## Wednesday, April 25, 2012

### Chasing the King

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In order to enhance the speed of solving tactical problems as much as possible, I work with high rated (2300 - 2400 std rating) problems. These often take me half an hour to an hour to solve. If I can speed that up to under 3 minutes, I'm 10-20 x faster. With easy problems it is much more difficult to speed up the same percentage. 3 minutes is the average time you have per move in a long OTB game. Another advantage is that when you need an hour to solve a problem, you can use a stopwatch and a logbook to write down what it is what you are actually doing and what exact costs so much time.

My search algorithm is actually developed for duplo attacks and not for traps. And it shows. Whenever I have to chase the king, I'm starting to consume time and to make errors. (I consider a mate to be a special instance of a trap.) This means I will have to work out a separate search algorithm for chasing the king. I will make a set of high rated mates with >4 moves to test it.

1. From a percentage point of view you are right. You need to train easy puzzles longer in order to double your speed.
This is especially valid for puzzles, that are difficulty rated, but are actually "easy" (you reported about that sort of puzzle, and they are often 2 or 3 movers only).

But even within a range (difficult or easy) it is like this: First you speed up a lot, and then every further improvement in speed gets smaller.
For instance it is not like this:
1st attempt: 30 minutes
2nd attempt: 15 minutes
3rd attempt: 7,5 minutes

But rather like this:
1st attempt: 30 minutes
2nd attempt: 6 minutes
3rd attempt: 4 minutes

Unless you remember the puzzle. Then of course the solution time will immediately drop enormously to under 20 seconds.

My experience is, that I am as slow thinking as before. I might breed over a puzzle for a minute - and suddenly I remember I had it before! As soon as I remember it, it only takes me a few seconds more. It is strange: I often remember that I had a puzzle before only AFTER I solved it (or just a few seconds before I solved it).
But it can also be, that I see a puzzle, and I know pretty soon that I had it before. It looks familar to me.
It is hard to tell which case is happening more often: looking at a puzzle and thinking "I think I have seen it before", or the sudden strike when I suddenly remember the solution.
I guess (but am not sure) that at the beginning the "it is somehow familar to me" was more often the case, while later I usually encountered more often the strike: No idea at all - and suddenly I remember the solution.

For chasing the king:
These are very deep calculations. Often they are found incrementally. What is important here is a good "feeling" for squares: "If the king goes into this direction, I will be able to check mate him, and hence I only need to calculated what happens if the king trys to hide behind his pawns."
Looking at squares becomes more and more important. And this (sorry to be repetitive in this point) requires you to see at ply 3 a simple square pattern tactic. Since you only look 5 seconds at this point in your search tree, you need to be able to see the easy tactic here very fast. Or it will take you an hour to find it: you repeatedly go to this very point at ply 3 in your search tree, look for 5 seconds and discontinue this tree and try s.th. else. After you looked at it several times for 5 seconds, you suddenly see the simple tactic.

you can verify this (if you can) by watching yourself: after you found the winning tactic after 30 minutes or so I want you to aks yourself the following question: how often did you look at this direction, how often did you consider the right move (= the first move) but discontinued the search because it took you very long to find the 2nd or 3rd move in this variation?
Of course you cant answer how often you looked at the right move. But probably you can tell by feeling, that you actually looked at it pretty long. You might have found the main idea even pretty fast, but you had some problems in the little variations in between. You may call them "right move order".

2. @Munich,
you have discovered a screwdriver, and now you use it for every task. Of course you can hammer nails with a screwdriver. Of course you can saw wood with a screwdriver. Or scisel stone. But it is not the best tool for every task at hand.

When solving a puzzle, there are several tasks to perform. Some can be automated, some can only be performed consciously.

It is true that every task that can be automated has probably pattern recognition involved. That makes you think that you can train them all by using the same trainingsmethod. By using only a screwdriver. But the tasks require a different kind of intelligence to be add. Learning the constellation of the pieces requires a total different kind of intelligence to be add than learning the patterns of the empty squares. If you are not aware of that at storage time, you will never going to be able to remember the patterns of the squares.

The patterns of the squares are not tagged in CT. Without tagging, learning happens only accidental. Of course, with crunching big numbers, more accidents will happen. But it is far, far from efficient. Like hammering with a screwdriver.

Adding intelligence means adding the appropriate tags in your mind during storage time. Tags that are most suited for the task at hand.

At average, a >2000 problem at CT has about 6 duplo attacks in it. I recognize those within the first 30 to 60 seconds. Which indicates that there is little or nothing to gain in this step. But the following steps are suboptimal. These require separate training. But before I can train them, I will have to identify them. With todays post, I identified one of them: king chases.

And I'm not going to throw a screwdriver at it in the hope it will all fix itself.

3. It is not at all clear that it is easier to improve by a fixed percentage on harder problems than it is on easier ones. Back in the days of the Bain Experiment, I found that reducing my solution times by a fixed percentage for my first pass through the first batch of problems gave a good fit to my solution times on the first passes through the later batches of problems. That appears to be roughly right for Woolum too.

It is true that you have an average of about 3 minutes per move in a standard time limit game, but how much time can you afford to spend on checking that your chosen move is proof against a tactical shot? I would have thought that 1 minute would be optimistic. Hoping for a sixty fold improvement in your solution time is too optimistic in my opinion.

What failure rate is acceptable when checking for tactical shots? 10%, 1% or less… There are typically about 40 moves in a game, and many or most of them could fall foul of tactical shots. If you accept a 10% failure rate, you are going to “blunder” once or more in most games. Even if you get your failure rate down to 1%, you will regularly lose to tactical shots.

4. About the nature of puzzle:

There are more possible reasons why we miss puzzles:
a) they are simple (like this example) but somehow, the set up is so uncommon, that we miss it. (= difficult rated, but are actually easy):
http://chesstempo.com/chess-problems/48770

b) they are complicated. They are difficult, because they are indeed difficult. (You may define it better, what makes them "difficult").
Example (with CT Blitz rating 1988):
http://chesstempo.com/chess-problems/90978
or this example (1860 rated):
http://chesstempo.com/chess-problems/62321
or this example (just 1715 is almost underrating it!):
http://chesstempo.com/chess-problems/88387

c) The position is already reached to win. This puzzles us so much, that we keep searching for new threats, while we only have to keep the threats in place. Usually we only need to get the piece that is attacked to a safe square (ideally to a square where it attacks something. Sometimes where it attacks the same piece again, but from a differnt angle.)
The funny thing is, that we cant solve it as a puzzle, but if we had it OTB, we would probably simply get our attacked piece out of the danger, and hence find the solution usually in a few seconds OTB.
example:
http://chesstempo.com/chess-problems/74969

or this example:
http://chesstempo.com/chess-problems/61520

There might be more reasons why we fail them. But these 3 types are pretty common. For reason b) - well there is little we can do about it.
but a) and c) I believe it must be possible to train it by repetition.
Maybe c) is not so easy, but then again it doesnt matter: in a real OTB game we wouldnt miss it anyway!

5. Here is type d):
Aox calls is "the anti tactic".
example:
http://chesstempo.com/chess-problems/47920

For type d) the solution how to avoid failing it could be to train easy puzzles. Probably training easy puzzles up-side-down. The anti-tactic is not so hard to see, but usually you didnt look long when you moved your wrong 3rd move.
This is a very example where it is very helpful to be able to see easy tactics within 5 seconds.

I guess there are some more reasons why we fail puzzles. When I encounter a new reason I will post it here.