Category Archives: Endgames

Basic Endgames Teach How To Tie Together Mathematics And Logic

In the game of chess, each lowly Pawn has the potential to promote to a powerful Queen by advancing all the way to the 8th rank. Also, there’s a remarkable rule that if one side cannot make any legal moves, the game is actually a draw, rather than a loss for the paralyzed side. These two facts create the phase of a chess game called the endgame, where a player has the opportunity to out-think and out-trick the opponent.

Logic

Chess has a well-deserved reputation for being a game of logic. Indeed, fundamentally the game really is a matter of logic, in the sense that everything is about managing the fact that everything boils down to “if I do this, then she can do that, but then I can do this other thing”, and therefore a decision tree of immense breadth and depth. Nowhere is this more true than in the endgame, where being one move ahead of the other side may mean the difference between a win and a draw: and in fact, being one move ahead does not always win, but sometimes even loses (in situations called Zugzwang where getting somewhere first means the other side can make a waiting move and then pounce).

For example, a basic endgame position everyone must learn is the following King and Pawn versus Pawn position. Black to move, there is only one move that draws; the other two moves lose.

This is a perfect position to use to teach children how to think logically, even if they don’t otherwise play chess. They don’t even need to know how to checkmate with a Queen against King. You can just teach them how the King and Pawn work, and set the goal for White as being to get the Pawn to the 8th rank without its being captured. In fact, I think chess would be much more useful in teaching logic if play was arranged starting from simplified positions in endgames, skipping the much more complex phases of the opening and middlegame.

Meta-reasoning

Once a chess player begins applying logical reasoning, an observant player will observe that she is reusing certain patterns in reasoning again and again. This is where reasoning about reasoning, or meta-reasoning, comes in. The concept of “taking the opposition” in chess is one of the simplest examples. In the position above, Black draws by arranging it so that if White’s King advances, Black’s King is in position to “take the opposition” and prevent further progress. So the principle of opposition is not a part of the game of chess, but part of how we can reasoning about the game of chess. A chess player could in theory just apply the “rule” of opposition to play chess well, but without actually understanding why it works, would be missing a huge part of what chess is about: discovering patterns, proving facts about them (this is the “meta-reasoning”), and applying the patterns as building blocks.

Mathematics

This leads to the topic of mathematics in chess. I take the point of view that certain ways of effectively making decisions in chess amount to doing mathematics, going beyond just logic: arithmetic, algebra, geometry. There are many connections to be made here that, when made explicit, can greatly aid in transferring skills out of chess itself.

For today, I’ll just mention a connection with arithmetic and geometry. In the position below, White to move can win, but only by very precise play. The aim is to prevent Black from taking the opposition, and then for White to take the opposition and reduce the problem to the previously mentioned position. The concept of reducing to a previously proved fact is fundamental to logical reasoning, of course. So where does the mathematics come in?

First of all, it must be understood that there is a race between the two Kings to get to one of the critical squares in front of White’s Pawn that will determine whether White can win: White must get the King to d6, e6, or f6. So there may be some kind of counting implicit in whatever logical reasoning is used.

From a geometrical point of view, what is important to understand is that because Kings have to move either horizontally, vertically, or diagonally, “distance” on the chess board is not the same as the “bird’s eye view” visual spatial distance: chess operates on a more abstract geometrical space where, for example, all things being equal, diagonal moves can get a King somewhere much faster than just horizontal or vertical moves.

Arithmetic comes in to tie in this geometric insight with the logic-based goal-setting and reduction: the simple way to determine whether this position is a win for White is to count how many moves it takes to reach a desired square, and to count whether Black can stop this. Arithmetic is basically a meta-reasoning shortcut for otherwise engaging in low-level “if this, then that” logical reasoning. Here, we see that White can, in 3 moves, reach d5 unimpeded, because in 2 moves, Black can at most reach f6. Then we tie up the reasoning with one bit of logic/geometry: after White’s King is on d5 and Black’s King on f6, Black’s King must go to e7 to prevent White from getting to d6. But then this allows White to get to e5, taking the opposition and winning the game.

I believe that this endgame position is very instructive for showing how to apply multiple levels and styles of logical and mathematical understanding to be able to guarantee a desired result. Any student who can master (as tested by playing out as either side to the optimal result) and be able to explain the evaluation of each position in which the Pawn is on e4 and the other Kings are on any other squares on the board will have demonstrated a real understanding of logical reasoning.

Franklin Chen

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Clash of the Titans

OK, both my opponent and I are experts, not yet masters. Still, this chess game was hard fought by our chess engines! We both were posting our analysis on the playchess.com server. I could see what he was analyzing with Stockfish 5.0 SE and he could see what I was analyzing with Houdini and Deep Fritz. Truthfully, I doubt that either one of us would have found half of the moves that we played had this been an OTB chess game. Again, ICCF rules allow us to use chess engines.

This chess game is one of two draws that I have in this section. I also drew the player that Miloslav defeated, so Miloslav is temporarily in first place, I am in second place and Don Pedro is in third place. If I can finish my remaining games with at least a draw in each one I may remain in second place in this section.

Against unknown opponents I will often play the Modern Defense. It did not take long for my opponent to get me out of my database of games and into unique analysis. About half way through this game I realized that someone was anonymously following my analysis on playchess.com. From that point on, my opponent was playing whatever moves Stockfish recommended. There were a couple of times in the thick of it that my chess engines thought that something else was better for White. The notes that I made during this game (see below) explain the rest.

Mike Serovey

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Attack on Godzilla

My opponent is from Japan, which is why I used the Godzilla reference in my title. The only other Asian player that I have faced on ICCF was Graeme Hall in Hong Kong.

This win gives me three wins, two losses and six draws in this section. That temporarily puts me back into fourth place out of thirteen players. I need a second place finish in order to advance to the next round. I have one game remaining in this section and I have Black in it. In that game I have even material. If I can win that game I may get my second-place finish.

Initially, I started off with a queenside attack while my opponent played a kingside attack. My opponent’s attack stalled out while I switched my attack over to the Kingside. Like many of my opponents on ICCF, once he started losing he slowed the game down big time and he had only 3 days of reflection time left when he resigned. At the point in which my opponent resigned he was down 6 passed pawns and was four moves away from getting checkmated. I have no clue why people play out hopelessly lost endgames in correspondence chess!

Mike Serovey

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An Instructive Ending With Bishop Up For A Pawn

My student Eric (currently rated USCF 15xx) showed me a recent tournament game of his in which a rather fascinating ending came up. As Black, he had a Bishop and four Pawns versus White’s five Pawns. At first it seemed obvious that this ending should clearly be a win, but actually, it is not so obvious, because the semi-blocked nature of the position meant that it was not completely trivial for Black to break through White’s wall of Pawns. It turned out that he did come up with a very clever idea that is part of a good winning plan, but he did not manage to follow up on it, and seeing no way to make progress, accepted a draw with his opponent.

Winning an ending given a material advantage is very important, because at some point during one’s chess development, one plays well enough in the middlegame to get a material advantage, but if one is not able to convert in the endgame, it is a shame. In particular, when up more than two Pawns, there is usually a way to win, by taking advantage of imbalances on the board appropriately.

Looking at the game position carefully, we worked out a winning plan for Black. I think it is instructive because it brings together many important principles in endgame play. There are not any forced variations until the key transformative positions are reached. There may be other ways to win than the method I explain below; I would welcome feedback on other ways to win!

Initial position

First, let’s look at the initial position. The fundamental material imbalance:

  • Black has an extra light-squared Bishop.
  • White has an extra King-side Pawn, a g-Pawn that therefore could potentially be converted to a passed Pawn. However, Black is not in any danger of losing, because Black’s Bishop can easily sacrifice itself if necessary to prevent successful Queening.

Other interesting features:

  • White is lucky to have most Pawns on dark squares, out of attack from Black’s light-squared Bishop.
  • Black’s Pawns are currently all blocked up and therefore Black can win only by using an active King somehow to penetrate White’s position and either win some more Pawns or transform the position in order to create a passed Pawn.
  • But while activating the King, Black has to be careful about not letting White’s g-Pawn Queen. However, note that Black’s Bishop control’s the g8 Queening square.

An active King

The single most important lesson in endings is that an active King is critical. Where can Black’s King go? I think Eric was led astray because he was looking for a way to use the Black King to get through on White’s King side, but that is where White is actually strongest and has an extra Pawn. But if we look at the whole board, we see that Black can try to reach c4 or a4 in White’s position, to attack the d-Pawn or the b-Pawn with the King. Granted, White’s King could move over to the Queen side to defend the Pawns, and at least prevent Black from getting to c4. Black could get to a4, but then White can protect the b-Pawn with a3 and protected the a3-Pawn with a King shuffling between a2 and b2. These static considerations make it look like Black’s King cannot make progress.

Eric was also worried about how to get the Bishop involved in case of going over to the Queen side, because what if the Bishop got too far and White played g6 and then g7? We’ll see later how to address this concern.

Notice a Pawn asymmetry

However, Black has another imbalance to use: the Pawn situation on the Queen side is not symmetric. This is important. White has a b-Pawn while Black has an a-Pawn. This means that if Black can prepare the Pawn break …a5, if White ever trades the b-Pawn for Black’s a-Pawn, then White ends up with a passed a-Pawn but Black can then use the second Pawn break …c5 to create either a passed c-Pawn or passed d-Pawn. In an even-material ending, the “outside” passed Pawn (White’s a-Pawn in this situation) is advantageous, but with Black having an extra Bishop, there is no advantage to having the outside passed Pawn, because Black’s Bishop can cover it while Black’s King is free to press on with its own “inside” passed Pawn.

If White protects the b4-Pawn with a3, then Black can just trade Pawns, leaving White with a weak b4-Pawn. In that case, the ending is easy to win for Black, because Black can simply gain the opposition (using waiting moves with the Bishop) to break through and win either the b-Pawn or the d-Pawn.

Therefore, our conclusion is that if Black can safely manage to get the King to b6 or b5 in order to prepare a5, the game is a win. Note that no calculation of sequences of moves is necessary to come to this conclusion: all that is needed is

  • Fundamental understanding of Pawn breaks and passed Pawns
  • Understanding how to win by “taking the opposition” (in a King and Pawn setting)

The final question then is, how to perform this King manoeuvre while preventing White from trying to Queen the g-Pawn?

A clever Bishop manoeuvre

Eric hit upon a clever Bishop manoeuvre that, if followed up, would have worked great.

First, he played …f5 to force White to play g5. Then he moved his Bishop to d3, a6, c8, e6, and finally f7, in order to protect the g6 and h5 squares from White’s King invasion. This was a fine creative plan.

Unfortunately, he agreed to a draw shortly after this manoeuvre, not being able to find the winning plan that involved activating the King and using two Pawn breaks. He saw that after getting the King around, if he ever tried to bring the Bishop around, that would risk White’s g-Pawn advancing. This is in fact a valid concern, but the missing part of the picture was the importance of the …a5 Pawn break and the subsequent follow up. It turns out that there is something very subtle for Black black needs to do to time that Pawn break just properly, to avoid a draw.

Triangulation

The concept of triangulation is very important in endings. The main idea is to “waste time” in order to force the weaker side to reach a position on the move from a position in which the stronger side is on the move (but does not want to be on the move). In the analysis below, a critical position arises in which Black needs to prevent White’s King from becoming too active after a planned Pawn break. By triangulation, Black forces White’s King to the rim at a3 before playing the Pawn break …c5.

Control of the Queening square

It is also important to note that Black can wander just far enough with the Bishop to win White’s a4-Pawn, because of the control of White’s Queening square g8. Black’s Bishop has enough time to make it back to d5 after White plays g6 and g7, to stop White from Queening on g8. Whew!

Conclusion

I thought this was an instructive ending to work out, because of the many themes necessary to understand and integrate in order to create a winning plan.

Full analysis

Franklin Chen

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Guidelines For Teaching Kids Endgames and Tactics

Once a student is familiar with piece movements, attacks, check and checkmate, my next topic is to teach him or her elementary mates. This was explained by Capablanca in his book Chess Fundamentals.

“The first thing a student should do, is to familiarise himself with the power of pieces. This can best be done by learning how to accomplish quickly some of the simple mates.”

In my view tactics and endgames should be learned in parallel. For tactics it’s best to proceed step by step to develop tactical skills very gradually and effectively. I have had very good results with that. But for the endgame I referred to many books before finally choosing ‘GM RAM’. This seems very strange at first as there are just 256 dry positions to work out without even knowing who is to move! But once you go though the you realise that the first 58 endgame positions are really essential. I realised that 70% or more of my endgame knowledge is based around those 58 positions, and these cover the following topics:

– Key Square
– Rule of Square
– Opposition
– Shouldering
– Pawn breakthrough
– Essential Rook ending (Philidor and Lucena)
– Queen vs. Rook endgame
– Essential Queen endgames

These elements are all vital for practical endgame play. And as there is nothing ready-made it can actually actually inspire us to work through them in our own way.

There is a problem when a coach focuses on the endgame. A few of my students see the endgame as boring, insisting that I teach them more and more tactics, but the problem is that they can’t understand that they are not knowledgeable enough to decide what is good for them.

Accordingly I have not changed my way even at the cost of some students going elsewhere for lessons. Quality demands sacrifices.

Ashvin Chauhan

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Blind In One Eye And Can’t See Out The Other One

The game below is from the second round of my most recent event that I played in Colorado Springs. This game was a comedy of errors. I lost the first round and I think that my opponent did too, but I am not sure of that. Roger appears to be about ten years older than I am and I think that fatigue may have played a part in the way that he played this game. I took a lunch break between the first round and the second round and thus I arrived about five minutes late for the start of this game. That lost time may have hurt me in the endgame when we had a time scramble.

I was disappointed with a draw in this game because I thought that I was winning the endgame. We were the last game to finish that round and we got only 15 minutes to recover before the start of the third and final round. I ended up drawing my third round as well due to fatigue from this round. However, when I played over this game with a chess engine I became grateful for the draw because it was then that I realized that Roger let me get away with some horrendous blunders!

The first eight moves was pretty much what I wanted to play as White. Black’s ninth move pretty much started to mess up my plans because I had never seen that kind of setup against the Botvinnik System before. I misplayed the next ten moves or so and I ended up in an inferior position that Roger eventually let me out of.

On move number 16 I had achieved equality only to give Black a slight edge on move number 17. I outright blundered on move number 19, but Roger failed to take advantage of that. Judging by his facial expressions at a couple of points in this game Roger was actually impressed by some of my blunders!

I blundered again on move number 21. At move number 23 Black was clearly winning. Black missed a winning move on move number 24. I blundered again on move number 26 and Black let me get away with it. My moves number 27 and 28 were again blunders. Black finally finds a winning idea on move number 28. Black gives back part of his advantage on move number 31. Once again, I blundered on move number 35. Black blunders on move number 36 and allows me to regain equality. Black plays some inferior moves on numbers 44, 45, and 46 inclusive that allow me the opportunity to win, but I failed to take advantage of that. It seems that from this point on, every time that one of us made a weak move the other one matched it. I gave away my passed d pawn in the time scramble and then agreed to a draw.

Mike Serovey

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Completing My First Tournament: 7th Round And Summary Of What I Learned

Here I conclude my coverage of my first chess tournament, the 1980 Michigan Open (Reserve Section), achieving my first provisional USCF rating of 1546 after scoring 3.5/7.0 points. I also won a trophy for 2nd place Unrated in the Reserve Section (my father, also playing in his first tournament, won the trophy for 1st place Unrated in the Reserve Section). It was a great way to start my chess tournament life!

My goal in analyzing the games of my first tournament has been to begin exploring the development of a new chess tournament competitor (my young self of 1980) and examine common patterns of thoughts and behavior. I will continue further to track the evolution of my skill and style through analysis of further tournaments from 1980 and 1981.

Round 7

In my round 7 game, as Black I faced the Ruy Lopez (against White rated around USCF 1600), and as in round 3, did not know what I was doing and quickly gave up the center. My opponent did not know what he was doing either and we traded quickly into an endgame. As with many other endgames I played in this tournament, positions that are clearly draws at a higher level of play nevertheless contained imbalances and opportunities for going astray, and I played poorly, deliberately trading into what I should have known was a lost King and Pawn ending.

Summary of tournament

Openings

Move numbers after I was out of any theoretical knowledge:

  1. 1 (Bird’s Opening as Black)
  2. 5 (Petroff Defense as White)
  3. 9 (Closed Ruy Lopez as Black)
  4. 5 (Exchange Ruy Lopez as Black)
  5. 4 (Open Sicilian as White)
  6. 6 (Philidor’s Defense as White)
  7. 9 (Closed Ruy Lopez as Black)

Nobody lost a game straight out of the opening (except for the Open Sicilian where I won quickly as White), although poor positions of course arose. We could have used a better understanding and use of principles (such as development and central control) to improve beyond this 1500 level of play.

Middlegames

  1. I did not understand the value of the Bishop pair, or that Knight on the rim is dim, and got destroyed on the King side.
  2. A lot of piece trades. My opponent did not understand the value of the Bishop pair.
  3. Highlighted the importance of using Pawn breaks.
  4. My opponent should have opened the position because of my poor opening development, but instead closed it, allowing me to consolidate and in return attack his King with a Pawn storm.
  5. (I won the game out of the opening because my opponent ignored development and created holes.)
  6. A lot of piece trades. I did not understand the weakness of my isolated Pawn and lost it.
  7. A lot of piece trades. I did not understand the weakness of my opponent’s isolated Pawn and dissolved it instead of attacking it.

Endgames

5 of 7 games went all the way to an endgame. Many errors occurred, so the lesson is that there is much to be gained from studying the endgame. In addition, knowing what endgames are advantageous would have allowed me to make better decisions in the middlegame (regarding Pawn structures and Bishop vs. Knight). I feel that in the absence of clear attacks against the King, middlegame play often tend to be aimless simplification at the 1500 level. At top levels of chess, one plays openings with a goal toward certain kinds of endgames. Club level players who are no longer hanging material all the time and want to improve should also start to think this way.

  1. (I lost in the middlegame.)
  2. I had the Bishop pair advantage but squandered it. Comedy of errors resulted in my winning because my opponent did not realize the King and Pawn ending was lost for him.
  3. Draw: I dawdled and simplified in an endgame I could have won.
  4. Draw: I simplified too much, then my opponent allowed a won King and Pawn ending but I did not know it was won for me.
  5. (I won in the opening.)
  6. Draw: one Pawn down, but Bishop vs. Knight; comedy of errors, but eventually I won a Pawn back and simplified to a draw.
  7. I mistakenly simplified repeatedly, resulting in a lost and King and Pawn ending.

The complete annotated game

Franklin Chen

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World Rapid Chess Championship

The FIDE World Rapid Chess Championship 2014 recently concluded with Magnus Carlsen winning, followed by Fabiano Caruana in 2nd place and Viswanathan Anand in 3rd.

There was an interesting endgame between the FIDE World Champion, Carlsen, and former World Champion, Anand. Carlsen uncharacteristically went wrong in an ending. In taking a pawn with his knight he missed a simple rook move that skewered his bishop and knight. Anyone can make such mistakes, especially in rapid chess, but when the World Champion does it, it’s called a blunder! Despite this loss, it wasn’t enough to stop Carlsen becoming the 2014 World Rapid Champion. You can view the ending play with commentary on the clip below.

Angus James

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My 4th Tournament Game: First Time I Attacked in the Middlegame

In my last three posts here, I analyzed the first three tournament games of my life, as a new unrated player in 1980:

  • I lost the first upon being attacked effectively in the middlegame.
  • I won the second in a very uneven game in which both players simplified quickly and reaching an endgame which I won only because my opponent blundered into an obviously lost King and Pawn endgame.
  • I drew the third after bumbling into an advantageous endgame but not knowing how to win, and allowing simplification to a draw.

Fourth game

My fourth game (my opponent was rated around USCF 1550) is interesting because for the first time in the tournament, I actually had a clear middlegame attacking plan in a blocked position, and correctly followed through on it, castling Queen side and attacking on my opponent’s vulnerable King side with an obvious Pawn break as well as activating my pieces toward that side of the board. For the first time in the tournament, really, I displayed an active search for an initiative in the middlegame.

Unfortunately, a few moves before forced mate, I apparently did not realize the strength of my position and mysteriously simplified repeatedly, into an endgame with a useless Pawn up, and a draw resulted. The irony is that my opponent allowed me at two points the opportunity to trade my Bishop for his Knight, in which case the Pawn-up King and Pawn endgame would have been an easy win for me. Apparently my knowledge of King and Pawn endgames was still very limited, illustrating yet again how important it is to master these basic endgames.

The classic pattern I see in these early games is that of unwarranted simplification in advantageous middlegames and endgames, probably a result of the early emphasis on “counting points” of material, and not realizing that an active piece is worth more than a passive piece.

The complete annotated game

Franklin Chen

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Lessons From My 3rd Tournament Game: The Nature Of Endgames

I have now shown the first two tournament games of my life, from 1980: I lost the first game and won the second game. My third game, discussed here was a draw.

It was an instructive experience for me in my first tournament to experience all three possible results in the first three rounds! I believe it might have been devastating if, for example, I had lost too many games in my very first tournament. Instead, I was involved in some very long and interesting games from the start.

My opponent was rated around USCF 1500, and this shows in his play.

Common errors in 1500-level chess

Opening

In the opening, I had no idea how to play the Black side of a Ruy Lopez. Nobody had taught me the plans for White or Black. I was just winging it. I gave up the center at move 10; my opponent returned the favor by playing apparently mechanical moves that would have applied in a “standard” line, instead of more principled developing moves fitting the situation.

The first thing someone at a 1500 level can do, after mastering basic tactics, is to understand the basic principles of what to try to achieve in the middlegame after the first several opening moves. Many games at this level are decided, unfortunately, by “unorthodox” opening continuations that lead immediately to not knowing how to cope, being outside of one’s memorization. Pointlessly giving up the center for Black should have led to trouble for me, but by accident, actually kept working well for me, against 1500-level opponents, even after this game, because they did not understand what to do any more than I did, and it became almost random who would enter the middlegame with an advantage.

Middlegame

One thing I noticed while looking at my first tournament games, including this third one, was that at the level of play of myself and my opponent, we shuffled a lot of pieces around, either

  • “attacking” without enough backup, or
  • playing passive-looking retreating moves without a clear plan of reactivation.

In particular, I did not understand the importance of looking for Pawn breaks. Here, for example, c5 was crying out to be played, repeatedly. However, I did use a g4 Pawn break to achieve a lasting advantage, so I get some credit for that.

Also, I got into tactical trouble, hanging a piece in an elementary way. Luckily, my opponent got bamboozled and missed an elementary “capture Pawn with check and double attack” that would have left me completely lost, and instead allowed me a recapture with check that led to a Queen trade into an endgame favorable to me!

1500-level chess is still largely decided by big swings in evaluation resulting from missed tactics.

Endgame

The endgame was an unbalanced one, with Black having a Rook and two Pawns for two minor pieces. It favored Black because of the noticeable lead in development. My opponent as White made the elementary mistake of trading pieces in a bad endgame, rather than keeping them to maximize defensive possibilities. Trading the single remaining Rook led to a terrible Rook and two Pawns versus two Knights endgame.

However, again I did not know yet to aggressively use my Pawns, especially here the Queen side Pawn majority. There was a lot of random shuffling around of pieces, then an insidious swindle by my part when I finally realized I should attack on the Queen side. I succeeded in achieving a tactically won position against the pair of Knights, but never saw the win. After too much simplification, the result was a dead draw.

My observation about 1500-level endgame play is that players trade pieces and Pawns too readily, not realizing that there are times when a trade helps and there are times when a trade harms. As a result, many quick draws happen in actually interesting and unbalanced endgames. The 1500-level player who understands endgames can often survive terrible openings and middlegames and win in the endgame. I wish I had learned this lesson earlier in life. I now think that “working backwards”, by knowing what to aim for in the endgame, and then approaching the middlegame with a goal of reaching a good endgame, and approaching the opening with a goal of reaching a good middlegame, should be addressed by students of chess who have reached a 1500-level and are no longer just making extreme tactical blunders constantly.

The complete annotated game

Franklin Chen

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