immune to transpositional tricks, but on the same side you can reach their middlegame positions as Black anytime. At best, you will need two openings -> against 1.e4 and against everything else.

As I have said, there are two choices:

FIRST CHOICE :

CARO-SLAV PAWN STRUCTURE

You can use Caro-Kann defense against 1.e4 and Queen's Gambit against 1.d4. These two openings have a lot of similar middlegames and studying pawn structures for both sides will greatly help you. Compare the below diagrams to see what I mean:

[Title "Queen's Gambit"]
[fen "8/pp3ppp/2p1p3/3p4/2PP4/4P3/PP3PPP/8 w - - 0 1"]

And this one:

[Title "Caro-Kann"]
[fen "8/pp3ppp/2p1p3/3p4/3PP3/8/PPP2PPP/8 w - - 0 1"]

Now consider exchange variations that can crop up from those structures:

[Title "Queen's Gambit declined"]
[fen "8/pp3ppp/2p5/3p4/3P4/4P3/PP3PPP/8 w - - 0 1"]

And notice that this is the same position only with the colors reversed:

[Title "Caro-Kann"]
[fen "8/pp3ppp/4p3/3p4/3P4/8/PPP2PPP/8 w - - 0 1"]

This means that if you take time to learn Carlsbad pawn structure you could cut down the amount of work drastically.

Furthermore, both Caro-Kann and Queen's Gambit declined are immune to transpositional tricks so White is unable to "kick you out" of your opening choice:

[Title "Caro-Kann"]
[fen ""]

1.e4 c6 2.c4 d5!

This is a line from Caro-Kann and is considered unclear. On other moves Black simply transposes into well explored lines as well.

[Title "Queen's Gambit"]
[fen ""]

1.c4 c6 2.e4 d5!

And you are back into Caro-Kann. On other moves Black simply transposes into well known lines.

On 1.e4 you could also use French defense, but it will require more work on middlegame structures, as they differ from the ones in Queen's Gambit. Still, the total number of lines you need to learn is lesser than the ones in Caro-Kann :

[Title "French defense"]
[fen ""]

1.e4 e6 2.c4 d5!

This is a good line for Black, covered in any repertoire book for French defense. Also, if White tries to trick you to not play Queen's Gambit he will fail and you can transpose into French defense:

[Title "Queen's Gambit"]
[fen ""]

1.c4 e6! 2.e4 ( 2.d4 d5! ) 2...d5!

And in both cases you are "in your opening", thus refuting White's try for tricking you out.

SECOND CHOICE:

The second choice is Sicilian defense-Dragon variation or Modern defense for 1.e4 and King's Indian defense on 1.d4.

A lot of work is required here, but these openings give better winning chances for Black than Queen's Gambit and French / Caro-Kann defense. They are also immune to transpositional tricks.

The pawn structure is nearly identical for all of these openings:

[Title "KID, Sicilian Dragon and Modern"]
[fen "8/pp2pp1p/3p2p1/2p5/8/8/8/8 w - - 0 1"]

It all depends on what you want:

QGD + Caro-Kann/French give you positional play, yet KIA and Sicilian/modern tend to be much sharper.

I chose QGD and French, and never regretted it, because I always "stayed in the opening" and the ideas are clear and simple. Still, I must add that these are harder to play then KIA and Sicilian/Modern, and achieving victory with Black is nearly impossible against quality opposition.

In the end, I recommend you Andrew Soltis-Pawn Structure Chess to help you grasp the middlegame concepts. With proper repertoire books you should be OK.

Hopefully this helps you a bit, if you have further questions leave a comment and I will try to help you.

Best regards.


Reasonable engines to test against (Not StockFish)

Since your engine supports UCI, I would suggest checking out lichess.org. You can make a BOT account there and test against several other BOTs and people as well! Also, you can get your BOT rated in different time formats!!

I must warn you that most of the BOTs on lichess some version of StockFish or other strong engine but you can find ample other BOTs.

Among strong BOTs (apart from Stockfish ones), I would suggest checking out:

LeelaChess: A neural net based BOT.
ASMFish

There are many more BOTs on lichess, you can view them here on lichess BOT team.

You can also find many not so strong self-implemented engines that you might like testing against, for example this.


Has SALC-armageddon been seriously discussed?

I think it is clear that it has not been seriously discussed, and it is not likely to.

First, at the highest level, the elite have spent their entire lives getting that good, and draws are just a part of it. There can also be beauty in draws as far as I am concerned. Overall, I doubt that they want to learn to play a different game just because it uses some of the same rules.

Second, Kramnik recently proposed a variant with no castling at all, and the kids they were coaching even played an informal tournament. It has not been heard from since. If Kramnik, and his idea was mostly panned in the comments to the various articles I read, cannot get a variant to be widely accepted, it probably is not going to happen on some very unknown website by someone no one has ever heard of.

Lastly, chess, while not a big industry in the grand scheme of things, still is an industry; and the people with money, who back it, are generally adverse to change for risk of losing any money they may have invested.

At best, and it would take a long time to gain the necessary popularity, if one of the main servers like chess.com were to pick it up as a variant, and it were to gain HUGE popularity there, something might happen...I would not count on it though. I have been around for a long time, and variants are still looked upon with disdain by most.

People do not like change, in general, and they love chess. It is not a problem at the lower levels, so it is not likely to catch on en mass, and work its way up.


6...Ng4 doesn't look good at all.

Tactical flaw:

Black is behind in development, so White should aim for direct play with 7.Bg5 and then:

7...f6 8.Bc1 [8.Bh4] Be6 9.h3 Nh6 10.Bxh6 gh6 11.Nh4 [11.Be2] and Black has huge weaknesses on the light squares.
7...Be7 8.Bxe7 Qxe7 9.Nd5 [9.Qd2, 9.Bc4] Qd8 10.Bc4 with a nice bind is probably the lesser evil for Black.
7...Qb6 8.Qd2 [or 8.Bh4 Qxb2? 9.Nd5 and Black cannot block Nc7+] Qxb2 is too greedy: 9.Rb1 Qa3 10.Nd5 Qc5 11.h3, or 11.Be3 and 12.Nb6 winning material, or 11.Rb3 with a huge attack.

Strategic reason:

It the structure with a hole on d5, the fight for the white square is essential and probably more important than the bishop pair. White often plays Bg5xf6 in Boleslavsky, Najdorf and Svechnikov variations. Thus trading the knight for the Be3 is not a big achievement, especiallly at the cost of two tempi, even if White plays the simple 7.Qd2 Nxe3 8.Qxe3 Be6 9.0-0-0 or 9.Ng5.


Petrov Defense, 8...Bg4 easy equality for Black?

No, it is not "easy equality". It is "complex fight where Black has good chances for equality, with theoretical debate still going on".

Anyway, 3.d4 won't be the only try for an advantage in the Petrov. 3.Nxe5 is still the main field where White looks for advantage. He can deviate from this game Kasparov-Wolff in several ways, including 5.Qe2 (recently renewed by Carlsen and Kramnik), 5.Nc3 (the main try for an imbalanced position, see Karjakin-Caruana, 1-0, in this year's Candidate tournament), or later 8.c4 (a lot of heavy-weight fights involving Anand, Kramnik, Leko or Naiditsch in the 2000-decade).


Should Black avoid the Two Knights Defense because of the Fried Liver Attack?

In Two Knights defense black doesn't have to play 5...Nxd5?! The main line is 5...Na5, where black sacrifices a pawn, but gets active play for compensation. The game could continue like this:

[FEN ""]
1. e4 e5
2. Nf3 Nc6
3. Bc4 Nf6
4. Ng5 d5
5. exd5 Na5
6. Bb5+ c6
7. dxc6 bxc6
8. Be2 h6
9. Nf3 e4
10. Ne5 Bd6
11. d4 exd3
12. Nxd3

Besides 5...Na5, Black also has 5...Nd4 and 5...b5.

A very interesting continuation is the Traxler attack (4...Bc5!?):

[FEN "r1bqk2r/pppp1ppp/2n2n2/2b1p1N1/2B1P3/8/PPPP1PPP/RNBQK2R w KQkq - 6 5"]

Black does not defend the f7-square, and it first might look like a blunder, since 5.Nxf7 leads to a fork. However black has plenty of attacking resources after 5...Bxf2. Therefore, white usually plays 5.Bxf7, black is down a pawn, and loses castling ability, but has some compensation due to semi-opened file and piece activity.


Is chess.stackexchange.com a good site for someone learning how to play chess?

No, it's not, but it might still be very beneficial to you. (Chess) Stack Exchange is a question and answer site, so:

  You should only ask practical, answerable questions based on actual problems that you face.

(taken from here).

So don't expect any tutorials here, or the possibility to play an actual game against someone. However, browsing through the site you will find a lot of resources which might help you - this question for example. If you need a resource on a specific topic, and nobody has asked it before, please go ahead and ask for it.


Why is c4 bad when playing the London against a King's Indian?

It may be to the fact that you are making his bad Bishop into a Monster.
After 6...c5, 7. d5 Nh5!  and the dark square bishop is free to roam.

[FEN "rnbq1rk1/pp2ppbp/3p2p1/2pP3n/2P2B2/4PN2/PP1N1PPP/R2QKB1R w KQ - 1 8"]


Is calculation the most important aspect of playing chess?

Would the person who calculates better normally win?

If everything else is equal then the answer is obviously "Yes".
However, everything else is rarely equal. Fixating on calculation is very common in chess players. Here is another question about calculation which clearly demonstrates this fixation.  The fixation is so clear that the best answer easily pinpoints this in the first two paragraphs. BlindKungFooMaster then goes on to make the key point which is -

In my experience ratings first and foremost reflect positional
understanding. Calculation skills make a much smaller difference, at
least above a certain threshold.

This fixation with calculation is, when considered rationally, obviously wrong. The strongest chess is not pure computer chess, chess based on pure calculation, it is correspondence chess where a human being moderates pure calculation with their positional understanding.
This was certainly the case before AlphaZero. AlphaZero's recent success is down to an attempt to incorporate positional understanding into computer chess which has worked better than more simplistic ideas like adjusting scores according to ideas like doubled pawns, central knights versus dim knights on the rim, king safety in the middlegame, centralised king in the endgame, etc. It would be very interesting to see correspondence players being able to use AlphaZero-like computers in their competitions.


Can playing too much chess make you see everything as chess moves?

Quite possible- this would be a special case of the Tetris Effect, as would what you described with your experience with Breath of the Wild.
Anecdotally, someone I knew once played a lot of chess online and experienced similar effects. About 9 hours per day were spent on chess, roughly equally divided between play and study. This person experienced such effects as:
They sent a one-word message and became anxious that they blundered since it was "hanging"
Noticing two socks were on the floor and immediately thinking "good, they're connected"
They also dreamed about chess, which is almost universal among players that play a lot of chess.
I wouldn't expect this happening to you - 9 hours is a lot, and anecdotally, I've spent a lot of time on chess myself and have yet to see any such effects beyond just dreaming about it. They also mentioned that they had tetris effect tendencies.


What does the annotation symbol "TR" mean?

Descriptive Notation. It is an alternative notation for recording chess games.

From Wikipedia:

  Descriptive notation is a notation for recording chess games, and at
  one time was the most popular notation in English- and
  Spanish-speaking countries (Brace 1977:79–80) (Sunnucks 1970:325). It
  was used in Europe until it was superseded by algebraic notation,
  introduced by Philipp Stamma in 1737.

The abbreviation TR seems to refer to the spanish descriptive notation:

  The initials are taken from the equivalent Spanish words: dama for
  queen, rey for king, torre for tower (i.e. rook), caballo for horse
  (i.e. knight), alfil for bishop and peón for pawn. The files are named
  after the initials of the pieces on the back rank, with those on the
  queen's side being suffixed by the letter "D" and those on the king's
  side suffixed by the letter "R". From left to right along the back
  rank, this gives: TD, CD, AD, D, R, AR, CR, TR.


Frankenstein-Dracula variation and other variations with funny names

You can just browse through this list:

http://www.webcitation.org/query?url=http://www.geocities.com/siliconvalley/lab/7378/eco.htm

I suspect a lot of the names out there aren't official like the Reversed Rat (1. d3 e5) and Double Duck (1. f4 f5 2. d4 d5), while the Pterdoactyl variation appears to be recognized.

Some other funny or interesting names: Creepy Crawly Formation, Bayonet attack (recognized), Pork Chop, Nescafe Frappe attack in the Budapest Gambit, the Apocalypse attack in the Caro-Kann.


There is an online chess league, All Nations Chess League, pretty much the same as a regular chess league, but online. I used to play there 7 years ago, at the time they were playing league matches on playchess.com, probably the same today too. ANCL community was quite respected in playchess.com.

And about cheat: They are investigating games upon complaint, there are statistical techniques to reveal cheaters. But it rarely happens in ANCL. All the players there are real chess fans, they simply don't play for cheating. After all, who would like to spend tons of time playing chess to cheat? It's not like cheating in a blitz game, a cheater wouldn't devote that much time to chess.

I recommend you to play there.


You might want to post your best game here (cut and paste the pgn is sufficient). There are many different stages of 'beginner' in chess.

Anyways, what I suggest you do is to:

1) Keep playing every day. Experience is king.

2) Learn basic opening principles - you do not want to get caught out with your king in the centre, your pieces sitting on the first rank, or your rooks dusting off in the corners.

3) learn all the basic mating patterns - what good is being up two pieces if you cannot finish him off?

4) Do chess tactics daily, without fail - chess24 has a pretty good chess tactics trainer and it adjusts to your level. You will lose games because of tactics more than anything else. You will win all your games because of tactics. I've been playing since 1973, and to this day, I do tactics every day.

5) record and review all your games (if you are playing online you are all set - all servers record the game for you), and maybe once a week or as frequently as you see fit, review your losses and understand where you went wrong. Make some friends online on your chess server with people who are better than you and ask them to review some of the games with you. This is the most single valuable thing you can do to improve your game.

6) Ignore all opening advice and play what you like. If you fail in the opening, understand why and fix it (books, better players, online resources, chess engines, etc.) If you really want to develop your chess openings at such a nubile stage, then Chessable is a good place to start and it's free, but unnecessary.

7) acquire a basic chess strategy book - someone mentioned Ludek Pachman's book but that might be too advanced, I think. You may grow into it, however. Jeremy Silman's Imbalances book(s) are popular. There are many.

8) Lastly mentioned, but not lastly important, learn the basic endgames necessary.

Good Luck and Good Chess!


Pressing the clock using the same hand you use to move the pieces

The numbers refer to rules in the FIDE laws of chess.

  6.2. A player must press his clock with the same hand with which he made his move. It is forbidden for a player to keep his finger on the clock or to ‘hover’ over it.

The rule that you have to press the clock with the same hand that you use to move the pieces is there to prevent players from pressing the clock before they have completed the move: if one is in such a time trouble that this rule matters, he/she would very probably, perhaps unconsciously, press the clock before he has clearly released his hand from the piece if this rule was not enforced. Nobody wants to see their opponent's hand over the board when their clock is running and they need to make a move quickly.

Often, the player with the black pieces is allowed to decide which side of the board the clock is on. Technically, the arbiter may place the clock on the side of the board where he sees it better [rule 6.5]. Often the player with the black pieces may choose on which side of the board he sits on, amounting to the same. (But this is no longer a rule in the Fide laws; some tournaments may not allow even doing that, for example because of carefully adjusted digital boards; in these cases the clock is almost always on the queenside (black's right hand side and white's left hand side).


How do I seriously analyze my tournament games and become stronger doing so?

I think engines only help for tactical improvements, not strategical. I saw a lot of moments where engine suggestions was far from perfect, strategically.

Also, in endgames, you can't depend on engines even tactically.

I used to use Fritz GUI with strongest engine(for that day) for blunder checks and tactical misses, in Fritz GUI you can do it easily with one click, give the game, leave the computer for 30 mins and when you return you get an tactically annotated game. With this, you can improve your tactics ability.

But remember, use engine suggestions only for finding answers for tactics, if you can't understand why the answer is correct, then you can't benefit of using engine.

For strategy, best way is to find someone who is at least 300 elo higher than you, and analyze games together. Also read every strategy classic, if you didn't read yet.

And for endgames, you need to be a real geek in reading endgame books. Best way is to read quality endgame books, and try to solve endgame studies.

Studying endgame is really beneficial for elo improvement, because people under 2000 elo don't care much about endgame. If you get a good endgame knowledge, then you can go for exchanges happily and solve your problems in endgame. Also, it's said that a good endgame knowledge requires an excellent grasp of pieces and their abilities, which also naturally boost your tactical ability.

My favorite endgame book: http://www.amazon.com/Secrets-Pawn-Endings-Karsten-Muller/dp/1904600883 which is an excellent and complete source for pawns.

Lastly, about openings, don't memorize, but understand. Don't memorize and use popular strong lines just because they are popular and strong, if you don't understand the harmony in the moves, then the opening won't be strong in your hands.

When you use an opening which you understand the strategy within, deeply, you almost always arrive a better middlegame/endgame comparing your opponent, which makes you win the game.

I won a lot of matches against strong players with openings which are quite unpopular, but I understand very well. And I saw these strong players fail to find correct continuations :)

To give an example, I used to play Dutch Defense with blacks successfully, later I wanted to play it with whites, which found silly by others from time to time. But because I knew Dutch very well, it went good with whites too, and I got quite good results.

A bit long but, these are my advices. Hope it helps.


Because of the distortion of the computer era, is it preferable to study mainly old opening lines?

I never played Sicilian Defense as Black for this reason.

A quote from Larsen:

  Had I not played the Sicilian with Black I could have saved myself the trouble of studying for more than 20 years all the more popular lines of this opening, which comprise probably more than 25 percent of all published opening theory!

Constantly following updates and remembering a modern, popular line has no benefit for a non-professional player (if you are professional, that's different). Instead, a chess player who wants to improve himself/herself should focus on understanding openings (not remembering them).

What improves your chess is to understand an opening, ideas behind, advantages, disadvantages etc. Remembering openings are like remembering opening traps, they can help you win the game without much effort, but they don't improve your chess.

A quote from Fischer, about memorizing opening theory:

  I don't know when, but I think we are approaching that [the end of chess] very rapidly. I think we need a change in the rules of chess. For example, I think it would be a good idea to shuffle the first row of the pieces by computer ... and this way you will get rid of all the theory. One reason that computers are strong in chess is that they have access to enormous theory [...] I think if you can turn off the computer's book, which I've done when I've played the computer, they are still rather weak, at least at the opening part of the game, so I think this would be a good improvement, and also just for humans. It is much better, I think, because chess is becoming more and more simply memorization, because the power of memorization is so tremendous in chess now. Theory is so advanced, it used to be theory to maybe 10 or 15 moves, 18 moves; now, theory is going to 30 moves, 40 moves. I think I saw one game in Informator, the Yugoslav chess publication, where they give an N [theoretical novelty] to a new move, and I recall this new move was around move 50. [...] I think it is true, we are coming to the end of the history of chess with the present rules, but I don't say we have to do away with the present rules. I mean, people can still play, but I think it's time for those who want to start playing on new rules that I think are better.

He propose random starting position chess which is widely know as Chess960, because chess is becoming more and more a memory game.

My experience tells me, if I play an opening, which is playable but not the best, and out of the book I get better results comparing to a popular line. Because I know the ideas behind, while my opponents often only memorize the best continuations. This is similar to what Aronian did in his game.

So, what sources are there? Actually, every good opening book covers the ideas behind, you don't need special sources. Just focus on the ideas next time when you read them, instead of variations.

Edit

I remembered that this FritzTrainer with topic of creativity in e4 was really good: https://shop.chessbase.com/en/products/e4_for_the_creative


Is the Grand Prix Attack a poor response to the Sicilian?

I don't have any statistics to back this up, but many openings where black has a large plus against white it isn't necessarily because the opening is actually so bad that it gives black a significant advantage, but because the opening is more popular at a lower level (which is normally because it actually is worse than other openings) so the players who play it are on average lower rated than their opponents and would most likely score less than 50% anyway.

Normally the openings with low percentages for white are slightly worse than other openings for white, but not necessarily so bad as to give black the advantage, but then the fact that they're worse than others kicks in and the higher level players play them less often, leading to that opening to score a lot of losses for white, even in a game which is even or with a slight edge for white after the opening.


It's game over for Black. Down by material, mating attack, zero counterplay etc. The Black's rook is under attacked.

  1...Rd6 2.e5 Qxe5 3.Qg4+ Qf5 4.Qxh5 winning easily

1-0 unless White makes a horrible mistake.


Dumb question, but what are some good chess resources to learn from?

I'm an older player (84), but in my youth I read several chess manuals which explained all the basics and gave hints for improvement, such as books by I.A.Horowitz, Fred Reinfeld and Reuben Fine.  These are still available on eBay at reasonable prices.  And there are certainly more modern books that cover the same area, by Bruce Pandolfini, Jeremy Sillman, and Yasse Seirawan for example. But now in the era of the computer and the Internet, there is a readily available source of this information at your fingertips.  Just Google tips for chess improvement.  GM Arthur Bisguier for instance has written "Ten Tips for Winning Chess" which you can find there. And I'm sure there are countless others.  Then there's "YouTube" which has many free chess tutorials and also game analyses, such as by Agadmator and Mato.  I watch them there myself. Those are all good starting places. And of course you have to supplement what you learn by applying it in actual play.  Good luck on your chess journey!


Why was move 26 in Carlsen-Anand 2014 WC Game 6 a blunder by both players?

Carlsen's 26.Kd2 is a a blunder because it exposes the White King to a tactic that wins two pawns and gives Black terrific pressure. The tactic is effectively a guarantee of victory for Black:

[FEN "6rr/1k3p2/1pb1p1np/p1p1P2R/2P3R1/2P1B3/P1BK1PP1/8 b - - 0 1"]

1...Nxe5! 2.Rxg8 (2.Rxe5? Rxg4) Nxc4+! {The Knight gets out of danger, with check and an extra pawn--you couldn't ask for anything better!} 3.Kd3 (3.Ke2 Rxg8) Nb2+ 4.Ke2 Rxg8 {Black is now two full pawns ahead, with lots of pressure on the weak g2 pawn and vastly better pawns for the endgame. }

The point is that 2...Nxc4+ wins Black a second free pawn, by virtue of the check against the White King. Without the ability to get the Knight out of danger with check, ...Nxe5 is not possible (because White could then simply trade Rooks and then recapture the Knight with a winning position).

Anand's mistake on his twenty-sixth move was that he missed this tactic, playing 26...a4 very quickly and allowing Carlsen to correct his mistake by moving his King away from d2.


What is the difference between a human player of approximately 1600
  ELO rating and a competent chess engine like Stockfish 7 set to ELO
  1600 ?

The main difference is in the way each chooses their moves.

The human player will predominantly use pattern recognition combined with some form of plan recall. So, I recognize that this position is winning for white and this is the winning plan. This might involve specific moves for a tactical plan and more general aims for a strategic one.

The computer will predominantly use brute force calculation with an element of pattern recognition for position evaluation

  Is it possible to determine the ratings of players with the pgns of their games?

In theory, yes. Both FIDE and certain online chess providers have looked at tools for detecting cheating which essentially do this although without producing a rating. They look at moves which are not opening book / standard theory moves and calculate the percentage of moves which are engine 1st, 2nd, 3rd choices etc. In principle this work could be extended to develop a way of rating pgns but it would be a lot of hard work.

  I'd play with the computer and wanted to know what is my ELO. Is it
  possible through Fritz or any software?

No. Too much work to develop such a system for too little reward.

  Is there any site that explains what is ELO in lucid terms?

Since you appear to know what ELO is (an internationally recognized rating system) presumably what you are really asking is whether there exist  explanations for the mathematics and statistics behind ELO.

The killer part of your question is "in lucid terms". Of course such explanations exist which are lucid for mathematical and statistical experts but just as clearly if you lack the expertise they will not be lucid for you.


Theoretically, shouldn't analysis of any chess move have exactly nine possibilities?

You are somewhat correct. In theory, each position can be correctly categorized in one of three ways -- win for the side to move, loss for the side to move, draw, all presuming "best play" by both sides from that position. That last caveat is required to make the ideas of "will win", "will lose", and "will draw" well-defined. But that caveat also means that the side to move can never improve on the position categorization, because that categorization already presumes (prices-in) that the side to move will make its best move. So the only possibilities for move categorizations are: (W,W), (W,D), (W,L), (D,D), (D,L), (L,L). I.e. six instead of nine. The side to move can only hold or worsen (blunder) its theoretical value, in other words.

As for severity of error, presumably (W,L) is worse than (W,D), but other than that, blunder is blunder, yes ((W,D), (D,L)). And any move that maintains value is a theoretical non-blunder, yes ((W,W), (D,D), (L,L)).

As to engine scores, they are in most cases theoretically "meaningless" I suppose, as above, but not objectively so. They could be considered to be trying to estimate the probability that the theoretical value is closer to W, D, or L, on some scale, given the data they have been able to glean so far in their forward position search. And sometimes they do produce theoretical values (forced-mate detections). But I've also got to think that the error-bars on non-theoretical engine values are also pretty large, meaning that we're talking about estimates of estimates of probabilities, which is pretty, well, non-definitive...

Also, see Saibot's answer regarding so-called Tablebases. Chess has been solved theoretically for all positions with 7 or fewer pieces on the board (two kings plus up to any five pieces). Here is an online resource for most of the 6-piece tablebases: http://www.k4it.de/?topic=egtb&lang=en

Another wrinkle on theoretical categorizations is "distance to mate" for W and L positions. Presumably a win in fewer moves is theoretically "better", so a (W,W) move that doesn't reduce "distance to mate" could be considered a "blunder" as well, as could a (L,L) move that shortens "distance to mate".


What was the biggest blunder made by Boris Spassky in Game 6?

I am tempted to say "agreeing to continue the match after Fischer's protests!" which some argue was a key psychological defeat.  If you're looking for specific moves that were mistakes, there are a few candidates.  I haven't looked at all annotations, but have Kasparov's My Great Predecessors, vol 4 handy and looking over his notes, it would be either (notations and comments are his):

...d4?
"This move, conceding the important c4-square, was rightly condemned by the commentators.  20. ...Nf6 really was better...but the most accurate solution was the continuation 20. ...c4"

and

...Rb8?!
"The last critical moment."


John : I need a new car.

  Joe : Ok, let's buy one!

  Mark : Wait. Why do you need a new car?

  John : Because the battery in my car is really bad and my car doesn't
  start quickly.

  Mark : Have you tried installing a new battery?

  John : Gosh! Why didn't I think of that?

It seems to me you are saying something similar to "I need a new car" when you say "I need to get rid of Black's light-square Bishop".

That bishop is NOT necessarily your problem and if you think it is, then you still have a lot to learn.

First of all, if you play d4 and the system you described (Bf4, e3, c3), you cannot always prevent the bishop from coming to the b1-h7 diagonal. If you forcefully try to always achieve this, you will definitely compromise your own position.

It seems to me that the reason you find this bishop "irritating" is because you are limiting your plans to checkmating Black on h7. The bishop on the b1-h7 diagonal does foil these ideas. But maybe that should teach you that the "checkmate on h7" plan will not always work. So you should ask yourself, "What else can I do instead of checkmating on h7?" instead of asking how you can get rid of black's light squared bishop.


Of course there are others!

For chess, there are many chess problems including retrograde analysis problems and many, many, many other types of problems that you would likely find interesting:

Retrograde Analysis - Problems that show a diagram and ask a question in which you must deduce the answer from the position.
Proof Games - Figure out how to get to the diagram from the starting position in a limited number of moves.
Help mates - Figure out how to checkmate black in a certain number of moves (you get to play both sides).
Reflex mates - figure out how to mate yourself given that each side must reply with mate in one if given the opportunity.
Series mates - Black makes a series of consecutive moves and then white mates in 1 move.
Studies - Usually orthodox chess endgame problems that demonstrate an interesting or important or impressive way to win.

There are journals or magazines that publish chess compositions and give out awards to the best problems. The best problems have an artistic quality which demonstrate a certain concept, have interesting interactions among pieces, or achieve some specific goal.

Every problem usually has a stipulation (what it is you are trying to accomplish) and conditions. A stipulation is what it is that you are must accomplish and the conditions are the set of rules that must be followed, which can be different than orthodox chess. Some problems use one more fairy pieces which are one of many non-standard pieces that move in a variety of different ways.

Basically, there are many chess problems (compositions) and composers (people who create them). A friend of mine introduced me to the world of chess problems and I've composed only a few myself. Here are just a few of the places you might find some more problems including retros:

The Problemist
Strategems (Proof Game and Retros Link)
FIDE Albums (FIDE actually gives out titles similar to GM/IM/FM for chess composers)

edit:

Since you already know what a retro is, here is an example of a famous helpmate.

[FEN "8/8/q7/8/1R4K1/k2N4/8/8 w - - 0 1"]
[White "Henry Forsberg"]
[Black "1935"]

Helpmate in two (black moves first and after two moves from each side, black is mated):

diagram
replace queen on a6 with a black rook
with a bishop
with a knight
with a pawn


In a tournament game, what should a player do if he find that his opponent's position is impossible, which was caused by an earlier illegal move?

Section 7.5.1 of the FIDE Laws of Chess has the answer:

  7.5.1 An illegal move is completed once the player has pressed his clock. If during a game it is found that an illegal move has been completed, the position immediately before the irregularity shall be reinstated. If the position immediately before the irregularity cannot be determined, the game shall continue from the last identifiable position prior to the irregularity. Articles 4.3 and 4.7 apply to the move replacing the illegal move. The game shall then continue from this reinstated position.

The player found guilty is not penalised for the illegal move, provided their opponent has intended to play a move:

  4.7.1 A player forfeits his right to claim against his opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it.


Is there a standard way of scoring a position for chess programs?

This is certainly not the case. Traditional engines "score" a position by running their evaluation function (which differs from engine to engine) on the best position at the end of their search tree (which also differs from engine to engine, since this position depends on their search algorithm).
Sure there are standard concepts for scoring a position - e.g. which side has more material, which side has doubled pawns, which side has rooks on open files - but ultimately each engine does it differently, and there are positions which one engine can be very optimistic on while another is not. There are even positions where one engine thinks White has an advantage and another engine thinks Black has an advantage. Example from the ongoing TCEC Season 18 superfinal.


Marshall Defense 1.d4 d5 2.c4 Nf6 — transpositions

If you don't take on d5, I think the only advantage black has gained is flexibility. That means he can choose his opening according to your move. But you can be almost 100% sure that the opening will be transposed into some traditional line so white can't be worse, for example:

Slav Defence:

[FEN ""]
1. d4 d5 2. c4 Nf6?! 3. Nc3 (3. Nf3 c6) c6 {with the possibility of both Semi-Slav and Classical Slav Defence}

Queen's Gambit:

[FEN ""]
1. d4 d5 2. c4 Nf6?! 3. Nc3 (3. Nf3 e6 (3... dxc4 {Queen's Gambit Accepted})) e6 (3... dxc4 {Queen's Gambit Accepted})

Grünfeld Defence:

[FEN ""]
1. d4 d5 2. c4 Nf6?! 3. Nc3 g6

and there are probably many other transpositions...

In my opinion you have no reason not to play 3. cxd5. The position after 3... Nxd5 4. e4 (I think this is logical and even better than 4. Nf3) is very comfortable for white. You have a great center and black has to lose time again...


I like to play 1. e4 but I dislike 1. ... c5. Can I continue with 2. c4?

You can, but if you like most openings with 1.e4, it's probably not the most adequate choice for your "style" (the resulting position will be "slow" rather than a fast exchange of tactical blows. 2.c4 is a legitimate option, but here are a few alternatives you may want to consider:

Find some line in the Open Sicilian: this is the ideal, but requires a lot of work to be put in tournament practice. I'd definitely go for it when playing "just for fun". There are a lot of crazy middlegames resulting from this option and you'll also  "learn a lot of chess" from them.
Play the Alapin with 2.c3. Still a solid, more positional option Probably more ambitious than 2.c4.
Play the wild Morra gambit! (2.d4 cxd4 3.c3) This would be my favourite way to go if not for the fact that that Black can transpose to the Alapin if they want to.
Play some f4-based scheme, like the Grand Prix (more aggressive) or the Closed Sicilian (more solid)

As a final consideration, there is nothing wrong with 2.c4. Don't blindly believe the Statistics. It could be that there is a player skill bias against 2.c4, or perhaps that players who opt for this line haven't often studied it deeply. Filtering for games at different ratings could dramatically impact the result. In my opinion, the main problem with 2.c4 is that Black can choose between a closed, symmetrical position with an eventual ...e5, or simply try to exploit the d4 square with ...g6, ...Bg7, ...Nc6-d4 and so on....


Why is Nb5 a strong move here? Why is there a guaranteed material gain?

This is a familiar tactic I often get to use myself in another opening line. If black plays 1... Rf8, then comes 2. Bc7! Qe8 3. Nd6 Bxd6 4. Bxd6 and black loses the exchange anyway.

[Title "White to move"]
[FEN "r1bqr1k1/pp1nbpp1/4pn1p/2pp4/2PP1B2/P1NBPN2/1P3PPP/R2Q1RK1 w - - 0 1"]

1. Nb5 Rf8 2. Bc7! Qe8 3. Nd6 Bxd6 4. Bxd6

Chess is about patterns. Since I was familiar with the pattern, I spotted this tactic immediately.


Which chess site has the most rapid players?

The vast majority of online chess games played on any site are played with very short time controls. Because of this fact, if you want to play longer games, you will have to wait longer, on average, than you would for a game shorter time control.

If you are looking for quality chess games and you want relatively long time controls and decently high-rated players then you can try limiting your searches to high rated players.

You can select custom rating ranges on lichess and on ICC. This will allow you to, for example, filter out lower-rated opponents if you want a strong opponent.

Another possibility is to play in the long-time-control tournaments that most popular chess sites have on a regular basis. Both ICC and lichess have regular tournaments with relatively long time control. The advantage of this is that once the tournament starts, usually the wait time between games is not that long.


What's the point of early a2-a4 in the Modern Italian?

White obviously doesn't want to give light square bishop for knight. He can waste two moves with Bb3-c2, which is the old main line. Or he can just create escape on a2, after which Na5 doesn't make much sense. It gains space while it doesn't have to be so bad to exchange the bishop after Be6, if it didn't make additional moves.


I remember reading somewhere in an opening book that the c5 line against the Saemisch is the primary reason why the Saemisch has stopped being popular among the elite. Moreover, it is recommended for black in two repertoire books on the King's Indian Defense: one by Bologan and one by Dejan Bojkov.


How to deal with an opposing pawn storm?

It's a mistake to view the pawns themselves as overextended targets that you might get to "pick off" as you say in your post. After all, Black's main objective with the pawn storm is probably to open up lines to attack your king, and so your snapping up such overextended pawns really only furthers Black's goal.

As already pointed out in comments in this thread, the strong engine Stockfish recommends the move 1.f4 in your diagram position. And when I opened your post and looked at the position, that was my almost immediate reaction as well. Why? Not because I'm even remotely as strong as Stockfish, of course; rather, I was just reflexively applying a classic positional maxim:

  An attack on the wing is best countered by play in the center.

That advice really goes double in this position, where the opponent's king is still in the center, and would need a few moves to get out of there. (Moreover, since Black has overextended on both wings, her king ultimately doesn't have anywhere all that safe to go.) In particular, 1.f4 carries a direct threat of capturing on e5, and if the knight on f6 gets forced to move, White is ready to capture on f7 with dire consequences for Black in the form of a vulnerable king open to attack in the middle of the board. Black's best response is probably nipping any ideas of fxe5 in the bud with the en passant capture 1...gxf3.

You might object that we've given Black what I claim she wanted out of her pawn storm, providing a half-open g-file to attack our king, but the point is that we can show Black's pawn storm to be premature by continuing to follow the above maxim. After e.g. 2.Nxf3 Bd6, we just continue to pry at the center with 3.c3! Note that Black is nowhere near getting an attack off the ground, but we've again given her something concrete that she needs to deal with immediately: 4.cxd4 is a serious threat because of an e5 pawn fork in the air.

Bottom line: Black's pawn storm is an overextension, but not because those pawns are now ripe for the taking. The real flaw in Black's play is that she's been pushing pawns for an attack that she's not yet ready for. That's why the proper response is to fight back in the center, demonstrating that she should have been spending her time developing some pieces first and taking care of her own king's safety. Here are just a few short variations, some featuring very poor Black moves just to illustrate the threats; but even in the lines where Black plays more sensibly, note that in the final positions, White is fully developed and ready to play in the center (and against Black's king), while Black is in no position to harass White at all.

[fen "r1bqkb1r/2p2p2/2n2n1p/1p2p3/p2pP1p1/P2P2B1/BPPNNPPP/R2Q1RK1 w - - 0 1"]

1.f4 gxf3
( 1...Bb7?? 2.fxe5 Nh7 3.Bxf7+ )
( 1...exf4 2.Nxf4 )
( 1...Bd6 2.fxe5 Bxe5 3.Qe1 )
2.Nxf3 Bd6 3.c3! dxc3
( 3...Bg4? 4.cxd4 Nxd4 5.Nexd4 exd4 6.e5 )
4.Nxc3 *


[FEN "8/8/8/8/8/8/2R5/k3K2R w K - 0 1"]

From this position, Kd2 Ke2 Kf2 and O-O deliver checkmate


Why can't a piece (that isn't a pawn) capture en passant?

I believe the en passant rule is designed to cope with the fact that pawns do not move backwards, hence if the en passant rule did not exists you could have a lot of blocked positions, making play slower and probably more drawish.

Differently from pawns, pieces can move backwards, so the black Knight in your example still has the possibility to move backward and stop/capture the white a pawn. Therefore no need of allowing the en passant rule for pieces.

Said that, there is in a special case a sort of en passant like rule for pieces: castling is not allowed if an opponent's piece controls one of the squares that the King would go through while castling. You can see that as a sort of threat of hitting the King "en passant" during the castling move.

At a large extent chess rules are what they are because they resisted the test of time and made an interesting game. Same goes for pawn moves. The 2-step move from the pawn initial position did not exist either from the beginning, it was introduced later to make play faster and more dynamic; the en passant rule was likely introduced shortly afterwards to avoid large pawns blockades.


Which elements of chess are best to focus on for extended "crash course" learning?

Depends a bit on your level.

Assuming you are rather a beginner player, the best way to improve is by studying tactics/solving tactics puzzles. You can do this on many websites, which is quicker than doing it from a book and also most websites will present you puzzles suited to your level.

For a beginner I find chesstempo.com quite useful because after you solve a puzzle (or after you fail to solve), it will tell you the name of the tactical motif. Take note of these motifs, understand them and try to look for them when solving puzzles. Once you have stored a number of motifs in your brain, solving tactics puzzles will be much easier since you will not have to calculate move by move, but can think in patterns. Also chesstempo have a list of tactical motifs which you might want to consult.

As a second major topic you should learn general principals of play (e.g. develop pieces to active squares, occupy the center, king safety...) and perhaps a bit later positional motifs.

Opening theory is not very relevant for beginners, because in general it can only gives a small positional edge and most beginner games are decided by blundering a piece somewhere. Also for making use of openings you need to play opponents who also play theory, which is usually not the case with beginners. So don't waste your time with openings at this point in time.

And of course you should keep on playing games. Personally I'd rather play humans (online or over the board) than computers, but whatever suits you. Play games with longer time controls (10 min or more) in order to reduce the chance for blunders and to give you the opportunity to think about the position. For me lichess works best and has lots of features, but there are other options for playing online.

How to split time between studying and playing is up to you. After all you want to enjoy playing chess.


What are the average Elo and USCF ratings?

I took the following data from the September 2013 Golden Database1 and "active" players are players with a USCF membership expiration date later than January 1, 20132.  All ratings are regular ratings.  Note that players have an established rating after completing 25 games.

USCF Active Players

Established Ratings

46,574 Players
1315.99 Mean Rating
1390 Median Rating

Provisional Ratings

33,692 Players
537.09 Mean Rating
410 Median Rating

All USCF Rated Players

Established Ratings

252,989 Players
1165.77 Mean Rating
1148 Median Rating

Provisional Ratings

303,153 Players
631.46 Mean Rating
576 Median Rating

Distribution of active, established USCF ratings

Note that unrated players were discarded and that no checks were done on the data (duplicate entries, placeholders, etc.).

Distribution of ratings by age

This image comes from the uschess forums.

1: The Golden Database is a database provided to USCF affiliates and TD's that includes the names, ratings, and expiration dates.  It can be downloaded from the USCF website
2: I picked January 1, 2013 as an arbitrary cutoff date.  If there's a better and easy check for whether or not a player is active I'm happy to add additional data or update these stats.


How to improve positional chess understanding?

My suggestion ist to take a book on positional chess and look through it.  For example "How to Reassess Your Chess" by IM Silman is, in my opinion, a good book to get started.  It walks you through all of the positional elements and gives you at least a good idea on what you might want to look out for.  Of course this can only be a start and at some point you may have to look beyond for some ideas on pawn structures, for which also several good works are available.

One word of warning is that, often, while you may feel that the weakest part of your game is positional chess, this might not be correct.  You can be sure only if a show a couple of your games (especially losses or games where you ended up in an uncomfortable position) to a (quite a bit) stronger player and ask their opinion.

In any case, I would like to recommend also the book series by Yusupov, in particular for your level the Fundamentals series (orange color).  These books contain positional chapters, but also endgame, tactics, openings and much more.  The goal is to raise the level of all your abilities to the same level.  If you can breeze through the tactical parts, this is good for you, then you will mostly gain from the positional chapters. However, it is likely that you will find further parts where you can learn a lot.


King safety is a big issue for white in your position.  White would be much better if the f3 pawn were at g2 instead.

I would probably play kg2 and if the black queen checks along the g-file try to hide the king on e2 via f1.

As for general principles, I would say king safety is the first priority.  Then probably obtaining advanced supported passed pawns and active pieces are next most important quality.  Material balance is always important, but the key to winning these endgames usually comes down to queening a pawn and the more advanced one is the more dangerous one.


Defeating 1600 rated chess computer on chess.com

I want to understand, how is that possible - was it a computer that
  was wrongly rated at 1600+? or did I just outperform it really?

Neither.

You don't understand rating systems. There is no absolute rating system in which to say the computer was or wasn't playing at 1600 strength. All rating systems are relative. They measure the relative performance of the players results in that system. There is no judgement of the quality of the moves.

If the computer rating system is accurate then if you set the computer program to play against the same computer program (with you feeding in the alternate moves) on another computer and one is set to play like 1600 and the other like 1700 then over a large number of games the 1700 computer should score a certain percentage against the 1600 computer.


Substitution would be another. With a trade/capture, you can set up another tactical motive like a skewer or a fork.

In the position below (taken from the ChessTactics link above), Black wins an exchange with the following combination:

[Title "Black to move"]
[StartFlipped "1"]
[FEN "2r2rk1/p1p1qp1p/1p2n1pb/8/n7/1PB1PBN1/P2Q1PPP/R4RK1 b - - 0 33"]

1... Nxc3 2. Qxc3 Bg7


To me the easy human way it is to start from the square that you want to go to (backtracking approach), lets call it 'A' and exclude from the path calculation the direct linked paths from 'A' that you can't go to because they are attack or there is a piece on it.

For example, you want to go to the square c4, so the directed linked paths will be from by a5, a3, b2, d2, e3, e5, d6 and b6, but if only the square a5 and b6 are available you can reduce your calculation to only to 2 paths now. Furthermore, if you use this "technique" you can check if the target square is reachable at all (if have at least 1 directed linked path not being occupied or attacked).

After doing that, you go to the position where you knight stands and you check which are the squares that you can go to. Using this two phase approach you reduce you tree of calculation immensely.

You should also know beforehand how many moves you need to go from one square to another with your knight, in order to avoid the calculation of larger paths than the ones really need it. I din't check online to find any heuristic for this but I can give you some inside tips about it:

The Knight on a black square can only go to a white square and vise-versa, in the next move;
Every square on the diagonal of the actual square of the Knight can be reach in only two moves. Square (x,y) to the squares
(x-1,y+1), (x+1,y+1), (x+1,y-1) and (x-1,y-1) takes 2
moves;
The squares up, above, right and left of the actual square takes 3 moves;
Every square on the diagonal of the actual square with a one square between them (e.g actual  square = c4, target square a6),
takes 4 moves.
Every square on the diagonal of the actual square with a 2 squares between them (e.g actual  square = c4, target square f7), takes only
2 moves.

Finally, if you are in a given color square you will take a odd number of moves to reach the opposite color square. If the target square have the same color as the square that you are in now it will take a even number of moves.


Analyzing your own games is the best and fastest way to improve in my opinion.

As soon as possible after the game, write down the variations that you were thinking about during the game, especially the ones that were not played.  This will be useful when you come back to the game after days, months, or even years.  As you improve, it will be helpful to see what you were thinking during the game.  That way, you can pinpoint how you can improve your thought process in future games.

When you start analyzing, use a chess board, but don't use an engine at first.  Look for moves where you made a mistake or missed something important.  If you lost material, go back and find the moment where you blundered.  If you got into a bad position, try to identify the moves that led to that position and evaluate some alternatives.  Put everything you come up with into your chess program/database (you are using some kind of a database, right?).

After you've gone over the game "by hand" (this should take at least half an hour for a slow game, even more time if it was a complicated position), now it's time to use a chess engine.  Go through all of the moves and take note of where the engine says that you either made a poor move or missed an opportunity for a better move.  Again, add variations to your database.  If it's not clear why something that the engine suggests is good, investigate it further.  Try out some lines and see what the engine says.

At this point, you have an awful lot of moves in front of you.  Now it's time to try to take away some lessons from the game.  Go back through the game again and decide what specific thing you could have done better.  Did you make a very poor positional move?  Did you blunder material?  Did you neglect development?  Did you put a piece on a bad square?  Asking questions like this will help you in future games during the game.

The last thing that you can do is to ask a stronger player for help.  Bring all of the information you have to the stronger player and then go through the game once more.  The stronger player can give you suggestions for how to think in certain positions.  Basically, a chess engine can tell you what the right move is, but a stronger player is often needed to tell you why a move is correct.

You should try to develop your own analysis style as well.  If you are a strong tactical player, try to go through the game without making moves on the board, just analyze in your head.  If you are good at endgames, switch colors and analyze where your opponent went astray in the endgame.  Hopefully analyzing games is fun and not a chore!

Additional thoughts

I didn't mention studying the opening moves because that is less important than finding the specific points in the game where you made a mistake.  After you have looked at the game as a whole, studying the opening can often help you as well.  The best way to do this is to look for grandmaster games in the same opening that was played.  Find out what moves are commonly played, and then go through some games of stronger players in order to find good, general plans for the opening.  Try to see where you varied from these plans and determine why you didn't do what the stronger player did.  This is much more important than memorizing moves (although you will probably find that you've memorized many variations just as a matter of course!).


What are good resources to use to learn how to best use pawns and pawn structures?

A lot of chess is “what pawn break am I looking for, and how do I accomplish it?” These answer that in depth.

“Complete Chess Strategy” volumes 1,2 and 3 by Ludek Pachman. (This teaches about many basic plans, and what you are striving for with your pieces and pawns, especially. This made a light go off in my head, and THIS is what made me a master.)
“Pawn Structure Chess” by Andy Soltis. (This extends the above to specific opening structures.)
“Chess Structures: A Grandmaster Guide” by Mauricio Flores Rios (This is an extension of “Pawn Structure Chess”, and is deeper, and covers more structures. It is outstanding especially if you have already covered “Complete Chess Strategy”.)

I have not read this yet, but another book that seems to be right up that alley by a renowned player is "Winning Chess Middlegames: An Essential Guide to Pawn Structures" by GM Ivan Sokolov (2706 peak rating and #16 in the world in 2004).

Of course, the original book in this genre was "Pawn Power" by Hans Kmoch, but he used a lot of funky terms.


Was I right to capture the pawn in this position?

N.B. This answer is without the aid of a computer. Here I compare 1...Rh4 to 1...dxc3

1...Rh4

The material difference in the given position is exchange + pawn vs. minor piece. This is a difference of 3 pawns. After 1...Rh4, white can win a pawn with 2. Bxa5. On paper this is now a difference of 2 pawns, but computers tend to overvalue pawn structures, so is probably penalizing black for the doubled, isolated c-pawns.

1...dxc3

I think that Black is better after this sequence, because:

Black will soon be up 2 pawns
Black has better placed pieces
Black has the long term strategy of making the light square bishop a spectator by placing most of the pawns on dark squares

[FEN "r2q2k1/2p2ppp/2p2n2/p7/P2pr3/1BB2P2/1PPQ2PP/5RK1 b - - 0 1"]

1... dxc3 2. Qxd8+ Rxd8 3. fxe4 cxb2 4. e5 Nd5 5. Rb1 Nc3 6. Rxb2 Re8


Why is Carlsen criticized for poor preparation at World Chess Championship 2018?

Carlsen is being criticized for his preparation with white, particularly e4. He knows that Caruana is going to play the Petrof yet nevertheless Caruana equalizes effortlessly. Carlsen appears to have no new ideas in this opening. Since there is no more important competition he could be saving novelties for it tells us he has no novelties. No novelties = poor preparation. If he doesn't have an answer to this he shouldn't play 1. e4

Note that we have seen novelties from Caruana, not necessarily good ones. As black in one game he played Rd8 in a Queen's Gambit looking to provoke the reply Nd2 from Carlsen. That looked like it would be a strong response from Carlsen but he chickened out and played a much more drawish move suggesting that he believed Caruana had some big improvement planned.


How to calculate percentage of accuracy of game-play based on the number of mistakes, blunders and inaccuracies?

The gameplay accuracy is a scale from 0 to 100 and it is calculated based on the accuracy of each of your moves. Chess.com collects a lot of data from played games that they use to evaluate which moves are more important for the final accuracy.
The final accuracy is a weighted average and that explains when you play a game with two book moves and a blunder why you can get an accuracy of 0.7 and not 66.7.
The average of a single move is determined by how close the evaluation deviates from the top engine suggestion and how far is the evaluation rank placed. If the move played was the 2nd best but was -3 instead of best -1, then that is more accurate than if the same move had 9th rank.
Chess.com has released these two articles that give some insight on the analysis:
How is it measured?
How to use game analysis?
Note:
Chess.com isn't open source and they haven't shared all the details of the calculation, so more explanation needs more speculation.


What factors define changing popularity of different Openings over time?

Why in Chess there is no obvious trend?

Because in chess there is no theory. The best you can get is the sorted list of moves that are currently considered strongest.

Furthermore, chess allows you to choose and to express your way of thinking/approaching the game. In chess you have a chance to create your own position while nature is already predetermined and we can only try to understand it and adapt to it. Rarely we get the chance to change/reimplement something.

Since we have a choice in chess, of course there will be different trends -> some will like quiet positional play, some will go for sharp bloodshed and some will be somewhere in between.

  In other words, what factors (other than formal) define how each opening changes its popularity over time?

Factors are listed in "the first thing that came to my mind" manner, not by their importance :

1. Number of lines player must learn;

Small number will be good for amateurs, since they can actually "have a life" and be able to learn all the intricacies of the opening.

For chess professionals the opening should have lots of branches and lines.

2. Can I obtain counterplay and how sound this opening is ?

Professionals dodge the forced opening lines because they might be refuted with computer analysis or with a strong analysis.

Amateurs love these since they can leave a computer to work 2 days and do all the "dirty work" for them ( and will do it better! ).

Opening must give the player equal chance to win the game, and player must have active counterplay. Days of waiting for opponent to make a mistake or "run out of steam" are gone.

3. How much explored it is?

New lines offer a lot of chances for winning, while explored ones usually end with a draw. This partly explains why some old openings got resurrected.

SUMMARY:

Opening trends are dictated by leading grandmasters and factors I described above.

With the emerging of strong chess software amateurs got the opportunity to compete with equal chances if he uses opening that is suitable for computer analysis and if he has decent playing strength.

Since popular openings are very well explored thanks to chess engines and enormous amount of games played, there was a danger of all grandmaster games ending in a draw. .

This was also foretold by Capablanca in the 1930s. In those days Black had a variety of good choices against 1.e4 so White turned to 1.d4 since all black had was Queen's gambit. This was an important thing since White had variety of lines to choose which can't be said for Black. Technically speaking, only White could win. Games became dull and technical for Black so after Second World War Black tried to find openings that gave him equal chances to win.

After Indian defenses were invented, Black entirely switched to ...Nf6 leaving 1...d5 as a relic of the past. Since the King's gambit was refuted and Italian game gave White nothing but a draw, people started playing Ruy Lopez.

Then came 1980s and computer revolution. After realizing that computer can calculate every forcing line with 100% precision people started to turn their attention to 1.e4 again, and to other forcing openings for Black hoping that the masters of the old missed something. In those days almost every opening was thoroughly played and many of them got revived. Especially is important Queen's gambit since many players like Kasparov and Karpov liked to have a solid opening that gave them a chance to outplay their opponent after defending successfully. The beauty of the Queen's gambit is that it embodies all the good sides of the 3 factors listed above: it remained sound/reliable for centuries, it is reasonably explored and can give Black equal chances. Indian defenses are prone to being "refuted" temporarily until someone with hard work resurrects them.

As for 1.e4, Ruy Lopez gave White permanent advantage ( although minimal one ) so Black tried to choose opening that gives equal chances but preserves solidity and soundness they had from 1...e5. There came Petroff's defense to the rescue. After a lot of analysis it has been proven it fulfills 2 factors listed above -> it was prone to refutation by a novelty at that time. Meanwhile, people also found that Marshall attack in Ruy Lopez can offer Black equal chances too so again people started playing 1...e5 more frequently. However, positional players disliked the sharped lines that could be refuted by a novelty and searched for solid openings. Then came Karpov and resurrected Caro-Kann. This opening suddenly got a burst in popularity since Karpov proved it satisfies all 3 factors listed above.

With the progress of chess software openings are analyzed very fast with little room for error. This results in professionals facing the "Capablanca prophecy" again, so they will again try to resurrect less known openings or invent new ones. One such example can be Scandinavian defense or Sokolsky attack, even Polish opening or Grob attack...

This is too broad to be explained here but I gave my best to explain it. If you need anything more leave a comment and I will reply.

Best regards.


Implementing Late Move Reduction (LMR) inside iterative deepening

LMR is a general technique and there is no rule on the best implementation. That is why chess programming is hard, because you are expected to come up with your own interpretation and implementation.
LMR works like this:

if (this is a late move)
{
    if (this late move satisfies certain conditions)
    {
        Find a reduced depth to search
        Search alpha-beta with the reduced depth
        Do a full-search if the result is greater than alpha
    }
}

LMR is easy to understand but hard to master. Let's go through one by one. We will use Stockfish for our example. The code is https://github.com/official-stockfish/Stockfish/blob/master/src/search.cpp.

If this is a late move. What is a late move? We know the first move in iterative deepening is definitely not a late move, because we assume the first move is most likely the best move. Stockfish defines a late move like this:

if (... moveCount > 1 ...)

Stockfish starts LMR search if there's enough  depth to reduce and the move is not the first move in iterative deepening (moveCount > 1). There is no right or wrong answer here, in my engine I refused to reduce for the first two moves and I like my idea. Your implementation might be different, but you should always find a move that you think most likely to fail-low. The CPW wiki suggests:

  Typically, most schemes search the first few moves (say 3-4) at full
  depth, then if no move fails high, many of the remaining moves are
  reduced in search depth.

This is just a recommendation, as Stockfish has implemented more aggressive reduction.

This late move satisfies certain conditions. Generally, you don't reduce if:

Tactical sequences
Checks
During reduced search
PV node

You should consider to minmise reduction for PV nodes. The PV nodes form the most likely sequence of moves your engine reports, thus it's important to be as precise as possible.

You should also be careful if the move is a capture, because it's easier to make a search horizon mistake if you reduce the move too much.

This is Stockfish's implementation:

if (    depth >= 3 * ONE_PLY &&  moveCount > 1
  && (!captureOrPromotion || moveCountPruning))

Find a reduced depth to search. This is hard because nobody knows how much to reduce. You'll need to play hundreds and hundreds of games to tune your parameter. Generally, you reduce more if:

Cut node
Poor SEE
Quiet move

Again, there's no right or wrong here. Stockfish has the following:

 // Decrease/increase reduction for moves with a good/bad history
 r = std::max(DEPTH_ZERO, (r / ONE_PLY - ss->history / 20000) * ONE_PLY);

 if (cutNode)
     r += 2 * ONE_PLY;

 // Decrease reduction for moves that escape a capture. Filter out
 // castling moves, because they are coded as "king captures rook" and
 // hence break make_move().
 else if (   type_of(move) == NORMAL
             && type_of(pos.piece_on(to_sq(move))) != PAWN
             && !pos.see_ge(make_move(to_sq(move), from_sq(move)),  VALUE_ZERO))
      r -= 2 * ONE_PLY;

Stockfish considers the history, node type and move type.

Search alpha-beta with the reduced depth. This is standard. You will need to recursively search for the reduced depth you calculate. Stockfish has this:

  value = -search(pos, ss+1, -(alpha+1), -alpha, d, true);

Note that the reduced depth is passed to the search function.

Do a full-search. This is also standard. If your alpha-beta returns something greater than your lower bound (alpha), you have no choice but to do a full-search. If your LMR implementation is correct, the benefit you gain by reducing should outweight the cost of doing a full-search. Otherwise, LMR is a liability. Stockfish has this:

// For PV nodes only, do a full PV search on the first move or after a fail
// high (in the latter case search only if value < beta), otherwise let the
// parent node fail low with value <= alpha and try another move.
if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))

EDIT:

You don't have to add a check to PV node if you don't want to. But in chess programming, there are lots of things you should and should not be done in PV nodes. For example, we typically don't reduce for PV nodes. Your engine might lose rating if you don't check.


Average centipawn loss is the difference of your move to the best computer move averaged over all moves.

Inaccuracies/Mistakes/blunders as defined per lichess are moves that are at least 0.5=50 centipawns / 1=100 centipawns / 3=300 centipawns worse than the suggested computer move.

This rule is not strictly enforced in situations where you have a clear winning position and a choice of several good moves.

So if you have a choice between a move that leads to +10 advantage (best computer move) and +9 advantage this will count to your centipawn loss, but will not show up as mistake.

Even without it, it is possible to collect centipawn losses < 50 that don't show up as inaccuracy.


Ways to notice opponent's threats during one's own move

I am not 2000+ rated, but I experience this myself from time to time (I actually got better).
Reasons I found why I do this:

Being to excited about my plan, e.g. I see a nice tactic, which my opponent might not see, he plays a move which does not prevent it (apart from his threat).
"I am winning feeling", I get this when I won previous games against someone and am in a winning position again. Sometimes (especially when tired) I start to "just play it down". Then I start missing things like a Zwischenzug.

For countermeassures:

I focus more on opponents threats during his time, while developing my plans during my time. If he plays an unexpected move, I take my time. This way, I am constantly up to date about my opponents threats and I distribute enough time to think about his plans. If he plays really fast, I have to spend some of my time. Since I am used to spend more time for his plans, I do this quite automatically.
If I am feeling happy about a position, I tell myself, "Nice position, lets focus and find the closing moves". This helps me to focus (again).


The Game of the Century - why didn't Byrne take the rook after he forked Fischer?

Short answer: Since after the bishop recapture on f8 (and not the rook recapture!) white is tactically and positionally completely busted, with 5 active black pieces against a completely exposed king in the centre and no foreseeable chance of consolidation in order to eventually benefit from the material advantage.

First observations:

15...Bxf8 is with tempo as it attacks the queen on a3
White king is still stuck in the centre and being at least two tempi away from castling, not even sidestepping from the open file with Kf1 is possible.
With the bishop recapturing on f8, Bb4 becomes a constant threat, which means Nxc3 is unstoppable for white as Qxc3 falls to Bb4 winning the queen in all ensuing lines.
Although white is an exchange up temporarily, one of their rooks and the f1 bishop are completely out of play still and therefore it is in fact black who effectively appears to be material up (with last piece being the a8 rook that comes into play with check in fact Re8+), not in the raw count of pieces but most definitely in terms of the positional compensation.
Most important consequence of all these observations: black is well in time to prevent white from ever consolidating, which means even without concrete assessment of the different lines we can safely bet that everything's about to fall apart for white quite shortly after 15...Bxf8 as black's initiative on the white king seems to lead to tactically and forcibly winning variations in every scenario.

Brief concrete assessment:

Now let's look at a few candidate lines concretely (by no means exhaustive, please make sure to check these and the connected sidelines with an engine on your own)

 [title "after 15. Bxf8 Bxf8"]
 [fen "r4bk1/pp3p1p/1qp3p1/8/3Pn1b1/Q1P2N2/P4PPP/3RKB1R w K - 0 2"]

 1. Qb3 Nxc3 2. Bc4 (2. Ra1 Re8+ 3. Kd2 (3. Ne5 Rxe5+ 4. dxe5 Bb4 {and the mating net is set, white's completely defenseless.}) Ne4+ {and black's at least winning the f3 knight after for instance Kc2 and Qa5}) (2. Qxb6 axb6 3. Ra1 Bb4 4. Bc4 Ne4+ 5. Ke2 Re8 {only way to avoid the discovery is to play Kd3 but after Nxf2 Nxh1 we're back to a quite similarly lost endgame compared to the 2...Nxd1 Qxb6 line}) Nxd1 {and black is up a clear piece as white cannot in any way recapture the knight} 3. Qxb6 (3. Qxd1  Qb4+) (3. Kxd1 Qxd4+ 4. Qd3 Qa1+ {and the h1 rook is lost, notice the Bxf7 trick doesn't lead to anything for white.}) axb6 4. Kxd1 Ra4 5. Bb3 Rxd4+ 6. Ke2 Re4+ 7. Kd1 Bb4 {and black's clearly winning considering the bishop pair, the 2 pawns up and a passed one already, the exposed white king under constant threats and the out of play white rook.}

these lines clearly demonstrate why the f8 rook is in fact not hanging and why white's best chances lie in Bc4 creating Luft on f1 for the king (or even short castles if black allows on a good day) side-stepping (at first glance) most of the tactical shenanigans we just witnessed after 13...Bxf8.

 [title "15. Bc4 only attempt at consolidating"]
 [fen "r4rk1/pp2Bpbp/1qp3p1/8/3Pn1b1/Q1P2N2/P4PPP/3RKB1R w K - 0 1"]

 1. Bc4 Nxc3 2. Bc5 Rfe8+ 3. Kf1 {and the rest is as you see in the real game, with Fischer's devastating attack despite the tucked away king on f1, which is just too little too late.}


What is the value of most starting positions in dobutsu shogi?

The first surprise is that if we change the starting position to have mirror symmetry (like western chess) instead of rotational symmetry (like Japanese chess) we get a drawn position in which any lion move is losing.

1. setup S/elg/-c-/-C-/ELG/
1. show board
  ABC
 +---+
1|elg|
2| c |
3| C |
4|ELG| *
 +---+
1. show lines
Cb3xb2 : 0     (50.00%)
Gc4-c3 : 0     (50.00%)
Lb4-c3 : #-46  ( 0.00%)
Lb4-a3 : #-46  ( 0.00%)

Giraffes and elephants are freely exchanged in winning lines, so they must be very close in value. Still, elephants (like bishops in western chess) suffer from being restricted to half of the squares, which probably explains that giraffes versus elephants is a win for the giraffes.

1. setup S/ele/-c-/-C-/GLG/
1. show board
  ABC
 +---+
1|ele|
2| c |
3| C |
4|GLG| *
 +---+
1. show lines
Lb4-c3 : #25   (50.00%)
Lb4-a3 : #25   (50.00%)
Cb3xb2 : #53   ( 0.00%)
Gc4-c3 : #53   ( 0.00%)
Ga4-a3 : #53   ( 0.00%)
1. setup S/glg/-c-/-C-/ELE/
1. show board
  ABC
 +---+
1|glg|
2| c |
3| C |
4|ELE| *
 +---+
1. show lines
Lb4-c3 : #-32  (50.00%)
Lb4-a3 : #-32  (50.00%)
Cb3xb2 : #-24  ( 0.00%)

Or is it?

1. setup S/lee/-c-/-C-/GGL/
1. show board
  ABC
 +---+
1|lee|
2| c |
3| C |
4|GGL| *
 +---+
1. show lines
Ga4-a3 : 0     (50.00%)
Lc4-c3 : 0     (50.00%)
Cb3xb2 : #-62  ( 0.00%)
1. setup S/eel/-c-/-C-/GGL/
1. show board
  ABC
 +---+
1|eel|
2| c |
3| C |
4|GGL| *
 +---+
1. show lines
Ga4-a3 : 0     (50.00%)
Lc4-c3 : 0     (50.00%)
Cb3xb2 : #-58  ( 0.00%)

Starting giraffes draw, but beware of chick fights...

1. setup S/lgg/-c-/-C-/EEL/
1. show board
  ABC
 +---+
1|lgg|
2| c |
3| C |
4|EEL| *
 +---+
1. show lines
Cb3xb2 : 0     (33.33%)
Eb4-c3 : 0     (33.33%)
Eb4-a3 : 0     (33.33%)
Lc4-c3 : #-48  ( 0.00%)
1. setup S/ggl/-c-/-C-/EEL/
1. show board
  ABC
 +---+
1|ggl|
2| c |
3| C |
4|EEL| *
 +---+
1. show lines
Cb3xb2 : 0     (33.33%)
Eb4-c3 : 0     (33.33%)
Eb4-a3 : 0     (33.33%)
Lc4-c3 : #-50  ( 0.00%)

...and starting elephants also draw, but beware of lion moves.

What about side lions in the standard position?

1. setup S/lge/-c-/-C-/EGL/
1. show board
  ABC
 +---+
1|lge|
2| c |
3| C |
4|EGL| *
 +---+
1. show lines
Cb3xb2 : 0     (50.00%)
Lc4-c3 : 0     (50.00%)
1. setup S/egl/-c-/-C-/EGL/
1. show board
  ABC
 +---+
1|egl|
2| c |
3| C |
4|EGL| *
 +---+
1. show lines
Cb3xb2 : 0     (50.00%)
Lc4-c3 : 0     (50.00%)

Central giraffe with lion to the side is a draw.

1. setup S/leg/-c-/-C-/GEL/
1. show board
  ABC
 +---+
1|leg|
2| c |
3| C |
4|GEL| *
 +---+
1. show lines
Eb4-a3 : #65   (100.00%)
Cb3xb2 : 0     ( 0.00%)
Ga4-a3 : 0     ( 0.00%)
Eb4-c3 : 0     ( 0.00%)
Lc4-c3 : #-44  ( 0.00%)
1. setup S/gel/-c-/-C-/GEL/
1. show board
  ABC
 +---+
1|gel|
2| c |
3| C |
4|GEL| *
 +---+
1. show lines
Cb3xb2 : #51   (99.94%)
Eb4-c3 : #65   ( 0.06%)
Ga4-a3 : 0     ( 0.00%)
Eb4-a3 : #-64  ( 0.00%)
Lc4-c3 : #-52  ( 0.00%)

It is a win if the elephant is in the middle. Notice that moving the elephant towards the enemy lion is winning in both positions and moving the lion forward is losing, but in the mirror-symmetric case, chick fight is also winning and elephant towards the other side is losing. At least in this case shogi is more drawish than western chess!

In summary, it seems that trébuchets are quite rare (we did not find any), and most starting positions are draws with the occasional win for the starting player or loss for positions with an obvious weakness.


Checkmating the bare king with 3 knights – can the mate be forced on any edge square?

Here's how to forcibly checkmate the bare King on f8 or e8
(added later: or on g8 or h8) once it's been cornered on h8.
First put Kg6 and Nd7, so the other Knights can roam freely
as long as they don't accidentally checkmate or stalemate
the cornered King; then:

[Title "h8 to f8 (or g8 or h8)"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+
(1. Kh6 Kg8 2. Ne7+ Kh8 3. Nf7#) Kg8
2. Nde5 (2. Ne7#) Kf8
3. Kh7 Ke8
4. Nd6+ Kf8
5. Nd7#
(5. Ng6#)

and likewise:

[Title "h8 to e8"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+ Kg8
2. Nde5 Kf8
3. Nh6 Ke8
4. Nf5 Kf8
5. Nfe7 Ke8
6. Nd5 Kf8
7. Nce7 Ke8
8. Kg7 Kd8
9. Kg8 Ke8
10. Nc8 Kd8
11. Ncb6 Ke8
12. Kg7 Kd8
13. Nc6+ Ke8
14. Nc7# (14. Nf6#)

To answer the question Glorfindel asks in a comment:
White can start the same way, then set up the Knights on c5/d5/e5
to form a gauntlet and use the wK to push bK to the a8 corner:

[Title "h8 to a8"]
[Fen "7k/3N4/2N3K1/4N3/8/8/8/8 w - - 0 0"]

1. Nf7+ Kg8
2. Nde5 Kf8
3. Nh6 Ke8
4. Nf5 Kf8
5. Nfe7 Ke8
6. Nd5 Kf8
7. Kh7 Ke8
8. Nd4 Kd8
9. Ne6+ Ke8 (9... Kc8 10. Nc5)
10. Nc5 Kf8
11. Kh8 Ke8
12. Kg8 Kd8
13. Kf8 Kc8
14. Ke8 Kb8
15. Kd8 Ka7
16. Kc7 Ka8
17. Nb4 (17. Kb6 Kb8 18. Ne7)

and then use the previous analysis to force mate on any of a5/a6/a7/a8
(or b8/c8/d8), or push the King further to a1, etc.  So once the lone King
has been securely cornered it can be checkmated on any prescribed square
on the board's edge.


What are good ways to check blunders after the match?

Lichess.org has a free browser-based game analysis tool that allows you to copy and paste your PGN file for online analysis.

It's powered by Stockfish, and the analysis automatically:

Annotates the game with inaccuracies, mistakes, and blunders.
Graphs the game with an interactive move-by-move advantage chart (see below).
Suggests improved lines.
Names the opening.

It doesn't beat going through your games with your opponent and a good instructor, but it's a very useful free tool, and you don't need to install any software to run it.

The developer of lichess.org also has a blog post about Stockfish and the analysis tool.


Can my pc calculate to depth 125 in 15 seconds, if a chess engine is programmed well?

Sure it could, if you do a lot of pruning and consider only one or few branches. However it would likely not be a very strong engine, because it would miss lots of relevant sidelines/variations.

Longer answer:

The "depth" you see in engines does not mean, that the engine calculates all variations to that depth. This would be practically impossible because of the huge number of variations: After just 1 white and 1 black move you  already have 20*20=400 different games. With every move that you look ahead this number increases by a factor that is on average around 35.

Because of that, engines are (just like humans) only considering what they think are the relevant lines, by ignoring all other moves. This is called "pruning".

If you do this pruning very heavily you can end up with an engine that can look very deep. However it would look in a very narrow range, considering only one line or so.

It would miss lots of moves/lines and be very weak.  Roughly speaking you could say that engines are doing a compromise between depth, width (number of variations) and allocated time in order to optimize for playing strength.


Why different openings are used by computer players?

You may underestimate the number of games you need to determine the "best" opening by simulation. The differences between different openings are very small and to get a solid statistical judgment a few thousand games for each opening may be insufficient.

Then comes the question of the best response: There is an opponent, after all, and to build an opening book you must test for the strongest responses.

Still, this is all statistical and we know that it is not possible to solve chess computationally at the time being. A deep analysis may find a flaw in the "best" opening that is out of sight for current chess engines.

To your last question: For the chess variant "Schoolbook" (a variant of the Carrera-Capablanca type with rook-knight and bishop-knight compounds) its author Sam Trenholme has started to build an opening book using the method you propose, see http://www.chessvariants.org/index/msdisplay.php?itemid=MSschoolbook (comment at the bottom of the page).


What are White's main ideas in the exchange variation of the Ruy Lopez?

The main idea, in the exchange variation of the Ruy is "exchange." White will play d4 next, followed by offering the exchange of queens in order to head for an early endgame. That's because he's traded away his light squared bishop, his best attacking piece.

The "classic game" for this opening was played in 1914 between world champion Emmanuel Lasker and future world champion J.R. Capablanca.

In "Chess Fundamentals," Capablanca noted that immediately after the queen exchange, "The reader should note that if all the pieces were exchanged, White would be practically a pawn ahead and therefore have a won game."

White relentlessly strove for the exchange of pieces in the game and won.


You can download a PGN viewer for your phone platform, then search chessgames.com for your favorite players and their games for playback.  Having a PGN viewer installed is helpful also for sites like chessbase or chessvibes that sometimes link straight to the games file and not an online viewer.


How should black meet the Halloween Gambit?

After

[FEN ""]

1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Nxe5?! Nxe5 5. d4 Nc6 6. d5

Instead of moving the c6 Knight, black should continue with Jan Pinski's 6...Bb4. Black will just give away the c6 knight and then black will take the e4 pawn with the f6 Knight.  White can't take the Knight because his own is pinned and if white moves their queen to d4, black can just move their queen to e7 to protect both the bishop and the knight.  A continuation might be something like this:

[FEN ""]

1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Nxe5?! Nxe5 5. d4 Nc6 6. d5 Bb4 7. dxc6 Nxe4 8. Qd4 Qe7 9. Qxg7 Nxc3+ 10. Be3 Nd5+ 11. c3 Rf8

As you can see from above, if black plays accurately, there can be many discovered checks on white and if black wants, they can continue by taking the bishop on e3 eventually with another discovered check to follow or white will have to take the Knight, but either way, black will just take back with Qxe3+ and it is pretty much over for white.

Here is a professional game between Grigor Minchev and Aleksandr Pretov where black was unable to defend properly and was devastated.

  [FEN ""]
  1. e4 e5 2. Nf3 Nf6 3. Nc3 Nc6 4. Nxe5 Nxe5 5. d4 Nc6 6. d5
  Ne5 7. f4 Ng6 8. e5 Ng8 9. d6 cxd6 10. exd6 Qf6 11. Nb5 Rb8
  12. Be3 b6 13. Qe2 Kd8 14. O-O-O Qe6 15. f5 Qxf5 16. Qc4 Qe5
  17. Qc7+ Ke8 18. Bd4 Qf4+ 19. Kb1 Ra8 20. Re1+ Be7 21. g3 Qd2
  22. Bg2 Qxg2 23. dxe7 N8xe7 24. Nd6+ Kf8 25. Qd8# 1-0


Convert Stockfish analysis output to pgn

If you're in chessbase you can right click on Stockfish (where it displays its lines of evaluation), and press "Copy to Notation".


I use Stockfish, and have found it useful for analysis largely because of its multipv support (I switched from Crafty a couple of years ago), and it being free. I feel it lacks EGTB support, so it's not up to par with Rybka in that respect, but haven't felt willing to shell out the money for Rybka yet, just for that feature. It sounds like it also might do a better job of reporting forced draws, but I haven't confirmed that myself.

I agree with Ed, you should give guidance on what you want to hear in your answers. Rybka is a fine analysis engine.


Is it better to move a pawn or knight first?

You can see statistics at a site like this one.

There are four pawn moves (1. d4, 1. e4, 1. c4, 1. g3) and one knight move (1. Nf3) that form a top tier of first move choices.

The other twelve pawn moves and three knight moves vary in terms of viability.


Given that PGN files are just plain text, then you can create your own.

From wikipedia you need 7 tags:

  PGN data for archival storage is required to provide seven bracketed fields, referred to as "tags"...:

  Event
  Site
  Date: the starting date of the game, in YYYY.MM.DD form. ?? is used for unknown values
  Round
  White: the player of the white pieces, in Lastname, Firstname format.
  Black: the player of the black pieces, same format as White.
  Result: the result of the game. This can only have four possible values: 1-0 (White won), 0-1 (Black won), 1/2-1/2 (Draw), or * (other, e.g., the game is ongoing).

An example might be:

[Event "QGA: Main line with 7.Bd3"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Me"]
[Black "The other guy"]
[Result "*"]

d4 d5 2. c4 dxc4 3. Nf3 Nf6 4. e3 e6 5. Bxc4 c5 6. O-O a6 7. Bd3 *


The best chess websites or apps to play on

The best completely free website I know of is Lichess. Personally, I use Chess.com. It's free to play on, and many of the features it has can be used by anyone. However, to gain full access to the website (e.g. the video library), you do need to pay for a membership. It is relatively inexpensive though—$100 per year, which is equivalent to $8.33 per month. (Other membership options are even cheaper.)

Many people still prefer Lichess, and it does have the advantage that absolutely everything is free. Ultimately, I think the best way to answer your question is to try out everything:

Proprietary (to gain full access, you need to pay):

https://www.chess.com
https://chess24.com
https://www.chessclub.com

Open source (completely free, and run by volunteers):

https://lichess.org

Note that even the chess websites that offer paid subscriptions often come with a money-back guarantee. If you're organised enough to cancel your subscriptions, then you can pretty much trial everything before coming to a decision.


What happens should a clock fail during the game?

Per FIDE rules 6.10a and 6.10b (I am including the latter since it is so closely related in that it can require the arbiter to adjust the times based on judgment):

  6.10 a. Every indication given by the clocks is considered to be conclusive in the absence of any  evident  defect.  A  chess  clock
  with  an  evident  defect  shall  be  replaced.  The  arbiter  shall
  replace  the  clock  and  use  his  best  judgment  when  determining
  the  times to be shown on the replacement chess clocks

  6.10 b. If  during  a  game  it  is  found  that  the  setting  of  either  or  both  clocks  was  incorrect,  either player or the
  arbiter shall stop the clocks immediately. The arbiter shall install
  the  correct  setting  and  adjust  the  times  and  move  counter.
  He  shall  use  his  best  judgement when determining the correct
  settings.

Per USCF rules:

  16 O. Defective clocks. Every indication given by a clock is considered
  to be conclusive in the absence of evident defects. A player who
  wishes to claim any such defect must do so as soon as aware of it. A
  clock with an obvious defect should be replaced, and the time used by
  eachplayer up to that time should be indicated on the new clock as
  accurately as possible. The director should use judgment in
  determining what times shall be shown on the new clock. A director who
  decides to subtract time from one or both players shall leave that
  player(s) with the greater of either five minutes to the time control
  or at least one minute for each move the player still needs to meet
  the time control.

Again, I am going to include this since it is closely related, and is akin to what I posted for FIDE above.

  16 P. Erroneously set clocks.An erroneously set clock should be
  handled in the same fashion as a defective clock. As in 16O, the
  director should use judgment in deciding whether to make time
  adjustments. The most common situation of this type involves an analog
  clock set to expire at 7:00 rather than the correct 6:00. This is best
  handled by pointing out to both players that the time control expires
  at 7:00. Clocks can also be reset for the correct time controls and
  the correct elapsed timefor each player.Sometimes this hour difference
  is not pointed out and there is an eventual time claim. Even though
  the clock may show 6:00 with a flag down, or the signaling device on a
  delay or digital clock indicates a flag fall, if the total elapsed
  timeshown for both players is about an hour more than possible,
  considering when the game started, the player should not be forfeited,
  and should be given the hour in question.


Looking for an old problem that I can't quite remember

[Title "Carl Ferdinand von Jänisch, Der eiserne Käfig des Tamerlan, 1849"]
    [FEN "4N3/P2p1Np1/3Qp1R1/2pR4/2p1kpp1/b2bp2B/q3PP2/3K4 w - - 0 0"]

1.f3+ gxf3 2.exd3+ cxd3 3.Bf5+ exf5 4.Re6+ dxe6 5.Nf6+ gxf6 6.Rd4+ cxd4 7.a8=B Qd5 8.Bxd5+ exd5 9.Qe5+ fxe5 10.Ng5#

It's problem 59 in Max Lange: Handbuch der Schachaufgaben, Leipzig 1862, p. 79. Google Books.

It was published on p. 427 of the 1849 Schachzeitung. Google Books.

The chess puzzle can also be found with the search term tamburlaine's iron cage, e. g. Suren's YouTube video.


How to mate a king already in the corner with a knight and a bishop?

Normally, when mating with bishop and knight, the black king needs to be in a corner of the same color as the bishop. So this is actually the wrong corner, but thanks to the black pawn, it's still possible.

1. Be6 is the first thing I would try, as it confines the king to the corner; with the king on h6 and the knight on g6 it would be mate. However, the pawn will promote too soon (with check) which spoils this plan.

So let's try to move the king first: 1. Kh6 Kg8. Now 2. Be6+ forces the king back in the corner with tempo: 2... Kh8 and now the knight arrives in time: 3. Nf8 h3 4. Ng6 mate.

7k/7N/6K1/8/7p/7B/8/8 w - - 1 0

1. Kh6 (1. Be6 h3 2. Kh6 h2 3. Nf8 h1=Q+) Kg8 2. Be6+ Kh8 3. Nf8 h3 4. Ng6


How is chess viewed in USSR vs Post-USSR?

Authoritarian governments will punish its representatives who do not live up to the standards they set.

Iraq - Saddam later appointed Uday head of the Iraqi Olympic committee and soccer federation, and ... tortured athletes who failed to win.

China - Players that towed the party line and upheld Marxist values were rewarded. Those that didn’t were punished.

Bear in mind, these standards are not necessarily reasonable or attainable.


Is there any other notation system other than algebraic notation?

Other than the algebraic nomenclature:
Two off the top of my head are
Correspondence chess used 1:1 to 8:8 to label the squares.
Descriptive notation predated algebraic: 1. P-K4 P-K4 2. KN-B3 QN-B3 and so on.