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Why I (sometimes) HATE training.

But you gotta see mates in 1 almost instantly, duh. If you can't — train it.
except, I tend to trust my initial calcs that go all the way to the end and do no thinking while making the moves. Surely if I'm presented with a mate in one I would see it. Yes, I could just be more careful while making the moves, but my point still stands when there is a mate in 4 and a mate in 3 in completely different paths. You just go with your mate and hope it's going to be the best.

I'm not saying anything should change, if I'm not finding the quickest mate that's my fault. But I see in the OP why it is frustrating...
I can see both sides of this.

On the one hand, yes, mate is mate, and even more generally, a winning advantage is a winning advantage.

So, I understand the desire not to have multiple winning solutions, or at least not to get penalized for the alternative.

The trick is that any attempt to reasonably mark the difference is quite difficult. After all , K+Q vs K+R is forced mate, but I wouldn't find it unreasonable to fail someone for bailing into that endgame when there's a mate in 3 on the board.

Obviously that one is an extreme case, but it illustrates the point. At some point you probably should fail if your win is slow enough. That cutoff point will always be arbitrary, though, so there will always be some people unhappy.

On the other hand, this is training, not a game. In a game, sure, it's most practical to go for the first win you see. If you see a win, and you know it's a win, then fire away.

In training, though, it's perfectly reasonable to impose more rigorous standards than you would in a game. It's more challenging, and forces you to find things you otherwise wouldn't have found (the whole point of learning!).

Having said all that, I do generally dislike multiple solutions, precisely because it's so hard to fairly give people retries.

That's why my favorite approach is to cut this off at the pass, in the puzzle generation. Just add the criterion that the best move has to be the only winning move (or the only drawing move in defensive puzzles).

That's how chess.emrald.net does it, and I generally prefer that, since barring cases where the engine doesn't find the other win/draw, if you're wrong, you're definitely wrong :)

The other cool, but unfortunately impractical approach, would be to have puzzles set up as sparring sessions, where you play them against an engine. Then, if you actually see mate in 5, you'll still do fine if the best line is mate in 2.

However, if you only win a couple pawns when you could have won a rook, you might be in a spot of trouble :)
#9, yes of course, they are taken from games from Lichess, but generated by an engine. No human checked these "solutions". There was an extreme case, an obvious mate in 2. But this solution was wrong! The player in the game had already made this right move 2 times, but not given mate. So the engine shows 0.00 for this move, because of threefold repetition!
#13 "The other cool, but unfortunately impractical approach..."

There's a third approach: when the user plays "mate in X" instead of "mate in 1+", prompt the user "Good move, but you can do better." IMO "mate in X" (especially if easily calculable -- with a low "proof number" PN-search value) should never be rejected.

#14 An engine using Proof-Number Search could verify the solutions against "obvious" alternatives:
http://www.top-5000.nl/ps/Mate%20in%2038-%20applying%20proof%20number%20search%20to%20chess.pdf
The Opening trainer really takes the **** sometimes. Two examples: The Russian Game 1 e4 e5 2 Nf3 Nf6 3 Nxe5; name THREE good moves. What! There`s only one good move in the position - ...d6. That was of course my first choice. But the idiot box wants two more. Riiiiiight. Well let`s try ...Qe7, as played by Ruy Lopez. It probably doesn`t lose by force. That got the green. One to go and there are no good moves left. The only other move to have (long ago) been extensively analyzes is the losing ...Nxe4. Well you have to put three or fail, yes? So I entered ...Nxe4 even though I would not make it unless showing a kid what not to play. Again a green circle.

Secondly, the French Defence after 1 e4 e6. Four good moves? OK let`s go with d4. That went well. Very little else did. I managed to get to three, trying Qe2, d3 Nc3, Nf3, e5, b3, g3; in desperation I tried Bc4, Bd3 and Be2. I managed to avoid getting the red disc but will someone tell me what the great missing fourth move is???? Ba6 perhaps?
The opening trainer requires a major overhaul.

May I add, I think the best approach would be to require one move and grade that move. Perhaps A for strong, B for commendable, C for neutral and D for everything else.
Or evalute position after finishing and compare that to +5(clear win) or best posible.
Just played another problem. http://en.lichess.org/training/20799
I am not going to spoil it (against the rules), but you can play it and understand that it's just not right.

Chess problems are made to practice tactics for games. Point of the game is to win. It's win in either situation.

The example you put It requires a great deal of effort and accurate play to win against Stockfish 8 if one just takes the queen,
if I try Im sure I can but sometimes I would even draw or I can actually lose, specially if if I move in a bullet fashion without too much thought
what I am trying to say its that is not that easy to convert a win,
sometimes having an extra minor piece its a draw, two knights vs king for example, bishop vs king.
Yes in a normal game you play agaisnt someone with the same rating and thats not that important.
But here you can win against the best machine, so I dont like your example really, there is a huge difference between material advantage and checkmate.
Read OneoftheQ post which was very well written and contains my exact same thoughts.

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