There are 32 mates. When you know only 9 of them well, you cover about 70% of all mates that occur in practical games. See the previous post.
Every mate of those 9 mates, can be subdivided in a more intricate way. This clusters all patterns of the same type together. Look for instance at the dovetail mate. I have a problem set of 40 dovetail mates. Here are 7 of them. Can you see the resemblance between them?
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| 1. black to move |
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| 2. black to move |
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| 3. black to move |
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| 4. black to move |
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| 5. white to move |
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| 6. white to move |
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| 7. white to move |
Within the set of these 40 dovetail mates there are other subdivisions as well. I haven't counted them yet, but I would say there are at least 5 other subdivisions. The other 8 mates (other than dovetail) can be subdivided too.
I postulate that this is the way to study tactical themes. I have identified 32 themes (9 mates and 23 tactical motifs) that occur frequently. See the previous post. Get 40 examples of each (40 x 32 = 1280 examples), and divide each theme in 5 subcategories (32 x 5 = 160 subcategories)
I counted all subcategories of the dovetail mate. I counted 11 of them. Verbal description of those categories is awkward, so actually not possible or useful. Yet the categories are pretty clear, and not vague as you might expect. There were no positions that were not categorizable at all. If this is exemplary, it totals to 352 subcategories for all tactical motifs with very regular occurrence. Which is still manageable..
ReplyDeleteSo in order to speak the language of tactical chess, you need to absorb about 350 categories of patterns. That is perfectly doable. Without the absorption of these categories, it makes no sense to play blitz, and giving a simul should be next to impossible.
ReplyDeleteInteresting:
ReplyDeleteProblems 1, 3 and 4 have an alternative mate pattern, depending on where the White King moves after the initial check. The alternative mate patterns must be SEEn just as readily as the potential dovetail mate. In the other 4 problems, there is only one legal move for the White King after the initial check, and the dovetail mate is the only mate-in-2 solution, so System 1 suggests only one solution.
The RCCM apparently prioritized the alternative mates above the dovetail mate; the alternative mate sprang into consciousness first. Only after dispensing with that alternative (satisfying System 2) did the RCCM toss up the dovetail mate. Unfortunately, System 2 always processes things one at a time, sequentially. Only when System 2 directs System 1 to “Try again!” do we get the next lower priority ‘suggestion’ from the conveyor belt.
We have no conscious direct way of changing/controlling the embedded priorities of System 1. Or do we? Perhaps the priority can be changed by an intense focus on one particular theme/mate for some period of time, somewhat based on the idea of “Last in, First out” (the computer equivalent of pushing/popping the stack). However, we never know in advance which one of several tactic/mate patterns will be the most salient in a given situation, so I don’t think it really matters in which order we process them – as long as we (eventually) SEE all of them. There’s no way to speed up the overall process if System 2 has to make judgments which cause a switch back and forth from System 1.
Since there are only about 350 categories, it might be worth to invest some serious time in them. The only reason that position 2, 5 and 6 have NO additional mate on the other side, is that the escape squares on that side are covered by a rook. In position 7, the escape squares are blocked by a white and a black pawn. Positions 1, 3 and 4 prevent escaping by an additional mate pattern.
ReplyDeleteWe need to absorb all 350 endpoints in a light-way manner. Meaning that after absorption of the 350 categories by system 1, the endpoints must come up lightning fast. Just as words come up fast when you make a sentence. Like a language, you think about the story you want to tell, not about the words that you should use.
System 2 is the if-then-else story generator which decides where the attention goes. System 1 just follows the beam of the attention from the background.
ReplyDeletePosition 1: I simply found the checkmate in three: 1...Bg2+ 2.Kg1 Bh3+ 3.Kh1 Qg2#
I did not take into account the solution move and it looks like that "after Qh3+ the king escapes" (has too many space to run away).
Position 2: At this position I considered only two candidate moves: 1...Qg2+ and 1...Qxh1+
If it was in the game and I would not have "dovetail mate module/pattern" activated, I would not spot that!
Position 3: This one looks a bit weird to check the king with Qh3+. The c4-pawn looks so innocent and maybe it is too "weak" (especially as it is far away from the Black Queen) and hard to spot this mate pattern in 2 moves (in one I would find 10 times faster).
Position 4: This one I would start with Qg2+ (direct attack) or Qd3+. Recognizing Qh3+ and Qd3# mate is far from natural (obvious) to me.
Position 5: This position made me cry (and after I solved - made me shocked). I tried Qh8+ with Re1+ or Re3+ to follow and I was unable to solve the puzzle. I copied that into lichess (chessvision plugin is awesome!) and after that I saw the variation Qh6+ and Qxd6 mate! I was totally blind to the Qxd6 mate - probably I did not focus on the Rd1 FUNCTION (after Qh6+ the d6 square is attacked twice, not once!)
Position 6: After I knew the previous mates, I solved that in 2-3 seconds. I have a hypothesis - is this position a way easier to solve (find checkmate) due to the more compact position? I mean - many of the pieces (white and black) are very close to the Black's king position. Is that a helping (distracting) factor at this type of puzzles?
Position 7: First I started solving with black to move and saw the idea Qh1+ and Ke6 Qh3+ a skewer. After some analysis I found out it is white to move and therefore I tested Qd7+ (I spot that it does not work) and then I retrived from memory the mating position you posted at some previous article. That's why I could find the solution immediately - even if Qf7 mate in the second move looks completely weird to me (very hard to imagine/believe).
In general, I am very happy to find out there are ONLY 350 (sub)categories (I estimated it may be about 700-900) and I guess the faster we can identify all of them and the problems we face with the recognition of the specific categories (and subcategories), the faster we can create the method of efficient recognition.
And of course if we know which ones of these are the most practical - we can study them in the order of frequency. This way it is going to be a very efficient work towards tactical understanding (and efficient recognition).
You have been doing great work my friend Tempo! I am really glad I can have the access to all your discoveries and comments (the same as Robert Coble's!)