Accepted moves in training puzzles

It appears to me that the selection of accepted moves to a problem is quite strict: For example, if one plays a move that mates in 2 moves instead of giving mate directly, this is (sometimes/always?) marked as a bad move.

I understand that there is some value in finding the most elegant mate. However, it feels quite disappointing if one has solved the first key moves in a puzzle correctly and is punished for prolonging mate by one move, although one makes sure the win is never endangered. What would be wrong with accepting all moves that keep the win as "good" although not best moves? If this would make some puzzles too easy, the solution could be graded by the number of suboptimal continuations tried.

"It appears to me that the selection of accepted moves to a problem is quite strict: For example, if one plays a move that mates in 2 moves instead of giving mate directly, this is (sometimes/always?) marked as a bad move."

this is just normal stuff - you must allways find the shortest line for the mate because the shortest variation is forced to mate, and thats the goal.
if you feel punished by not finding the best variation in a training situation, how will you otherwise improve your calculation ability ?
in kunstschach (dont know the english term) a puzzle is solved only when the exact number of moves was found.

If you try to find a shortest mate instead of a certain mate in a real game, you may get punished for it by losing on time. So why would one try to train something that diminishes the practical chess abilities?

Seeing that the puzzle engine cannot possibly guess the reason why one makes a move, and all winning moves are good in practice, it would be best to mark all winning moves as correct and prefer puzzles in which there is a narrow path to victory.

You train seeing the shorter mate. Pattern recognition.

There are two reasons not to go for the shorter mate in practice: Robustness and speed of calculation. From an aesthetical point of view, shorter mates are usually more beautiful, but I believe that spending time on finding shorter mates in won positions is decreasing one's playing strength.

ROBUSTNESS: If you have, say, a KQRKQ endgame as white, and your opponent allows you to exchange queens, I believe the best practical decision is to swap queens and win the KRK endgame. This yields a thought-free and risk-free win in about 20 moves. Even if you are able to calculate a beautiful mate in 7 involving a Q sac at move 4, that would create chances for a miscalculation leading to a rather embarassing loss, so it might still be safer to just go for the exchange.

SPEED: Much of the progress in chess engine implementations of the last years is due to increased selectivity (humans with limited brainpower must be very selective anyway). Engines that calculate all moves up to a certain depth are sure to find shortest mates, but they are mercilessly outplayed by more selective engines that make better use of their time. Seeing that some future position is won or lost allows to stop spending time on lines leading to this position and increases the time one may use to think about more critical lines.

It has to be the shortest mate otherwise you could delay mate by 5 moves and still win...in many positions you can delay the mate and still win there are too many variants of mate if you delay it why should the puzzle accept all of of them.

"There are two reasons not to go for the shorter mate in practice: Robustness and speed of calculation. From an aesthetical point of view, shorter mates are usually more beautiful, but I believe that spending time on finding shorter mates in won positions is decreasing one's playing strength."
- its a big mistake to overvalue speed and to neglect calculation accuracy. to find the shortest line in a training situation helps to improve the calculation skills as said before.

I'd like to join this discussion by starting with the elephant in the room: Lindhorst is right. Pattern recognitions is not trained at all by calculating the shortest mate in positions with a huge material lead. It may even be counterproductive since a practical chess player should be concerned by finding the easiest win, not the win that requires the least amount of moves.
Pattern recognition is trained especially by tactics positions in which only 1 set of moves leads to Rome, while all others fail in some sort of way. This way, calculation will be based on falsification, i.e. on trying to find the flaws in your calculations and choosing the move in which you could find no flaws.
In the current puzzles, most calculations will contain no flaws: every move wins. In chess, a mate in two has the same value as a mate in one in every sense: both will get you a win. Therefore, the puzzles are not useful for training purposes. If you've ever participated in a study solving tournament, you'll know that it's true the other way around as well: a special kind of pattern recognition is needed to solve most mate in x studies that is different from regular pattern recognition.

"Pattern recognition is trained especially by tactics positions in which only 1 set of moves leads to Rome, while all others fail in some sort of way. This way, calculation will be based on falsification, i.e. on trying to find the flaws in your calculations and choosing the move in which you could find no flaws."
- this is not the way i solve tactics, because its too much time consuming. i look at checks and hanging pieces and (double-)threats and let the inspiration flow and hope the wanted pattern visualizes to my minds eye.

in generell it depends whats your requirements for a training situation. if i want to train and improve on calculation ability, i prefer mating puzzles. on the other hand, if you like to train pattern recognitation, then this training on lichess is probably not the right one, because the given tactics are may be too hard to solve and doesnt regard practical circumstances. there are some good sites, where tactics can be trained. but i doubt that there exists any site in the web where one can simulate a classical game situation in which you can choose a practical approach the way Lindhorst suggested.

I think the best overall training solution would be one where the moves in the variation to be found are clearly the best moves (i.e., the only moves that win/draw).

It makes the puzzles more clear from an educational perspective, since you don't have to figure out why the "best" solution is "more winning" than the other winning lines.

It also makes it easier to test/debug the training system, since you don't have to worry about correctly handling suboptimal lines.

Now, if there were a simple, reliable way to rank suboptimal winning/drawing lines, then that would be wonderful, since that system could handle positions with any number of solutions.

Alas, such a system is quite difficult to design (perhaps impossible, since there are multiple candidate features for ranking winning lines, and it's not clear that any of these features is more correct than the others).

The closest I've found to that sort of system is at chess.emrald.net, and I quite like what they've done there. I'd probably tweak the exact criteria for the "only" moves a bit, but that's a good example of the general approach I advocate.

You can see their exact criteria explained here, if you're interested: http://chess.emrald.net/ctsProbHome.php

I also like their aggressive use of time in the rating of solutions. While they did it primarily to avoid cheating on the problems, I think time is an important element to include in training, since most competitive chess (aside from correspondence) requires not just trying to find good moves, but finding them relatively quickly.

As always, just my $0.02 :)