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Suggestion for improving the training (puzzles) tool.

My general suggestion is to allow players to vote for changes, which will be updated automatically upon some set number of votes, as follows:

1) Add or remove moves. Sometimes a move or two at the end of a puzzle is extraneous, or another move or two would be a good addition to a puzzle. Mostly this seems to come in the form of extra computer moves at the end, but sometimes it seems like one or two fewer human moves would be good as well.

2) Allow part marks (partial increases in training rating). For when the position is improved to a winning one but not checkmate or totally winning. Similarly, the option to change "wrong" to "good move but try again" for certain moves would be an improvement to a lot of puzzles. While I prefer the flexibility of lichess puzzles over some other sites (such as multiple checkmating lines being allowed), losing points for improving to a winning position (even dominating) or making a decent but not great move after getting a winning position in a puzzle can be a downer.

I was thinking the votes could be like other sites use for tags (eg. pin, fork, skewer, smuggled mate, etc.), with a +5 vote and 70% of votes for any change resulting in the change being adopted.
In the case of controversial votes (i.e. significant disagreement between people), perhaps the problem could be segregated somewhere to be computer analyzed or voted on by higher-rated members of the site.

3) Add tags (pin, skewer, mate in 3, etc) for those people looking to improve by doing puzzles in specific areas. Not sure if computer analysis of an individuals game could point a person directly to their explicit weaknesses (eg. missing mates, missing forks, etc.), but this too would be an excellent addition in the future should it be possible to code.

4) Allow the computer to show why a move is bad upon user request (i.e. play the winning counter-move or reveal the line on-screen) when a person makes a bad move.

I think the training tool is pretty good, but implementing changes like those above would make it world-class IMO, much like the rest of this site.

Thanks for the excellent work so far;
-WT
I suppose 4 above doesn't belong in the list per se, but I can't see a way to edit my response... Maybe an edit button with a timestamp of the last edit made wold be nice too?
Regarding 1):

In my experience most puzzles have additional moves when pieces still need to retreat after an attack, which, believe it or not, needs to be trained, as well. Fewer moves aren't the worst thing either, as you've already improved your position, and if you've thought the puzzle through, you would easily see the actual gain of the piece.

Regarding 2) and 3):

The user is supposed to be analyzing the puzzle, not take a look at it and move on a whim. Adding those two "features" would just result in a rating inflation where there is no need for it.

Granted, a tagging system is not the worst idea, but it'd give away too much of the puzzle itself.

Regarding 4):
That's a good idea, but already partially implemented, as the user's able to head over to the Analyze Section to do exactly that.
@Burned beef:

Re. 1: The suggestion was mainly driven by the extra moves that the computer plays at the end of puzzles, which add a bit of extra processing usage to the site while sometimes leading people to not realize that the puzzle is indeed over. The other issues mentioned are less common, but still there in some puzzles. Some puzzles seem to have another winning move at the end as well, which would be nice to play out. With the safeguard I suggested (+5 plus 70%), I think this would be a net positive.

Re 2 and 3:

I was not suggesting moving on a whim, but rather not losing points for making completely winning but not best moves. For example, in one puzzle a player can either checkmate or win two rooks for free with no counter-attack for the opponent (i.e. a totally dominating position), this should not count as a loss despite being non-optimal.

That said, most of these would fall under the "not the best move, try again" prompt, which people could fairly easily figure out/vote on in most cases. Here is another example http://en.lichess.org/training/10951, in which winning a piece with a queen is "wrong", but winning it with a bishop is "right" despite trading down in a winning position.

Also, the tagging was not meant to show the winning idea before the puzzle is played, but rather to help train specific areas that a person wanted to work on. If giving away the winning ideas to those retrying problems was an issue, this could perhaps be hidden (via a check box on-screen or via user preferences) per individual preferences.

Re. 4: I'm aware that people can do that (both via Analyze and play vs. computer), I was simply saying that having the options closer at hand would be an improvement.
Re. the trading down thing, this seems to be an issue in a bunch of problems, i.e. winning while trading down is treated as a negative, despite being common advice given to players finding themselves in winning positions. Maybe having more pieces on the board works well with high-level computer play, but for most people trading down while ahead is the better play in most positions.

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