## Saturday, July 28, 2012

### From logical reasoning to trial & error

AoxomoxoA complained that when he started to do the problems at standard CT correct, his succesrate and his rating went up, but he became slower and slower. In the end he decided to forget about his rating and succesrate and he went for low level problems and speed.

For me it is more logical that when you want to get to masterlevel, that you try to do masterlevel problems. And that when you notice that you are slow, that you ask yourself  "why am I so slow and how can I speed up?". How can I change reasoning into automatic trial error? Of course by making a pattern of the logical reasoning.

Take for instance the following diagram:

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Black to move.
You can find the solution here.

I probed the position with trial & error for about 5 minutes, then I got stuck.

Then I started to reason for about 20 minutes, and all of a sudden I saw the solution.
Why on earth did that take me 20 minutes?

The problem is that I had looked at the initial move (Qh4), but I rejected it because of Qxe5 and the threat against h2 has vanished. At least so I thought. By reasoning I found that the white queen performs two defensive tasks: garding both Rf1 and g2.The next question was, if I can remove the gard, can I make use of it?

Our brains are evoluted in a way that they can create expectations of the future. Of course this can come in handy when you need to anticipate your actions during hunting a woolly mammoth. But this capability comes with a downside. You are inclined to see only what you expect. If for instance during a rapid game somebody puts his king en prise, I tend to overlook that since I don't expect it. The same happened in this position. I expected that after 1. ... Qh4 2. Qxe5 black had nothing since the threat against h2 was annihilated. But he has 2. ...Qf2 with two deadly threats.

Or take the following diagram:

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Black to move.
You can find the solution here.

The same story. It was immediately clear that I had to sacrifice Rh2 or Rxf2 since that are familiar patterns. I dabbled 5 minutes around with trial & error, then 20 minutes reasoning followed. All of a sudden the light went on and I see the first move.

The theme is exactly the same as the previous diagram. The white queen is guarding the  invasion square e2. With 1. ... Rxf2+ 2.Kxf2 Bxc5+ I can deflect the queen. The rest is pretty straightforward and easely found with trial & error.

Again a move that I would normally not consider because I don't expect it to be fruitful.

These are two examples of why times go up when the problems become more difficult. At the same time it becomes clear that there is no insurmountable reason why that should be the case.
In both cases my solving time would have been 20 minutes shorter. This overlooking of just one idea because of bias is extremely common in the higher regions of CT. On the one hand expectations help you to speed up your trial and error, but on the other hand when something has gone wrong and you reject moves for no reason, there is work to do.

1. Why are master quicker than we? Their solving of the same problem is quicker. There had been some scientific research on this "speed" effect. Master are using their LTM more intenese than beginners. They can prune their calculations by experience. They now more often, this is bad, that is lost, this is nonsens, that is won than we WITHOUT calculation. This superior experience is in their memory.
There is a second phenomenon why masters are quicker, they have a better/quicker chess modell in their brains, they have a better board vision. Its tested that masters can tell quicker if a position is a check, who has more material, who is mate asf. This all results in a higher mental speed in chess. Mental Speed is a (multiplicational) Factor in Fluid intelligence=ability to handle new situations. If you think quicker your Working memory works better (its only short time lasting). This way you can think of more things "at the same time".
To improve the "precise" thinking is a typical adult tecnic, especially for an engineer or scientist. As a mathematician i would love to agree on such an idea. but.. Children are learning by trial and error, they dont like to think and reason, they put experience in their memory, they play! Children are improving, adults not.
A few days ago is did test my abilitys at "Standard" again, my standard rating is ~2200. My standard is 400 better than my blitz rating ( its common, that these ratings are close together at CT)
This does mean my calculation ability is high, i have good visulaisation, i can reason but not quick enouf. Why is that? I have to calculate where a master simply judge. A maste says : won, where i have to look for winning moves and look at the responses.
My experience with Standardproblems which i blunder: most times i cant judge the position right which are calculation leaves. Calculation leaves are there, where the sequence of "forced" moves ends. Further calculations would result in an extreme increase of positions to calculate.
Example easy to understand:
For someone without any endgameexperience such a problematic leave could be an engamesituation say KPK. If you know what far opposition and "square" is then you can judge such a position without calculation. If you need to calculate such positions, then you are lost. Usually the judgement of leaves are not a matter of this type of knowledge: "remembering rules which can be explaind by language". Usually leaves are simply positions where you say +0.6 and the engine says -0.7. If you played such a position several times then you know how to evaluate/handle it correct. Humans needs to to Shannon B, for Shannon A we are to slow.

I think Chessity is a good place to learn calculation. These problems are designed for that, try Chessboard medium, i laugh a lot. But my results in Tactical Power where ehh not positive.

As far as i see there is only one possibility to improve for adults: store many and important (relevant) position&evaluation&movesequences in your brain and take care of quick access to this info.
So i think bright knights method is the only "working" method. But i think book positions are not relevant enouf they are interesting but not typical.

My "positional" server should generate (in the future) some of the missing positions together with a improved rating system and a learning by spaced repetition.

2. @Aox,
after reading it for the third time I think our opinions are essentially the same as mine. Allthough I would have said it differently;)

Up to this point: As far as i see there is only one possibility to improve for adults: store many and important (relevant) position&evaluation&movesequences in your brain and take care of quick access to this info.
So i think bright knights method is the only "working" method.

In fact I agree with this too, but I think I have a slightly different interpretation of the words many, important and relevant, due to my experiences and observations.