Please Explain Kotov's Analysis Tree Method

Can someone please explain me the analysis tree method used by Alaxander Kotov in his book Think Like A Grandmaster?

It seems very interesting and I cannot find it on the internet!

It is not a method just Kotov's jargon to describe how a master analyse.

Yeah. But what is that? Please, can you explain. Please. Please.

Kotov came up with the concept of "candidate moves". From this you analyse and thus build up a "tree". Each candidate could yield two or three replies and this replies could have their own replies thus the "analysis tree" is formed.

Which method do you use in calculating?

i dont have a "method".

Ok. Tell us your thought process while solving this puzzle.

It's not a formal method of Kotov per se. It's just jargon that refers to what everybody is already doing. IOW, what YOU are already doing to analyze a game is what it is.

More specically, when you consider a set of possible moves in a given position, then consider a set of moves for each of those in relpy and so on, this will build up what looks kind of like a tree when written down.

Here is an example: http://en.wikipedia.org/wiki/Variation_(game_tree)

If you follow the links there, you may find some hard to follow explanations for what you are surely already doing naturally without realizing. Don't be put off by the crappy explanations.

Since this is a puzzle, the first move is 1. Bxf7+ mainly because this is a sac in similar positions where the knight on g5 can go to e6 attacking the black queen and threatening a check on g7. After 1. Bxf7+ Nxf7 2 Ne6 the queen can go to two squares b6 and a5. White can then go Be3/Bd2 to attack the queen but the queen has too many squares so trapping the queen is out of the question. So 2...Qb6/Qa5 have to be answered with 3. Nxg7+ Kd8 4 Ne6+ Kd8. Which is a draw. Going the other way loses for Black after 3...Kf8 4 Ne6+ Kg8? 5 Qg4+ and white wins back the piece with probable mating attack as well.

I do not see a win for White or maybe I am just too bad at analysis :)

Kotov's 'analysis tree' itself is not a method, but it is part of the method he explains in his book.  The key components are:

1 - list ALL candidates so we do not overlook some important possibility

2 - calculate each variation in turn "according to your own preference"

3 - all possible lines can be pictured as a tree of variations

4 - player must only calculate each line only once and not return to previous lines

It is a good general process to follow. 

Yeah, there are lots of improvements to be made to his general method for sure.  

Like you said, you should try to focus on calculating one variation at a time but it's OK to jump back to a previous line if you just realized something you didn't see before.

He also gives zero explanation about how to find good candidate moves.  

He also skips the whole issue of which candidate to calculate first by saying "your own preference".  There are better ways to do this.

He also gives zero explanation of how to actually move through each variation.

But all that said, his general approach is sound -- find some good moves, calculate them one at a time, and then pick based on the best final evaluation.

Yeah. Thanks all of you for your insight. My question is how to calculate a candidate move to a variation?

http://www.chess.com/article/view/quotthink-like-a-grandmasterquot-by-alexander-kotov

I've done lots of Stoyko-type exercises and have posted 20+ blogs on this exact issue, so check out my blog for more on this.  But here is the short version.

You need to first understand when to calculate.  You should do blunder-checks of your own moves always.  In most positions that's just a quick scan to make sure you haven't left something hanging or allowed a mate-in-1 or some tactic you're not prepared to address.  That is the majority of positions in a game.  You also need to always look at your opponent's last move to see if it created any threats.  If you find a threat, you calculate.  In a few positions, usually in the middlegame, there will be serious tension between the black/white pieces or some threat you're responding to, and you have to decide what to do.  Those are the positions where you calculate.  You can also calculate in many endgame positions, but most that's a different kind of calculation logic.

You also need to know that you can only calculate forced variations.  I've seen many beginners "calculate" variations where their opponents play an unforced response.  Don't calculate moves that have nothing to do with the greatest threat on the board.  

Your goal with each move of any variation is to (1) force a position that is better than, or at least equal to, the current position (although in some positions you are going for the "least bad"), and (2) attempt to find moves for both sides that "refute" the other's play.

When considering which candidate moves within a variation to even consider, remember that there are only three responses to most checks (capture, block, move) and five responses to any other threat (capture, block, move, defend, counterattack).  You only need to search for candidate moves within those ideas.  Don't search for all captures, checks, or threats when looking at defensive replies unless they relate to the specific threat.

Remember that the ebb and flow of attacker and defender shifts throughout the variation.  You might create the first threat, but your opponent then responds with a greater threat, and now you're the defender.  And then you refute his threat, and he's the defender again.  Keep calculating the line until there it is obvious to you that the variation is over, and evaluate that position.

Within a variation, your goal is to "trim" the variations by proving them as bad for either side (eg, my opponent can block or capture, but he shouldn't capture because then I can force checkmate, so he must block).  That allows you to find and to focus your energy on the mainline quickly.  

You can choose which candidate within a variation to calculate first using one of two ways:  pick the move that is "obviously" wrong, or, pick the most forcing move.  Usually you have a mix of both, and I like to prove the "obviously" wrong moves as wrong quickly, and then from the moves that are left find the one that offers my opponent the fewest replies (eg, the most forcing).  

This approach is much for efficient than the brute force approach of calculating all checks, captures, and threats (CCT).  Here's a simple example and we'll try applying both techniques.  It is white to move:

Hopefully you see that black is threatening checkmate on the next move (...Rh1#).  Using the CCT approach we can count all of white's checks, captures, and look for threats, and then calculate all of black's checks, captures, and threats in response to each of ours, then our CCT's for each of those.  We can build that pretty little tree of analysis, and see where both our two captures take us...right to checkmate.  The CCT approach is only useful when looking at offensive moves, not defensive replies, and using that approach offers no helpful ideas for how to defend against the mate.

Instead, we can search for specific moves using the five defensive ideas for white based on the greatest threat (of checkmate):

capture: white cannot capture the rook, or the f3 pawn.  This idea can also be expanded to "do something to the attacker" like pin, restrict, or deflect, but we can't do any of that here.  

block: we cannot block the rook from getting to h1, but we can prepare to block by moving shifting the king (1. Ke1) to allow the bishop to block on f1.

move: the only square the king can move to we considered above, but that doesn't allow the king to escape...it only allows the block.

defend: we cannot defend the h1 mating square.

counter-attack: a counterattack must create a threat equal to or greater than the checkmate threat, which in this case would only be a check.  White has no checks.

Using this approach we find that there is only one candidate move to even consider!  And we can quickly see that 1. Ke1 Rh1+ 2. Bf1 stops the checkmate.  Since we have zero other candidate moves to calculate, we play it.

I appreciate your effort to answer my questions Doirse. I have really understood the process of selecting the candidate moves. My next question is how can I go deeper into a variation of a candidate move? All members are invited to answer the question. Sorry notmwain for being rude.

My answer was about calculating specific variations.  Within even one line you have a constant process of searching for the best moves for both sides that only ends when there is some sort of clear resolution -- like checkmate, forced draw, win of material, an improved position, or no more useful checks or captures.  There is no single answer on how to calculate a variation that covers all possible positions, and if you give a specific position we can talk about how to calculate specific lines.  

For example some positions are all about captures on a single square, and then there are some general guidelines you can use to help navigate it, like in the following position it is white to move:

White has lots of moves he could consider, but lets just calculate one candidate move 1. Rxd8+.  How do we calculate this line?  In general the defender is forced to go along with the trades in order to avoid simply losing material, unless there is an in-between move that is better.  Also a general principle is that you should retake with the lower valued piece first, unless there is a reason not to.  So of black's four candidate replies, the recapture 1...Rxd8 makes a lot of sense, right?  

[Now here's a quiz for you:  how would you evaluate black's other three candidate moves (and his only other legal moves in the position), 1...Qxd8, 1...Ke7, and 1...Ne8?]

So after black re-captures with the rook (1...Rxd8), white can capture again with 2. Rxd8+ and of black's three replies the recapture 2...Qxd8 makes the most sense.

Hopefully that was all pretty easy to visualize and the logic was easy to understand.  The "tree" of variations was puny -- zero branches.  Now why would white trade off two rooks?  That's a totally different issue, and we're just looking at techniques for calculating specific lines.  

You could also use a shortcut to calculate those captures called "counting" -- the "count" on the d8 rook is 2-2, meaning two attackers, and two defenders.  Since most of the pieces are the same value this is pretty easy to calculate, as long as you take with highest valued piece last.  We could use counting to see that the d8 rook is "safe", and that the captures would result in no change in the material balance.

Here's a slightly more complicated position again with a series of captures on one square:

Take a look at the c8 rook, and you can see the count is 3-3.  Let's just look at how to calculate the candidate move 1. Rxd8.  Black has lost a rook and should re-capture, but here is another quiz for you.  If black follows the general rule of capturing with the higher valued pieces last, what whould white play if black recaptures with his knight 1...Nxd8.  

So there you have two simple examples and techniques you can use to calculate one type of position (multiple captures on a single square).  These were only a few ply deep.  There are significanly more complicated positions with captures on single squares that you could calculate very deeply (say 15 or more ply) that use that same logic.

Then there are completely different kinds of positions, like say king hunts, where other logic would come into play.

Thanks a ton again Doirse for spending your valuable time to write this post. The answer to your 1st quiz question is Qxd8 loses the queen for a rook, and a win for white is inevitable. Ke7 loses a room after 2.Rxe8. 1...Ne8 Does the same.

2nd quiz question: After 1..Ne8 Qxa8 2.Nb6 Qa6 Rb8 loses for Black.

These questions were too easy for me. Well, I believe the goal was to illustrate different techniques of calculation. 

Here is another question for you: I sense a general pattern in all the calculation methods: to look at candidate moves of yours and then of the opponents. Can you reflect on that? Please try to generalise your answer with as few diagrams as possible.

And thanks again for your sincere answer.

Yes, I was just trying to demonstrate specific techniques for calculating that one type of position by showing a general rule, and then a position where that general rule doesn't apply 

The general pattern for calculating a specific variation is exactly as you said:  

• you make a move that threatens something
• your opponent has three types of responses to a check, and five types of responses to any other threat.  Look at the most forcing response first.
• for each response by your opponent, you look for creative ways to threaten something else.  Unless your opponent makes a counter-threat that is stronger than your threat, then you must defend!

Finding good attacking moves requires more creativity and effort than it does to find the right defenses against a specific threat.  Pattern recognition can help immensely.