Freedom versus security

In my previous post I described the three main components of piece activity (mobility, freedom, and coordination). While there are some minor points I will add to the final version, it seems to hold up to a second-look.

Making the dimensions of activity explicit, especially the 'freedom' dimension, has helped me get a better grasp on certain positions (roughly, a piece's freedom is the number of squares to which a it can move while still carrying out its important defensive roles). This concept of freedom can subsume a lot of seemingly disparate ideas under its heading. Here are some examples:

1. Overloaded piece. A piece is not all that free if it is defending against one threat, but when it has to defend more than one threat, its freedom is especially curtailed, often being reduced to zero.
2. The knight/knight lock. Many people like to put two knights so they are defending each other. This is a solid formation, but at the same time it limits the freedom of each knight. This was first pointed out to me in Josh Waitzkin's lectures provided with Chessmaster.
3. Pawn chains. While pawn chains are solid defensively (except at the base, and except for the fact that they can create a weak color complex), the pawns in the chain are giving up some freedom for this strength. Move one pawn and the enemy is given undefended pawns.
4. Pinned pieces. This was in the original post, but I find it a very useful way to think of why, exactly, pinned pieces are bad. It has spurred me to work hard to break pins whenever reasonably possible, rather than wait until it is necessary to do so.
5. Winning won games. They say, when you are ahead in material, to play defensively (i.e., safely), avoiding blunders until you simplify down to a won endgame. There is a tradeoff between safety and security, and when way ahead, this means it might be a good idea to sacrifice some freedom, stay in a secure formation (e.g., knights defending each other), and trade down when possible.

What this exercise has taught me, besides what piece activity is (before I ran all three activity subfactors together into an ambiguous pile, which hindered my ability to explicitly evaluate a position), is how useful word-based explanations can be. While examples are nice, and crucial, having them fit into a framework helps sort them into memory in ways that are more likely to stick. I think most of us have noticed this with tactics (forks, pins, skewers, etc), and the same should be true of the strategic themes.

I'm sure this is all common knowledge to the good players out there, but to me this is like discovering a new island of ideas in the chess world.

By the way, Howard Stern said he reached 1599 at ICC. Considering he's only been playing about a year, that is really bloody impressive. I'll see about finding the audio.

Piece activity (suggestions wanted)

The following is the section on piece activity from my 'chess thought process' manuscript (a drastic revision of the previous version). I'm including it hoping to get constructive criticisms (suggestions for additional subfactors, disagreements with the descriptions I've included, anything).

PIECE ACTIVITY
Piece activity is the most important strategic factor. There are three main dimensions of piece activity: mobility, freedom, and coordination.

A piece's mobility is the number of squares to which it can move. This is a simple subfactor to calculate: simply add up the number of such squares (e.g., a bishop cramped in on all four sides has mobility of zero). Also, note that all mobility is not created equal. The most valuable real estate is on your opponent's side of the board, where you will be able to generate the most threats. This is why it is so useful to have pieces (especially knights) in the center of the board.

Mobility is inextricably tied to pawn structure: the pawns determine which bishops are good and bad, which files are good for the rooks, where the outposts are for knights, etc.. Often a simple pawn move will free a piece from its prison or give a knight a sweet outpost in the center of the board.

The second activity subfactor, freedom, which is the number of squares to which a piece can move while still carrying out essential defensive roles. Even if a piece technically has high mobility, it could be tied down to playing a passive defensive role. A pin against the king leaves the pinned piece with no freedom to move from the line of the pin.

The third subfactor, piece coordination, is the most subtle dimension of piece activity. Pieces are coordinated when they toward a common goal. For example, one piece may attack an escape square of the opponent's king while another piece is poised to put the king in check. If your pieces have high freedom and mobility, but are not working in concert for an attack, then consider how you can increase their coordination. Goal examples: coordinate an attack against the f7 square to weaken the opponent's king, hammer at the c-file by forming a rook battery.

When evaluating a piece's activity it is often helpful to consider where it 'wants' to be on the board (e.g., a Rook wants to be on an open file). Often it would only take a move or two to get a piece to its most natural square, and often the trajectory involves making threats along the way. If there is a piece that is especially low in activity, increasing its activity should become a priority. You don't want it pathetically watching from the sidelines when an attack starts.

Do not blunder! (or, Check for threats!)

I have recently found that when I loudly (in my head) remind myself 'Do not blunder!' after my opponent moves, and right before I move, it seems to actually work. I seem to make fewer blunders when I do this, as the admonition forcefully reminds me to look for tactical possibilities before worrying about subtle strategery, and to blundercheck before making my own move.

Note added 2/25: for those who prefer to put things positively, 'Check for threats!' is a good one. I've switched to that.

Initiative/flexibility: how the computer should help

When going over games with computers, flexibility is one factor for which they provide no feedback, but is extremely important for human practical play. Given two moves to which Fritz gives the same evaluation, if one leads to an extremely sharp position for the opponent, and the other leads to an extremely flexible position for the opponent, then the former move is better (all else being equal). Conversely, if one of the moves leads to an extremely sharp variation for me, so that I have to walk a tightrope for the next 20 moves to end up with the same evaluation, that is much worse than a move which leaves me with a great deal of options in the follow-up. The fewer options you have, the more likely it is your opponent will be able to take back the initiative.

Fritz and the other programs should give us the option of displaying a flexibility measure in their evaluation function. There are many ways it could work, any of them being trivial to implement.

Most helpful for humans, the response-evaluation graph. For each move being evaluated, show a graph of the evaluation function for the responses to that move (on the x-axis is each response, with the best being on the left, and on the y-axis is the evaluation function for that move). Recall in interpreting such graphs that the best response will not change the evaluation but keep it the same, so the response-evaluation graph will have the same value as the present position where it intercepts the y-axis, and then will only go up (if it is presently white's move) or down (if it is black's move). If the graph has a sharp and fast change close to the y-axis, then you are putting your opponent on a tightrope and should weight the move more highly than a move that is given a similar numerical evaluation but with a flat response-evaluation graph. Programmers might use the derivative of the graph to help them make algorithms against human opponents.

Another possibility is the more computer-friendly flexibility measure F. First, set some threshold value, call it T. In addition to giving the numerical evaluation of each possible move, Fritz should tell you how many follow-up moves there are by your opponent that are within T of the computer's evaluation of the present position. Call that the flexibility measure F. For example, assume you are playing white and the present position is given a 0.3, and let T=0.5. Say the best move Fritz finds is given the evaluation of 0.3 but F=10 (your opponent has ten responses that will be between 0.3 and 0.8). Your second-best move is given 0.25 but F=2: that is, your opponent has only two moves to stay between 0.25 and 0.75!

Such flexibility measures would be helpful in many ways. When building an opening repertoire, pick moves for which F is very low for the opponent. Also, it will give you an idea of which opponent responses you need to book up on: those moves your opponent makes that leave you with little flexibility. All of the same could be said for evaluating middle and end-game positions. This could help explain why good humans often disagree with computers, and why we can't blindly follow the computer's numerical evaluation.

Circle 3.2 done

Tactics tactics tactics....This is a great program.

	# Circles	Percent Correct
Problem Set 1	14	98-99-100-100-100-100-100 100-100-100-99-100-99-98
Problem Set 2	15	90-93-96-99-99-99-99-99 99-99-99-99-99-99-100
Problem Set 3	2	85-93
Problem Set 4	0
Problem Set 5	0

NOTE: Circles undertaken with CTB.

Adding to the tactical toolkit

Based on a suggestion from my coach, I have been playing more blitz to give me more experience playing chess and hopefully improve at tactics. Each day, in addition to my Circles with CTB, I am playing a minimum of three blitz games at ICC and analyzing them afterwards with Fritz. Not closely, not deeply. I analyze them solely for tactical oversights on my part (blundercheck mode). When I find them (usually there are a couple per game) I study them for a little bit. This Patrick Method^TM of studying tactics in the context of games, indeed my games really burns them into my head. Mistakes stand out much more when they are your own rather than those of some dead white dude.

So far, there are two weaknesses that consistently pop out. When my material is pinned, I often play as if it weren't. I don't flat-out move the pinned piece, but I don't take the pin into account when considering moves of other material, moves that will ultimately affect the pinned piece. Second, I don't consider checks enough. Often a check is the perfect way to break a pin or to flush out the enemy king for a clever series of forced moves. 'Patzers sees check, patzer makes check' may be true, but so is 'Patzer doesn't consider check, patzer doesn't make check.'

I should finish minicircle 3.2 this week. That means in a couple of weeks things are going to get very intense, with 100+ problems a day and eventually 300 problems a day.

Chess Tactics Server: Some Data

Originally posted 12/05

I couldn't sleep, so I thought I'd do a little analysis of the data at the Chess Tactics Server (CTS). CTS has engendered more than a little interest amongst the Knights, especially in our intrepid Temposchlucker, whose mania in problem solving can only be described as insane. I got the data from all members who did more than 100 problems in the last month, and plotted rating versus number of problems solved. The scatter plot is here, where the x-axis is number of problems solved in the last month (on a logarithmic scale: most people have done a lot fewer than 1000 problems) and the y-axis is the rating:




The blue line is the best linear fit (slightly curved upward toward the right because of the logarithmic scale on the x-axis), the red dot is Tempo's rating, and the green dot is Jadoube's rating. Note that Tempo is right on the line: he is about at the average for people who have done ~5000 problems in the last month, while Jadoube is a bit below the line, as he is a bit below the average for people who have done ~2000 problems in the last month.

A couple of things to notice. The correlation coefficient of 0.09 is small but significant (p<.05), and the slope of the line is ~0.0132. Interpreting this is difficult, but it suggests that ratings are not strongly influenced by problem frequency. This is pretty clear by inspection of the data, which shows no clear upward trend. One possible interpretation is that for every thousand problems you do, you can expect to improve by 13 rating points. This is significantly higher than Tempo's fun estimate of 2.4 points/1000 problems which he hopes to gain in his training. On the other hand, interpreting such graphs is always problematic: it is likely that solving more problems is correlated with higher motivation to improve as well as other chess efforts which CTS doesn't measure. Remember, correlation does not equal causation: I could do 30000 problems in a month while watching TV, and have a rating of 10.

At any rate, I just geeked out during a bout of insomnia.

Lines of vulnerability, QGD, and CT-Art

A couple of other points I don't want to forget about the lesson this week. In a tournament game we went over, I missed a beautiful pin. Coach urged me to imagine not just lines of force emanating from my pieces, but lines of vulnerability from my opponent's pieces. E.g., imagine lines radiating outward from the enemy king, traversing through all the pieces on the board. If that line only intersects one enemy piece, that means a pin might be possible. You get the idea. I'll start trying out these visualization tools in real games.

Also, we've decided I should play the QGD rather than the QGA. This is somewhat of a relief, as the QGA seems like something I should put off until I am have matured more at the game. I got McDonald's book Starting Out: Queen's Gambit Declined, which seems like an excellent introduction. He even explains why in certain lines h6 is played and in others it is not.

I glanced at all the QGD games in Chernev's Logical Chess. There are 10 such games (almost a third of the book!), and every one of them is a win for white. This shows he did not put enough effort into choosing his games. QGD is a solid opening for black, and there are plenty of wins (or at the very least draws) from which he should have chosen. Given his proclivity to describe the game from the winner's perspective, someone reading his book would think the QGD is a slam-dunk for white.

Also, as part of my upping the tactical intensity, I have started working on CT-Art to supplement my circles with CTB. At level 10, the problems are about the same level of difficulty of those in Stage 3 of CTB. When I first began all this, even Level 10 CT-Art was a bit much for me. This is encouraging as it shows I have grown tactically, but I must remember that I am still but a wee pup.

Tactics, and also, tactics

The lesson tonight was good. Games reviewed, and we played a bunch of games to give coach a sense for what I need to work on. He suggested I need to work primarily on tactics, and that I should supplement it with some tactical study, and finally that I should add a little bit of tactics just to round things out.

Seriously, though, that was my most glaring defect. He said I was playing very well for my rating, but that I was missing tactics. He said that tactics are hard to teach, since the way to get better at tactics is just to do more tactics. When I told him I was doing the circles, he thought it sounded great (he hadn't heard of them before) and said that was exactly what I should be doing.

He also had a somewhat iconoclastic suggestion for getting better with tactics: play lots of blitz games to gain more experience. The thought of ending up like those players with 30000 blitz games at ICC rated 1100 scares me, though. It isn't clear how much they have learned by just playing lots. I'll chew on that one. At the very least, this motivates me to redouble my tactical study, and I may cut back on the chess lessons (once every two or three weeks) until I am tactically more proficient.

As Stean points out in his great book (extended beautiful quote given here), this is the natural progression.

Incidentally, coach is rated 78^th in the country. Damn.

Changed my mind

In my previous post, I said I was going to switch from the Two Knights to the Giuoco Piano as black. I've changed my mind, at least until there is a decent opening book, from black's perspective, on the Giuoco. The line that starts with 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4! is incredibly tricky for black, and frankly I have enough on my plate right now learning to play the Ruy as white. So, for now, I will stick with the Two Knights. I am familiar with it, so it won't take too much work to give it a spit-shine. Sure, I may end up a pawn down after 4. Ng5 (etc), but perhaps this will help me learn about initiative.

One of my favorite opening books, Emms' Play the Open Games as Black has five chapters on the Two Knights. Sweet.

Rule independence in the openings

It's time to start studying openings again. Not to the exclusion of all else, not even more than all else. After three weeks of not studying openings at all, after focusing on general "rules" for opening play, I have gotten worse in the openings. And I am taking more time to make my moves. What a useful combination!

John Watson, in Secrets of Modern Chess Strategy talks about how the GMs constantly break the classical "rules" of chess when the situation demands it. E.g., it is sometimes the best move is to put a knight on the edge, to move a piece twice in the opening, or to give up the right to castle. He describes this situation-responsive play as 'rule independence.' And that's what intelligent chess is: it is the formation of a plan based on an evaluation of the concrete position in front of you. Paraphrasing Patrick, the rules (and patterns) merely suggest plans, but concrete analysis tells you what the best move is, what plan should be followed.

So, why study openings, why not just analyze the concrete position in front of you in the opening, using the rules as mere useful suggestions? I can think of lots of reasons. The following are in order of importance:
1) I simply enjoy studying the openings. Why deprive myself of that? Rule-independent doesn't mean I can't study them on my own time, that I need to figure everything out for myself OTB.
2) To save time in games.
3) Avoid annoying traps. While such situations are really just tactical, that doesn't mean I'll see them before they are sprung on me!
4) I have improved at chess, and I am starting to see more varied and hard-to-handle openings. I want to know about them.
5) The opening is the only position that occurs in every game. Study it well, young grasshopper.

My plan: I am not going to study deep, but broad, following Heisman's approach in this excellent article. It is similar to Sancho's sketch pad approach. Note, J'adoube has a discussion of these general issues here, written in his usual understated style.

As for specifics, I'm overhauling my repertoire in a couple of key places. I'm giving up the Bishop's opening for the Ruy Lopez. As black I'll play the Giuoco instead of the two-knights' defense. I don't like the two-knights. The proper response to the Fried-Liver attack is basically to give away a pawn and destroy your pawn structure. While the Giuoco has a boring reputation because of its symmetry, as black I just want to make it to the middlegame with a reasonable position. The two knights doesn't let me do that. Also, Watson's new book has good coverage of the Giuoco. This will be a good opportunity to use his book. (Tak: I don't want to play the Traxler :)).

This is fun. Note this is partly inspired by my tournament games (and this weekend I went 0/3, which I don't even want to talk about right now).

It's what ya' know that kills ya'!

I had a lesson tonight. We went over my games from last week's tournament. I had two main problems. One, I need to think ahead, play real chess. I got tired and stopped blunderchecking (hung a rook) and looking for elementary one-move tactics. This is just sloppy and lazy. Second, I was weak in developing my pieces to their best (most active) squares, overlooking active/threatening development because of my overcautious nature.

Quote for the day from Heisman (and my original motivation for using a thought process): "Ask yourself the following question, “Of all the games I have lost recently, what percent were lost because of something I did not know, and what percent were lost due to something I already knew, but were not careful to look for?” If you are like most non-advanced players many, if not most, of your losses are due to a tactical oversight on a pattern that you already knew: putting a piece en prise, miscounting the safety of a piece, missing a simple double attack or fork, allowing a back-rank mate, etc. Since you already are familiar with those tactics, that means either that you played carelessly, did not practice “Real Chess”, or have no consistent thinking pattern."

I don't need to think six (or even four) moves ahead. I need to consistently look one or two moves ahead! Near the end of a one or two day tournament, even that seems like too much work...

I am enjoying not working on memorizing opening variations. Just focusing on principles is helping me learn more about what makes those "best moves" best, and has me playing more thoughtfully from the start. My guess is that this minimalist approach will serve me just fine until I hit 1500 or so at ICC. Schroer's four principles of opening development are very simple but good (to remind everyone: knights before bishops, move only the e and d pawns, move each piece only once, and develop kingside pieces first). While there are exceptions (3...a6 in the Ruy, and of course dealing with tactical exigencies), they typically lead to a solid position.

I completed the first minicircle of Stage 3 in Chess Tactics for Beginners. These problems are definitely harder than the Stage 2 problems (the image to the left is one example of a mate-in-two with white to move, though I do the problems without the category labels attached). There are some three-move tactics, and much more subtle two move problems (no obvious discovered attacks, for instance). That I still don't instantly see the solution to problems like those above shows I really need this tactical work!

	# Circles	Percent Correct
Problem Set 1	14	98-99-100-100-100-100-100 100-100-100-99-100-99-98
Problem Set 2	15	90-93-96-99-99-99-99-99 99-99-99-99-99-99-100
Problem Set 3	1	85
Problem Set 4	0
Problem Set 5	0

NOTE: Circles done with CTB.