Training Problems

Very nice puzzle, and surprised I was able to solve it

Hello all !
Just noticed, that GMs are able to calc deep and often a few sequences in 2-3 seconds O_O
Any1 knows some other ways to improve speed of calculations besides doing them a lot in puzzles/studied games? I'm doing calc very slowly, and often need to reverifying everything... Are there some specific exercises, which can speed up (and maybe improving to be more reliable) this proces by much?
Or it is the question of memorized many hundreds of pieces patterns with right sequences for them and GMs do not calc every move actually?

@Baldoslav It’s all about tactical pattern recognition, which comes from playing games and solving puzzles. That’s what they did, but they’ve been doing it for a lot longer than you, and from a very young age.

@KiriyamaKazuo
Thanks. So it mostly pure experience? They are playing much more, and playing from young age, when human learning faster, gives them another edge in it? It is understandable.
But how do you think, the ability to play blindfolded at full strength will add something to ability to calculate? As I saw, many GMs trying do not look at chessboard when calculating, so probably they visualizing chessboard, and doing calculations within head. But on other hand, there are others, which are able to do fast and deep calculation, staring at board... so I'm not sure, is it worth to waste time on such skill (good vizualization or playing blindfolded). It should not be easy, comparing size of board (64) with amount of things, human usually can keep in memory unstructured (between 5 and 10+, with 10+ is rarer). Some system can be required in this case. And long training also likely.
I'm also thinking about specific kind of puzzles (which can be extracted from any big gamebase by some criteria), where you do not need to give in answer the full sequence of best moves, but just (let say) to give the final position (after 3+ moves) one specific active piece - to eliminate/minimize mouse using dependency, to speeding up, and to focus more on deep calculations and minimizing time lost on anything else. Hopefully, it will allow to train pure calc-ability a few times faster and gives more precise estimates of ability.
If both methods works, hopefully they can be combined, hopefully further reducing amount of time needed to improve calc-skill. May be some other methods will be better, above are just free improvisation to illustrate thought direction.
Obviously, since not every GM is same in this ability, there should be individual ceiling to the improvement, but maybe player can get there faster than simply playing/puzzling more?
But to be practically usable, those exercise should be at least 3x or 5x, better about 10x effective, than usual "gaining experience" path, otherwise spending time on them will be not worth benefits gained (because any specialized training gives less general experience and of course gives much less fun, which will be demotivating). I do not know, if something like that is used in chess schools?

@Baldoslav I think that training visualization will definitely improve your calculation. Keep in mind, though, that if you want to pick a grandmaster’s brains, the way they learned those impressive visualization skills was by, precisely, calculating, not the other way around (reading books, for instance; after a while, setting up every position becomes tiresome, so the reader is basically forced into calculating more deeply). Praggnanandhaa, who is currently playing at the Candidates, talked about it in this interview. I didn’t understand the second method of improvement you were mentioning. Anyway, if you find a shortcut to improving your calculation, feel free to share it here, as I’d be most interested in learning about it.

Checkmate in 5-7 moves with three pieces (intermediate/advance).
Position is from today's game. Edit: Forgot to add the last move but it is pretty obvious. https://www.chess.com/analysis/game/live/166864522008/analysis?move=46

Very cool problem. 25…Be3+ is very instructive.

Find the best move for white (intermediate/advanced for one line) or (advanced/master for the alternative line). Position from https://www.chess.com/analysis/game/live/167242107168/analysis?move=31