Tips for Calculating Individual Lines (variations)

As noted in other blog posts, last year I reconsidered my approach to calculation and took down my more extensive series on "brute force" calculation.  However, there were many gems in there I am taking out as separate posts as I rethink other elements.  This post on line calculation is one of those gems! [Note: I have updated this now that I have almost finished my more extensive series on the "logic of forced variations"]

After you have identified the candidate moves -- using whatever process you use -- next comes the hard part of actually calculating each individual candidate one at a time.  These are some tips I found in several books on calculation:

• Calculation is like a debate between two people over which move is best, and the variations you find during line calculation are the specific arguments used.  The only way to win a debate is with good arguments, and the only way to select (or eliminate) a candidate move is by evaluating specific variations.
• Within each line you calculate the flow of force can change at any moment, and the attacker can suddenly become the defender, only to then become the attacker.  
• Finish calculating the line completely to quiescence (no more checks, captures, threats).  Do not prejudge the line!  You need to give an actual evaluation of each position at the end of each variation.
• Stay disciplined, and focus only on the current line.  Do not jump to other candidate moves until you finish the one you are calculating.
• Slow down!  Your speed will increase over time.  Go slow to go fast.
• Take time to visualize every move clearly.  If you a reach a complicated position or start to lose confidence, stop and create a stepping stone image.
• When defending, you don't need to calculate all checks, captures, and threats. Only calculate the defensive replies related to the biggest threat on the board using the Five Ideas (see later blog series).
• In fact it is a mistake to calculate moves that do not respond to the threat.  If your opponent created a threat you would respond the best you can, and don't fall into the trap of assuming your opponent won't make the best moves to defend himself against your threats.   
• Which move should you calculate first?  There are two choices.  Sometimes you can eliminate candidates as simply bad -- but you must prove it to yourself with an actual variation and an actual evaluation.  Most of the time you should always start with the MOST FORCING move first.  You find this by quickly counting how many replies your opponent has to each of your candidate moves.  This only adds a few extra seconds, which you often gain back by calculating the most forcing move first.
• Search for your opponent’s refutations FIRST. If you find one, discard your candidate and move on to the next in your list.  To do this, you follow the advice from the bullet above and start by calculating your opponent's MOST FORCING REPLY first.
• Be mindful of how you are tracking material exchanges during calculations.  Are you keeping track of material as captures are made, or are you re-evaluating material only at the end of a sequence?  If you're doing one, try the other and see how it works for you.
• If you're just starting out, keep your evaluations simple and just look at the balance of material and activity.  Over time you will learn how to do more elaborate evaluations based on pawn structure, endgame transitions, etc, but you need to make sure this step of the process is clearly in place first.
• Always have your initial evaluation of the position in mind when you start your line calculations, and compare your evaluations of each line against your initial evaluation, and against each other.
• If your first two candidates give you two good evaluations, pick the better of the two (based on material/activity) and make that your "King of The Hill" (KOTH).  As you calculate the rest of your candidates, compare those evaluations against your KOTH.
• Sometimes you have nothing but bad moves to choose from.  Keep your head, and find the "least bad" evaluation (based on material/activity).  Ironically, this is often an easier choice to make than when you have several good options assuming you can overcome your emotions!
• Try reversing the move order. It works sometimes.
• Whether you saw a specific pattern when you were developing your candidate list or not, your stored patterns will be a huge benefit during this step.  But remember you still have to calculate patterns you see.  And keep track of patterns you frequently miss, and train those until you don't miss them anymore!

Basic Attack and Defense

In previous blog posts I discussed the six checks and the very limited options available to defend, and later I discussed the broader options available to defend against a mate-in-one threat.  Here I want to go back to the basics again and look at the options available to defend against an attack by a piece (or pawn) against a piece (or pawn).

This can be the least forcing type of threat possible because the defender has a broad range of options to consider.  However, the options are not unlimited and the most interesting responses fall into the broad category of counter-attack.

The basic defensive options are very similar to those for defending against check and mate-in-1, with a few additions and expansions. Let's compare the options against checks and mate threats.

When in check, you can:

1. Capture the piece giving check
2. Block the path to your king
3. Move your king

When there is a mate threat, those three options are expanded to:

1. Do something to the piece/pieces threating to give mate (pin, deflect, capture).
2. Block access to the mating square of either/any of the pieces threatening to give mate, or reposition one of your pieces to be able to block the check.
3. Move your king, create an escape square, or move the king to allow a block.
4. Defend the mating square.
5. Counter-attack the king with the goal of:
   WIN - delivering your own mate
   DRAW - forcing draw by repetition, stalemate, or
   DEFEND - rearranging your pieces to allow one of the other basic defenses listed above.

Defending against an attack by a piece against a piece is very similar to defending against a mate-in-1 threat -- the exact same 5 options are available.  The major difference is the much broader range of counter-attack possibilities.  Counter-attacking to win against a mate-in-1 threat can ONLY be an attack against the king that starts with a check.  Counter-attacking to win against a piece threat does not have to start with a check.

Many authors will say you should first try to "ignore" your opponents threat at first, but I would make two points.  First, they are usually talking about broad "attacks" (eg, white's pawn storm on the king side is faster than black's attack down the c file) and not usually in relation to a basic attack by a piece against a piece.  Second, when they say "ignore", what they really mean is to create a greater threat...and that is the key.

Counter-attacks must create an equal or greater threat than your opponent's threat. And vice-versa...if you are considering attacking your opponent, look to see if they have an equal/greater attack they can counter with, and calculate the line to the end.

Some of this is pretty easy, like an attack against a pawn can easily be countered by an attack against anything -- from a pawn all the way up to the king.  An attack against a minor piece can be countered by an attack against another minor piece, rook, queen, or king. And on up the ladder until you get to an attack against your queen, where the options are pretty limited (you rarely want to "defend" your queen against an attack by a rook or minor piece).

One interesting point to remember is that if you are counter-attacking the same target with a piece of lesser value than your opponent is using (say he attacks your Queen with a Bishop, and you counter-attack against his Queen with a Pawn), that is a GREATER threat than your opponent's if the queens are both defended.  If the queens are not defended it is just an equal trade.

But when counter-attacking it is absolutely vital that you calculate, especially when a series of captures is involved (ie, both targets are defended).  I would note that most of the world's top players prefer to counter-attack.  Play through games of Fischer, Morphy, and Kasparov, and you'll find many games were won because they were incredibly stubborn and chose to counter-attack instead of retreating or passively defending.

So the moral is to make sure you consider the full range of defensive ideas availabe when you are under attack or are considering an attack.  These defensive "candidate ideas" should give you a lengthy move list to actually calculate -- then, you will calculate each option to the end, evaluate the final position, and pick the best defensive reply.

Here is one of my favorite examples from a Fischer game in 1968.  Fischer had the Black pieces against Matov.

White is preparing to shift his rook to the king-side, and just moved his knight from c3 to a4 attacking Black's queen -- a nice tempo gaining attack on the queen that will allow Matov to get his rook where he wants it.  Fischer can't capture or pin the knight, can't block it, and defending the queen doesnt' make any sense, so Matov expected Fischer to retreat his queen to c7 -- the only safe square.

But Fischer was incredibly stubborn and attacked White's queen right back with Nc4.  That not only attacks White's queen with an equal valued piece but also discovers an attack against the d4 knight.  Fischer found a way to counter-attack with a GREATER threat!

Right away you can see that White can't go ahead with his threat of capturing the Queen because after 1. Nxc5 Nxd2 both of White's Rooks are forked and he'll drop the exchange.  He now has to defend, so let's look at the basic defensive options for White.  White can capture the knight with 1. Bxc4, but after 1....Qxc4 both of White's knights and the rook on f1 are hanging, and he'll lose a piece.  You can't block a knight, and defending the queen doesn't make sense.  So White retreated the queen with 1. Qd3, doubling up on the c4 knight and renewing the threat of Nxc4.

Black consolidated with a series of equal trades in the center 1....Qxd4 2. Qxd4 Bxd4 3. Bxc4.  So a queen for a queen, and knight for a knight.  All's well that ends well, right?  If you can visualize that final position, can you find the simple tactic that forced Matov to resign?

Highlight for the answer:  [ Fischer played 3....b5 forking the knight and bishop.]

About Stoyko Exercises

There are many articles on google about Stoyko exercises -- what it is, and how to do it.  Basically you find a complicated tactical position that is well-annotated.  Write down everything you can.  You can do it with or without a clock. You can do it by moving the pieces, or only by visualizing.  Compare your analysis against the author's.  

I first read about Stoyko in an article by Dan Heisman.  I was even more encouraged when I saw Kotov recommend it is a training tool, and then what really convinced me was a quote in Chess Visualization Course:

"I believe the most important course of training I undertook was selfmotivated (no one had advised me) and difficult: I tried to simulate tournament conditions with studies and problems from books and magazines. 

I set a clock to time myself, filled notebooks with variations, tried to visualize the final positions – Who was ahead materially? Could I work out the win? Find the checkmate? 

The questions I had asked myself – How can one learn to calculate? How can one see three (or more) moves ahead? – were answered by studying this way, and I became a stronger player." 

Paul Whitehead
FIDE Master and USCF Life Master

After doing de la Maza's Seven Circles more times than I care to admit, I knew I had to try something else so I finally decided to give these exercises a shot.  At first it was incredibly frustrating -- my notes were incredibly sloppy and, I realized, so was my thought process.  So I stopped doing Stoyko and spent a few weeks reading everything I could about the process of calculation.  I developed my ideal thought process which essentially is:  Step 1 - list all candidate moves; Step 2 - calculate each line completely; and Step 3 - evaluate the final position.  I then put it to the test with over a hundred Stoyko positions, and have shared some of my notes from those exercises here.

As noted in that same post I am about to undertake this again as I am currently rethinking my own calculation process.  So I have decided to compile my lessons learned in one place for myself and to share with anyone who might be thinking of doing these exercises for the first time.

The basics:

• As you can see in the link above, I recommend using graph paper.  Tape the position on the paper for future reference.
• Set a timer for more of a challenge.  Don't use one the first few times.  It takes a while to get used to writing down variations while you think.  It slows you down.
• Set up the position on a board.  Allow yourself to move the pieces the first few times.  Visualize the moves for more of a challenge.
• Use pencil for your variations.  When checking your written analysis against the answers, write corrections in blue ink.

What positions to use:

• I strongly recommend you begin with lots of mate in 2 positions for a few reasons:
• Mate in two positions always end in mate (an absolute evaluation), and you know exactly how deeply you need to calculate. 
• Mate in 2's force you to find lots of candidate moves, which is the extremely important first step in calculation.  You completely skip the third and final evaluation step.  
• Mate in 2's still allow you to practice all of the tricks for the second step -- individual line calculation (eg, looking for refutations first, reversing move order, stepping stone positions, pattern recognition, etc)
• Once you have some experience writing variations and have a general idea of the thought process you want to use, you should be ready to move on to more challenging positions where the final position is not always mate.  This will teach you to evaluate (step 3) a variety of material and positional imbalances while also practice finding good candidate moves (step 1) and good line calculation technique (step 2).  Specific books/collections include:
• Hertan's 'Forcing Chess Moves'; Afek’s ‘Invisible Moves’; Soszynski's ‘How to Think in Chess’; Eingorn's 'Decision Making at the Chessboard'; Smirnov's calculation course; and Aagaard's entire 'Excelling at...Series'.
• Do NOT disclose the theme of the position to yourself.  If you know you are looking for a knight fork, you'll skip other candidate moves.  
• Do NOT disclose the final evaluation to yourself.  If you know you are looking to force a draw, for example, you'll skip other candidate moves that don't lead to a draw.

What to do with your notes:

• Compare your analysis against the author's, and write down any corrections in blue ink.  Make sure to review all of the lines you calculated.  If the author skips certain variations check it against a computer.  In two cases I found a better move than the author, and wrote to them with my analysis!  
• Keep a running 'error log' to keep track of (1) what mistake you made, (2) at what ply the mistake occurred, and (3) the lesson learned.  Here's an excerpt from my log:

I would love to share ideas with anyone who has actually done these exercises, so please comment and share your experiences.

Tricks to Create Threats

When calculating forcing lines it is important to look at checks, captures, and threats.  While checks and captures are the easiest to find and count, finding threats can require creativity and can be very challenging.  This is because the term "threats" is intended to cover a broad range of things that aren't checks or captures.  Threats can range from the very clear tactical devices (pins, skewers, remove the guard, etc) to the less obvious strategic themes (pawn structure, better minor piece, etc).  It can even include "threats" to simplify the position into a won endgame, or "threats" to force a draw.

It is impossible in this blog post to cover all of the "threats" that you need to be aware of in chess, but I have found two tricks for looking for mate-in-1 threats and tactical themes:

To find mate threats, pretend that you (or your opponent) can make two moves:

• Look for pieces that are currently attacking squares next to the king (helper). Can you add an attacker (hunter) to any of those squares that can give mate on the second move?
• Or vice versa – look for pieces that can currently give check (hunter) but who just need a helper.

To find tactics:

• Pretend you can pick up ANY piece, and place it on ANY square. Are there any queen forks on the board? Any rook pins? Bishop skewers? Knight forks? If so, look for ways to get your piece there.

So the next time you're running through your exercises or are doing Stoyko positions, give these ideas a shot.  They have worked for me!

Counting Checks and Calculating Replies

When calculating forcing moves you often have to consider checks -- how many do you (or your opponent) have on the board, and how might your opponent reply.  This is very basic, but sometimes it is helpful to reiterate the fundamentals.

First, to count the number of checks it is important to know the maximum number of possible checks each piece can give regardless of the actual position.

Rooks – (almost) always two:

• A Rook on a1 trying to attack h8, can move to either a8 or h1.
• The pattern will look like a square/rectangle, and the two squares will always be ON the board.
• Find both squares.
• If the Rook is already on the same file/rank as the target, it can only have 1.

Bishops/Knights – usually two:

• Bishop and knights can only attack (in one move) targets on the same color.
• The Bishop pattern will look like a diamond, and often one of the two squares will be off the board.
• Knights depend on color AND proximity. A knight must have four or less files/ranks between itself and the target.

Queens – no more than 12:

• Look for three squares on the rank, file, and both diagonals.  Sometimes the squares will be off the board.
• Like the Bishop, the Queen depends on color. If the target is on the opposite color, the Queen can only have two squares on the diagonals instead of three.

Queens by far are the hardest. Always look for three squares on all four lines (rank, file, and two diagonals). I find it easiest to look at along the four lines going out from the target.

Pawns -- maximum of two (one each on the adjacent files)

That gives a maximum of 24 checks (4 from two Rooks, 2 from one Bishop on the same color, 4 from two Knights, 2 from two Pawns, and 12 from one Queen).  

Usually you won't have that many because your knight might be too far away, or you might only have one bishop and the enemy king is on the other color square.  But I find knowing these numbers helps you find ALL possible checks!  

A second very basic but very important issue is the six different kinds of checks.  Some offer the opponent fewer options – and are therefore more forcing – than others:

1. Regular checks – allows your opponent all three replies (capture, block, or move) and is therefore the LEAST forcing.
2. Knight checks – cannot be blocked. More forcing than regular checks.
3. In-your-face checks – cannot be blocked. More forcing than regular checks.
4. Discovered checks – allows your opponent all three replies. More forcing because of the secondary threat created by the leading piece.
5. Capture-checks – allow your opponent all three replies. More forcing because your opponent has to reckon with the loss of material. (Even better is when the ‘capture-check’ is also ‘in-your-face’).
6. Double checks – allows only one option – to move the king.

Basic stuff, but extremely important to have engrained in your chess DNA.

Calculation

A few years ago I wrote a six part blog series (over 20 pages) on calculation that I  recently decided to take down.  It represented several years of work, but after reflecting on some very basic ideas in attack/defense I decided that I disagreed with my core premise and I only want to put out there my more thoughtful thoughts.

The essence of the blog series covered my experience learning about and practicing calculation.  I spent a year reading everything I could about calculation and doing 100+ Stoyko exercises to practice good calculation.  It was incredibly rewarding to see how my thought process improved with each session.  Here are a few scans of my hand-written notes from those earlier sessions:

I then spent a few months writing down everything that I learned and gave many, many tips on how to calculate better, and what common problems I found.  I got about 90% of my variations correct towards the end, but the most common mistake I found was not considering my opponent's most forcing response when visualizing a line several ply deep (usually 5-6 ply, but sometimes even at 2 ply...ack!).

So my core message was that, in order to calculate more efficiently, you should always calculate the most forcing moves first.  I sort of glossed over the issue of whether you have to calculate every forcing move at every ply...something that really annoyed me.

I gave calculation/Stoyko exercises a break for a while and went back to focusing on endgames, and in the course of not thinking about calculation, I made a personal calculation breakthrough that I am still trying to mold into my old theory.

Basically I realized that, when there is a concrete threat on the board (and you must first train to identiy ALL threats in a position, and then prioritize them) you do not in fact have to calculate all checks, captures and threats.  Instead, your list of candidate moves should be developed by considering the basic defensive ideas relative to the specific threat on the board: capture, block, move, defend, and counterattack.

Since then I've used this new "calculation logic", as I call it, when doing my regular tactical exercises and it has definitely helped me avoid calculating unecessary forcing lines that I would have otherwise written down when doing Stoyko.  I can't say that I have suddenly been able to immediately solve any problem, but this thought process has not/not prevented me from finding the right idea by exclusion.

Instead what I have realized is that my mistakes are now mostly "visual".  What I mean is that I now ask myself if I can, for example, counterattack with an equal or greater threat, but I might not actually "see" the move.  I use the right logic to look for it, but for whatever reason I sometimes don't see it.

In my opinion that is a much, much better problem to have.  I know I can then isolate the specific kinds of moves I'm not seeing, and train those until I always do see them.  That's better than not even thinking about the kind move in the first place, or wasting my time calculating lines that aren't relevant.

My next step is to try to apply this "calculation logic" in Stoyko exercises.

***UPDATE***

I am close to completing a 20 part series of posts on what I call “the logic of forced variations” that I am confident captures this logic rather comprehensively.  See the "Calculating Forced Variations TOC" in the top right-hand corner to navigate the series.

Blindfold Chess -- Resources and Ideas

I wanted to share a little of my experience with BF chess and to share some of the resources for blindfold chess and visualization that I have used.

I started playing blindfold chess about 15 years ago when I lived overseas and my coach had me focus on dynamic play, calculation, tactics and studying mostly Tal's games. One day he handed me a pencil/paper during a lesson and literally threw me into BF chess.  It only took a few games before I was comfortable with it, and since then I have intentionally tried to keep up my visualization/blindfold skills. I have also taught kids how to play blindfold using some of the basic mating patterns as building blocks.

There are lots of great techniques out there and I think any of them will do you well.  Here are a few I have used and would recommend to anyone:


Intro/Easy


1. Professorchess.com "Chess Blitz 3"

-- this covers a range of easy questions like colors of squares, knight movement, and openings. No board, no pieces. I use these questions to open up training sessions.

2. Basic Mates (no pieces, no board)

-- start with two White rooks on a1/b1, White king somewhere out of the way (like h1), and the Black king in middle (like d4). Mate using the staircase pattern up the a- and b- files, while being mindful of the location of the black king and the safety of your rooks.

-- to up the difficulty a bit, move the rooks to a8 and a7 and do the mate across the top, and then h8 and g8 and go down, etc, until you get the hang of it. You will definitely know when you're comfortable with it.

-- to up the difficulty a bit more, change the starting location of the white king on a square that it is 'in the way'. If your rooks are on a1 and b1, and the black king is on d4, put the white king on d6 or d8.

-- Once you're comfortable with two rooks, then do queen and rook vs king what I call 'walking the dog' (not the staircase pattern). Change the direction to go up, down, left, right, and change the location of your king.

-- then you can do QvsK and RvsK.

-- then you can move on doing simple mate in 1 or 2 problems using only 4 pieces.

These basic patterns are an easy way to get a feel for the board, because you already know HOW to mate (or you should!) with that material so you don't really need to calculate anything. You can just focus on remembering where the four (three really) pieces are on the board. You can even do these in your head for practice!


Intermediate


1. The Chess Eye program is available online and has 10 levels from easy to very challenging. I try to do 10 questions from each level every day, and it takes about 15 minutes.

2. Blindfold chess against Fritz 13 (handicapped). I try to play 1 game a day. I set it on the lowest handicap possible and then once I can beat that level without blundering a piece due to bad visualization, I go up to the next handicap.


Hard(er)


1. Chess Visualization Course -- available online, the exercises show you a position and then you have to visualize a series of moves that the book gives you, and then rate (1) the quality of the image in your mind, and (2) whether you evaulated the material properly at the end of the exchange.

2. Stoyko exercises -- I have written several blogs about this (here, here, and the entire series of 20+ blogs on calculation), but the BF piece is that you don't move the pieces at all.

3. Opening Traps -- Pandolfini has an excellent three book series on opening traps. The one I like best is the 'winning way'. To do this blindfold, just follow the text of the opening moves and look for the tactics (usually a queen fork or an initial exchange before a queen fork). Dont look at the graphic unless you're having problems finding the tactic. I would recommend though that if you have look at the graphic, you should really think about what you weren't visualizing and why. A common problem for me was not clearly seeing how pawns moves changed things, so now I spend extra time thinking about pawn moves.

I hope this is useful for everyone. I look forward to hearing what you guys are doing to improve your visualization and blindfold skills!