Friday, April 28, 2017

Revisiting the Game Analysis Process

Photo by Ryan McGuire. CC0 1.0
It's been a couple years since I wrote my first article on analyzing your games - 4 Steps to Analyzing Your Game for Improvement.

Since writing that article, I've analyzed a few of my games as well as discussed the topic with other players, including some chess coaches and masters.

In today's article, I wanted to give some practical advice for those seeking to improve their chess through analyzing their own games and revisit and refine a few of the points I made in my original article.

If you haven't read the original article, you may want to check it out for more context as I will try not to be too redundant.

In addition to this article, I also created a video series where I played a game online, and then subjected the game to the game analysis process. You can watch the original game with my comments here.

Self-Honesty 


One thing I've observed in myself is that when I'm "self-annotating" my games - the step of the process where I describe my thoughts, analysis, and feelings during the game. - is that sometimes I tend to paint my thoughts more positively then actually happened. Oversights become "misevaluations." Bad moves become "inaccuracies." Blundering material is described as "not getting enough compensation."

It is important when we want to improve to get an accurate assessment of where we are in the development process. Sometimes, this can be embarrassing because we have a certain expectation of ourselves. However, it takes humility and confidence to admit our faults and mistakes. We have to get over this hurdle though if we want to get to the next level.

In the first step of the analysis process, try to capture all of your thoughts. Sometimes, you will forget everything you thought about - that's okay! Even it is only a few moves that you are very clear about - the key is to try to figure out how you think. The fact that you forget what you were thinking of specific moves is insightful in itself!

What are Key Positions?


In the second step of the analysis process, we will try to identify a few key positions for further analysis. I describe in more detail the types of positions you will want to find in the original article, but there are a couple points I've been emphasizing more lately that I'd like to discuss with you.

The first is positions in which your evaluation during the game differed greatly from the actual evaluation of the position. For example, positions that you thought were drawn that were actually won or lost, and so forth. The reason why this is so important is that our ability to evaluate positions is one of the most important skills we can develop.

When we misjudge a chess position, it can be due to a couple of reasons:

  • We lack specific knowledge about certain positions - e.g. We don't realize that a specific endgame structure is drawn, so we push for a win only to throw away the draw.
  • Our emotions cause us to be overly optimistic or overly pessimistic of a position. We can look at the example of Kasparov's game two loss in his 1997 match against Deep Blue, where much analysis has shown that Kasparov may have resigned prematurely (although there is some debate over this).
This is one area that the chess engine can at least give us an approximation of a position's evaluation to compare to our own. I will discuss using chess engines in our game analysis next.

In the video below, I apply the first two steps of the analysis process to my game.



Using Chess Engines in Analysis


I've gone back and forth over using the chess engines in analyzing our games. I've currently settled on the view that chess engines can be very useful if used sparingly and in specific situations. I've written before about the limits of chess engines in helping us improve, but here I'll give a few tips on how you might use them to help you in game analysis.
  • You can run through the game with the chess engine on but only look at the computer's evaluation. Here, you can see where there are big jumps in the evaluation. This tell you where the big mistakes where made. If your opponent made them, you can see if you exploited them. If you are the one with the blunders, you can find out why. Some programs create an evaluation graph and you can see the peaks and valleys of the graph to identify key positions.
  • It's okay to come to your own conclusions, even if the engine disagrees with you. If after comparing your analysis and the engine's analysis, you think your move is better, then accept that. This may seem like odd advice, but the fact is that sometimes the computer engine is wrong...and even when it's not, the type of move it produces may be an exception due to the tactics of the position and may not be generally applicable in other cases. Also, it's important for you to develop your own voice when it comes to chess - although I encourage you to do this in an environment where you have access to good instruction or good books that can guide you.
  • Do not accept chess engine analysis if you do not understand it. Remember that the engine will not be with you in your tournament games. If a suggestion by the computer is too complex for your understanding or goes against what you believe are good positional principles, then let it go. You can always revisit the position at a future point when you are more experienced.
I feel a certain joy when I analyze a position on my own and then the computer confirms my thoughts! You cannot have this happen if you first turn on the engine when analyzing your games. I encourage you to do your own work first - at least a little - and then ask the computer for some assistance. 

Remember that your goal is not to find the best move in the position in your analysis. This is a by-product of your work, but your real goal is to uncover holes in your understanding or thought process so that you can correct it! The chess engine should be a tool - like a calculator - to check your own analysis and understanding of the game. 

When you find disagreements between your moves and the engine's, then do not blindly accept the engine's answer and move on. Why did your moves differ and - accepting that the engine in this particular case has the stronger move - how can you think differently (or what do you need to study) to help you find such moves in the future.

Accepting Uncertainty


One aspect of analyzing my games that I've come to appreciate more is that I won't always come up with the answers - at least right away. Sometimes we come up with positions that we just aren't sure what to do with. 

This could be in the opening. You or your opponent may play something that's out of your "book" knowledge and not listed among the various resources - e.g. databases, books, etc. You can spend some time and try to figure out the best response, but if after a reasonable effort you are still confused, it is okay to let it go for now.

Similarly, your analysis (perhaps with assistance from a chess engine) might reveal two or three viable moves in a middlegame position. It's okay if you can't decide which one is the best. Let it "simmer" for a while - maybe even months or years.

Sometimes, our future experiences and studies will cause something to "click" in our minds and what was once confusing now becomes very clear. This is the power of our mind to connect related information over time.

By learning to accept uncertainty in our conclusions, we can avoid some of the frustration that results in trying to find "the best moves" in our post-mortem analysis. All of this being said, it's important to put some effort into finding some answers, as we may encounter a similar position in the future and our efforts in the present will aid us when that happens.

Below is a video of the third and fourth steps of the game analysis process:


Time Constraints and Practicality


Finally, I wanted to share a insights that I've come to realize in studying chess that encompasses the game analysis process in general.
  • You won't often have time to do game analysis process in-depth. It's okay to focus on just a few areas in your games.
  • You may tend to spend more time analyzing your wins than your losses - resist this urge and seek out your weaknesses (if you are looking to improve).
  • Analyzing for your own improvement is different than analyzing and annotating for publication or for other people. It's okay to be sloppy or use phrases or jargon that only you understand!
  • Celebrate the insights you garner from your analysis - even the smallest of discoveries!
  • Organization is both overrated and underrated. Find a system that works for you. Check out my article on workflows for some ideas.
  • Seek answers as if you will be seeing your position in a World Championship match, but accept that you may not have all the answers right away.
  • Don't do step 3 (corrections) on the same day that you play the game...sleep on it to gain objectivity.
  • Some analysis of a game is better than no analysis. Try to find just one thing that you can improve if you're short on time.

Conclusion


I hope you found these reflections on the game analysis process helpful in your own game analysis. The four step process I wrote about is just a template. As I've studied chess over the last few years - squeezing time in between three children, work, and home responsibilities - I've realized that sometimes we need to take short cuts and truncate elements of the process. 

However, I've also realized the importance of analyzing my games, so I wanted to encourage you to keep up these efforts in your own training.

Until next time, I wish you Better Chess!

15 comments:

  1. PART I:

    Bryan,

    I watched the original video and the subsequent two videos explaining the analysis process you use. I think your suggestions for analyzing games are excellent!

    That said, I would like to critique your play, with your permission. I realize that it's very difficult to play and comment at the same time. I also realize that there may be considerable thought going on "out of sight" that does not get commented on. If I seem harsh, I don't mean to be. I've put the gist of your comments between parentheses; my observations are between brackets.

    Overall, I got the impression that you were playing move-to-move. Very little of your time seemed to be spent on concrete analysis. A move would be made, perhaps on general principles, without investing very much time in "seeing" the consequences of your intended line of play. You also seemed to jump back and forth to whatever seemed to grab your attention on the spur of the moment. Your "plans" seemed to be extremely short range, based more on generalities rather than specifics.

    From my own experience with the Colle, I thought you erred by switching to trying to control the c file, instead of advancing e4. The e4 move doesn't give you a Kingside attack (necessarily) but it does provide for some possible breaks in the center. It also is almost essential for creating possibilities for the White Bishop when it sits on b2. Otherwise, that piece is going to be severely restricted in what it can do by the pawn chain f2-d4. With the Bishop on b2, the Zukertort idea seems more feasible. Since you acknowledged that Black normally plays on the Queensde, it didn't make sense to consent to just holding the Queenside.

    I realize that you were attempting to control the Queenside, especially the c file, but the exchange of both sets of Rooks might have made that moot. While watching the original video, I noticed the tactical shot 21. Qc6! (before Black gets his Bishop to d6). Black cannot exchange Queens without allowing the newly minted c6 Pawn to promote because the Black Knight has insufficient room to maneuver. This would have been a big accomplishment and given White much better chances than the game continuation.

    There were a couple of generalizations that I found puzzling. One was that you had the advantage throughout most of the game. At best, I think the position was mostly balanced. Black had a little more freedom of movement, especially because of the miserable White bishop. There were several times when you were surprised by Black's moves, and yet those moves seemed fairly obvious, not requiring a lot of calculation.

    Given the "bad" nature of your Bishop, I thought you were in trouble going for the endgame. I noticed you classified the Black Pawn at d5 as "weak," yet you had no way to attack it. As the endgame progressed, you thought that the Bishop was dominating the Knight, when it appeared to me to be the exact opposite. The Knight was centralized on a protected outpost, and the Bishop was just hitting "air."

    I did not understand why you went into a forced line that allowed Black to get another outside passed Pawn on the Queenside. I think you could have kept the Black King out of the position by not forcing the a4 Pawn forward.

    You didn’t seem to understand that the White King was prevented from ever attacking the Black Knight and h Pawn with the f3 Pawn in the way. The problem is that the White Bishop was needed to stop the h Pawn, and the White King was needed to stop the b Pawn. Unfortunately, due to the domination of the relevant Kingside squares by the Black Knight, there was no easy way to get the White Bishop to the Kingside. As a consequence, the White King could not leave the square of the h Pawn. The consequence was that the Bishop had to be sacrificed for the b Pawn, and the White King was stuck waiting for the inevitable execution once the Black King returned to kill the f Pawn.

    I would like very much to get your thoughts on these comments!

    Thank you!

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  2. PART II:

    Bryan Castro (bankrankbrawler) 1823 vs. seeingoa 1826 - 28 APR 2017

    1. d4 Nf6 2. Nf3 c5 (A Benoni structure) 3. e3 (To keep my center) b6 4. Bd3 (I like to play the Colle with White) Bb7 5. O-O g6 6. Nbd2 Bg7 (I could play e4 here, after c3, but another idea is to set up a Stonewall formation with Ne5 because Black hasn't played the b8 Knight yet. I usually like to play that after Black has played d5. I want to play c3 first.) 7. c3 O-O 8. Re1 (with the idea of playing e4) d6 (The other idea is to attack on the Queenside with b4. Go with the b4 plan rather than e4, because there is no threat of e5. Consideration of Bb2 followed by Rc1.) 9. b4 cxb4 10. cxb4 (No tactical threats so far. I'd like to play e4 at some point, to control the center a little more.) Nbd7 (He wants to play e5. That's when I could push e4. Bb2 helps to protect e5, prevents an immediate e5 because of loss of a Pawn.) 11. Bb2 Rc1 (Qe2 is interesting here, hitting the Bb7. I don't want to play Rc1 because he takes and forces me to retake with the Queen.) 12. Qe2 Rc7 (A little worried that he will double on the c file, but he cannot get his other Rook to c8.) 13. Rac1 (Black's play is on the Queenside; must be aware of what he can do there.) RxR 14. RxR (I now have control of the c file.) Qa8 (Analysis of Ba6. If he takes Bxa6, I will have control of the c file. Rc7 may be good; Black pieces on the 7th rank are covered. If I could get my Queen behind the Rook on the c file, that would be good.) 15. Ba6 Rc8 (The c file may be fairly important; can I win control of it? My Bishop on b2 is better, so take on c8 first.) 16. RxR+ (Now sees that "this works out" because of Qc4. Stated "move to Qc5" twice, instead of Qc4. Speculation of what to do now.) QxR 17. BxB QxB 18. Qc4 (How to get my Bishop into play without allowing his Bishop to get into play?) d5 19. Qc2 (Black has now given me the e5 square.) e6 (Ideas: a4. Need another plan for my Bishop, like b5, maneuvering the Bishop to a3 and then d6. Sees Black playing Bf8. Looks at Ne5. Rejects a4 because of ... b5.) 20. b5 (Threatens Qc6, creating a passed Pawn.) Bf8 21. a4 (Bolster the b5 Pawn.) Bd6 (Contemplates e4, with Kingside attack.) 22. Qc1 (Trade off the Bishops, but that allows Black to get his Queen on the c file.) Kg7 (Black is planning for the endgame. I can bring my Knight around [to the Kingside] but it doesn't seem to do much. Bring it to b1.) 23. Nb1 (Gives Black the e4 square but gives him no penetration. Very important to keep control of the c file.) Ne4 24. Ba3 (Once I trade off the Bishop, Qc6 is important. He really can't take on a3.) Qc7 (Surprise! The position is fairly even. Does it help me to get his Bishop off the a3-f8 diagonal? I don't want to vacate the c file, so I'll take.) 25. QxQ BxQ 26. Nbd2 (Now I'm going to attack Ne4 and bring my King in. This endgame is pretty even.) [26. ... Nc3 wins the a4 Pawn. WHite cannot get his King there fast enough to trap the Knight on a4. 27. Kf1 Nxa4 and White has to figure out how to keep the Knight off c3, taking the b5 Pawn. 28. Nb1 Nb8 with 29. ... a6, freeing the Knight with an outside passed Pawn; Black is winning.] NxN

    (continued)

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  3. PART III:

    27. NxN (So now Black can't bring his Bishop back to d6.) e5 28. dxe5 (I don't mind taking this because now his d5 Pawn is weak but might not be enough for White to win but definitely gives White an edge. etaking with the Bishop is "okay for Black" but I can pin if he takes with the Knight.) Nxe5 29. Bb2 (It's not going to win material but it's not great for Black.) f6 30. Nb3 (I'll bring my Knight to d4. If I can get my Knight to c6, that will be great.) Nc4 (Surprise! Oh, I'll have to be careful.) 31. Bc3 (I'll ry to restrict his Knight to keep him away from the a4 Pawn. I also can attack with a5.) [Overlooking that a5 is protected 3:2 by Black, and also overlooking that Black wants to trade of the Bishops] Be5 (He wants to trade; do I? If I capture and he recaptures with the Pawn, I fix his Pawns.) [Not really; there is always a potential breakthrough on d4.] (Bd4? Does Nd4 pin my Knight? If he exchanges, my Bishop should be better than his Knight in the endgame.) 32. Nd4 (I can play f4 next, followed by bringing my King into play. This forces Black to make a decision.) Bxd4 33. Bxd4 (I now dominate his Knight.)(Actually, the Black Knight now dominates the White Bishop, which is somewhat restricted by his own Pawns.) Kf7 34. Kf1 (Now I can bring my King in.) Ke6 35. Ke2 My King cannot be attacked, while I can undermine his Knight. I could play Kd3, followed by e4, or play a5 - except his Knight is covering that square. It's not a won endgame for White but with Pawns on both sides, the Bishop can do quite well.) Nd6 36. g4 (? He wants to play Nf5, so I'll prevent it. I'd love to play a5 or h4.) f5 37. h3 (??? That's fine; I'll just do this.) [LOSING BY FORCE!] fxg4 38. hxg4 (Now Black can get an outside passed Pawn but I'm not too worried about that.) [This should have been "seen" BEFORE throwing the g Pawn forward!] h5! 39. gxh5 (Let's try this and analyze it later.) gxh5 40. f3 (To prevent Ne4.) Nf5 41. Bc3 (I don't want to trade the Bishop. Now I can play a5, but my main concern is stopping the h Pawn.) Kd6 42. Bb4+ (Check and push him "back".) Ke5 43. Kf2 [Overlooking that the White King cannot attack either the h Pawn or the Knight: there is a "box" {g3, g4, h4} keeping the White King at bay. Checking on c3 keeps the Black King out.] d4 (The "problem" Black has . . .) 44. exd4+ (I can contemplate coming around . . .) Kxd4 (Surprise!) [White apparently does not "see" that the Black Knight is totally dominating the White Bishop.] 45. a5 (?) (I'll force him to take because his Knight won't get back in time.) Kc4 46. axb6 axb6 (He has to take back, and then I can retreat. Unfortunately, I didn't "see" that he wins the b5 Pawn.) 47. Bf8 (Gets the Bishop out of the way.) Kxb5 48. Kg2 (I need to "attack" this Pawn.) [HOW?!? The White King is in a box of his own creation.] Kc4 49. Kh3 (Now we are fighting for a draw. Going to have to sacrifice the Bishop . . .) b5 (Finally realizes that he can't get in with the King.) 50. Kg2 b4 (I think this game went from even to losing.) 51. Kf2 (Bring the King over and see if it can help.) b3 (The Bishop can cut across and help.) 52. Ba3 Kc3 53. Ke2 (His King will be a little bit out of the action. It's probably losing.) b2 54. Bxb2+ Kxb2 55. Kf2 (I need to defend; it should be lost.) Kc3 (He can just brng his King in.) 56. f4 Kd4 57. Kf3 (If he moves his Knight. . .) Kd3 (This is the problem here.) 58. Kf2 Ke4 59. Kg2 Kxf4 60. Kh3 (My last hope here is some type of stalemate, but. . .) h4 61. Kh2 (Probably not gonna happen.) Kg4 62. Kh1 Kg3 63. Kg1 h3 64. Kh1 (Maybe he will!) Nh6 65. Kg1 Ng4 (All I have to do is take his Pawn.) 66. Kh1 Nf2+ 67. Kg1 h2+ (That pretty much should do it.) 68. Kf1 h1(Q)+ 69. Resigns

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  4. PART IV:

    My apology for the typos. I corrected them, but somehow copied the uncorrected version into the comment block.

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  5. Thank you Robert for your analysis. Not to excuse the mistakes in my play, but I found it quite difficult to play and comment at the same time and this particular time control is very fast for me. Most of my games (both online and OTB) are at least G/45 or G/60.

    Regarding the Colle...in my set-up against the King's Indian, Benoni, or Gruenfeld pawn structures, I shift my play to the queenside, as the fianchettoed bishop makes it a little harder for the characteristic Colle attack on the kingside. e3-e4 is definitely always a possibility, but with Black's characteristic pawn levers at ...c5 and ...e5, my focus i typically in making those more difficult. There are specific lines I've worked out with my coach against these set-ups, and although I am still learning them, there is a demarcation between positions where White plays ...g6 (Benoni, KID, and gruenfeld) and when he doesn't (traditional Colle posiitons after 1.d4 d5) with different strategic nuances.

    My endgame play was not very good and in subsequent analysis (some included in the third video in the series), I noted my ill-fated decisions.

    My general analysis led me to believe that the game was fairly even for the most part until I decided to play a5 at some point...there were several lines that I played out against hte computer where I lost one of my pawns on the queenside in the endgame but was able to hold because of hte bishop's mobility - these positions usually occurred after I had played f4 thought (as now my king had access to the f3 square). Again, this was very quick play for me.

    Not to make excuses, but I think being a little nervous contributed to my superficial view on a lot of the positions. I was a little mortified myself. However, some of the comments you make as well as my own observation of my play illustrated perhaps a few holes in my knowledge of this opening as well.

    You make a lot of other insightful comments that I will have to study further. As I mention several times in these videos, this particular game was not my best effort, but I had to have something to work with and the goal was to illustrate going through the game analysis process.

    Of course, I am the first to admit that I have a lot to learn and this is an example of that.

    I will be doing more videos of my play and hopefully I'll be more comfortable commenting on the fly where the play will be more representative of what I might do without commenting.

    Thank you for your comments. I hope this reply is understandable as I jumped to the middle to write a few comments after glancing at your analysis.

    Lastly, it is important for me to have humility and look to improve myself, so I appreciate you taking the time to analyze the game.

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  6. Overall, I thought you did a good job of playing and commenting. Practice may not make perfect, but it certainly should make it more comfortable to do both at the same time. I look forward to your efforts in the future.

    I'm always hesitant to make constructive criticism of another player. So much goes on "inside" that it's not always evident or obvious as to what is really going on. I infer from your rating that playing in generalities is not your usual way of thinking.

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    Replies
    1. Well, there were (and are) a few things at work. First, I tried to give the thoughts as they came, but there is a bit that goes on between my ears that doesn't get said. That being said, that particular game (and 15 mninute games in general) I tend to play almost like blitz, so you were somewhat accurate about my playing move-to-move.

      In a way though, whether or not I got 100% of my thoughts out through the video (and future videos), what does show is instructive for my own development.

      I am a big believer in transparency, Robert. What I mean by this is that although I write about getting better at chess, I am not worried about the fact that I have a long way to go myself. My friend and coach Nigel Davies noted that my "self-honesty" is a strength and helps me to be in a position to relate advice to others as well as help me relate "with" other players.

      That being said, I appreciate you pointing out any mistakes I may have made an any apparent "thinking process" errors I may be making. Although it is not fun to make mistakes, we all need to make many of them if we are to improve!

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  7. Hi Bryan!

    I also think it's helpful that you are so transparent with your thinking because it lets us comment on it, if nothing else. hehe.

    I don't think you should put in annotations which are subjective, which don't relate to the position at hand. I used to note whether I was hungry, full, tired, exercised or non-exercised, caffeinated or not, etc. Turns out that this misses the point. If you were hanging off a cliff with two fingers with an airplane propeller gnawing at your back and bleeding-out, it still wouldn't excuse only looking two moves ahead in a position that absolutely required looking three moves ahead, for example. hehe.

    It's more of a time-saver to be concrete, to get there as soon as you, can and list candidate moves only when you reach that mode, IMHO.

    So, in terms of playing b4 vs. e4 in the Colle, fuhgetaboutit. Most players at the top level are getting no advantage out of the their openings. That's useful for your opening prep for next time, but not central to what happened in your game/s.

    Likewise, we all have rationale's for why we got into a position, and in large part they may be based on panic and worry. The key is what you decide to do once you are in that position, not whatever crazy or non-crazy reasoning might have lead you there in the first place.

    When you stopped at a couple of positions in your video, I got really concrete with my reasoning and lines, rather quickly, while balancing the abstract ideas on a holding point in the meanwhile.

    I do agree that it's important to at least temporarily note a key concrete line that you had considered while playing. That may be more useful to you later than anything else going on at the time. In my last game the sun was in my eyes, and later my opponent and his mom stood against the window to block it. lol. Unfortunately, that had nothing to do with the problems I faced on the board and why I got there.

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    1. Thank you for your response, LinuxGuy.

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  8. Bryan,

    I forgot to point out something that MAY have been obvious in my comments.

    I tried to capture YOUR thoughts as closely as possible to what you commented. I did synopsize them somewhat in places. I think there is much more "food for thought" for your improvement in your own comments rather than any of my general observations.

    I certainly do appreciate your intellectual honesty and willingness to suffer the "slings and arrows of outrageous commentary" in order to improve! In that regard, you are very much like Temposchlucker (which comparison I consider to be a great compliment - to BOTH OF YOU). It's the primary reason I enjoy reading what you both write!

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    1. Thank you, Robert. I always appreciate your contributions. I don't intend for this site to be a personal journal of my own improvement, rather a resource for others...however, sometimes it is helpful to share of one's own journey as well.

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  9. Whether (or how) to use computers in analysis is something I've been struggling a lot with lately. Currently, I advise my students not to use computers at all, but I'm not too confident in that.

    My rationale starts with the question, What's the purpose of analysis? It seems to me the purpose must be to improve our in-game decision making. Viewed through that lens, computers aren't necessarily very helpful. If our goal were to know with a high degree of certainty which moves in our PAST games were mistakes, computers would work pretty well for that, but that's not really what we're going for. We want to know how to make better decisions in our FUTURE games. And having the engine on encourages us to shut off our thought process for doing that.

    So that's basically my argument against using computers. It's better to practice your own decision-making, even if it's flawed, than to short-circuit it by just looking at computer moves.

    I think the idea of people who use computers in their analysis is they will get the right moves from the computer, reconstruct the logic behind them, and implement it into their decision-making process. In my experience though this is highly unrealistic.

    Nonetheless, I've noticed computers do give something very valuable in analysis: a sense of resolution/completion, i.e., we know more now than when we started. A big problem with analysis for players who aren't already very strong is, the moment you dive in, you get into a thicket of confusing variations that seem impossible to analyze. Even if you spend hours analyzing a game, you may feel no closer to understanding it. This is very demoralizing and may cause someone to stop analyzing altogether.

    This is a real problem, but I think the sense of resolution you get from a computer is largely illusory, or at least not very helpful for improving. Possibly a better solution is to prepare your analysis as a presentation to a friend or coach. Then there is an end to it, even if it's not perfect, and you can receive a critique on what you've done.

    That's where I'm at right now, but I think this is one of the trickiest parts about trying to improve at chess.

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    1. This is definitely a tricky aspect which is why I tried to be cautious in my treatment of it in the videos.

      I've tried to cut it out quite a bit in my own analysis partly because I've noticed that I've become a little dependent on it a couple years ago.

      However, I do think they have their place. The question is whether an individual player knows when and how to use one to best effect.

      This perhaps is a topic for another article perhaps. Would you be interested in a little interview/discuss about it for a future article, Nate?

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    2. Sure, feel free to contact me at nate dot solon at gmail dot com

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