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Ideal trainer versus standard puzzles

Good positional play is founded on small tactics („simple“ tactics, don‘t know the exact translation). Jussupow/Dvoretzky had even training lessons on exact that topic.

Tactics, which don’t win material; rather to improve the position like occupying an important square with a certain piece. And it cannot be taken because of a hidden tactical refutation.

I had some „remote training“ with Jussupow, one of the 24 booklets had the name „Einfache Taktik“ and dealt with positional play.
@MoistvonLipwig Your definition of strategy is not exactly mine, but if it was, then my answer to the OP would be:
Strategical play can be taught by the computer to humans as little, as faster running can be trained by studying, how Lewis Hamilton wins a formula one race.
The way, the computer achieves his "strategical" decisions requires the exact calculation of millions of positions, while humans must obviously use a completely different way.
Well Sheckley, here's something to consider. In his classic book Think Like A Grandmaster, Alexander Kotov explains that he used to think in a "different way", as you called it: positional strength, development, good queenside chances, well- defended king, etc. And he was stuck at master's level and would get crushed by better players. Then, after some frustrating experiences thinking that way (which he relates in detail), he realised that if he wanted to go higher, he needed to CALCULATE more deeply. Kasparov also advises: calculate each possibility as deeply as you think is necessary, THEN CALCULATE ONE STEP FARTHER (for each plausible possibility). Humans have limitations, yes, but the best players minimise those limitations by thinking as much as possible like a computer in complex situations.
Further to my reply to Sheckley: Good strategic play often involves calculation. One of the most important decisions - on which so many games are won or lost at every level - is whether to attack or defend. You cannot make the right decision without calculating quite deeply. How else answer the key question: Will my attack succeed before hers does?
Sargon, I would like to get that book. But as I say, there is no reason a program couldn't select such einfache taktiken and be available on a site like this, as I suggested, mixed with standard puzzles.
@nayf I think on chesstempo you can set the mode to "mixed" to get a mix of winning and holding a drawn position.

@sheckley666 I can agree with your analogy, indeed just knowing what the computer thinks doesn't mean one can come up with it oneself. I was merely objecting to the statement that computers can't play "strategical moves".

@nayf I wouldn't call "creating future chances" necessarily as strategic though you do raise a point as that a perfect chess player (in the game theoretical sense) might not play very strong actually since he sees chess is a draw anyway so he would just pick one of the drawing moves. (and since he plays perfectly he has no understanding of what is maybe harder to defend for a weak player) However I would put creating chances in a different category alltogether which at its extreme are the famous swindles. These can be in some sense of strategical nature though more often they are variations where one hopes the opponent makes a mistake. (but as a human with imperfect calculation you can argue that since you can't see it all in advance it's not really a tactic for you) This category is very important for human chess since to win a game your opponent needs to make a mistake and this is a good way to lead them into making one. (e.g. I won many games OTB vs 2000+ players after having been down a piece or more) And the very strong engines aren't particularily good at human-specific swindles (e.g. they won't play a speculative sacrifice because they know that the opponent might mess up) which one could perhaps consider an engine weakness especially for analyzing.

But I stay to my point that strategic play is just a sort of approximation because the actual tactics would be way too deep for a human to calculate. Good players can approximate that very well which makes them "strategically" superior, also still calculating variations may give you a better approximation which is why even strategical players will calculate a lot. For computers that is a bit different, they also have a purely approximative part (that is what the evaluation function is for) however often times they don't need it since they can calculate it directly. (though worth noting that modern engines use really aggressive search heuristic to e.g. prune irrelevant lines, those in some sense are approximative too, or to use a human-chess word "intuition")
Btw, if some of you can program I would recommend you writing your own engine. I found that really eye opening and it gave me a different understanding to chess. (I'm not saying that actually makes you play stronger however it does give you a different view on this game)
Here's an example given by Jussupov with lots of "small" ("simple") tactics which improve the position. Hence these are examples for positional play. Just figure it out yourself, two hints are given:

23. ... Qf5! and 24. ... Ne2!

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