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Two possible minor improvements for the local analysis:

1. The suggested moves are written in a weird notation only consisting of the starting square and the destination square of the moved piece (e. g. d3h7 instead of Bxh7+). It's of course still clear which move is suggested (especially with the arrow appearing on the board), but I guess it would increase the readability even more if the algebraic notation was used.

2. The local analysis cannot be triggered on moves that have already been analyzed by Stockfish. This makes it difficult to find improvements for moves that haven't been marked as inaccuracies / mistakes / blunders by Stockfish. Also, if the evaluation of the final position deviates from what you thought about it (e. g. Stockfish says you're winning, but you had offered your opponent a draw), you can't use the local analysis to find out the winning continuation.

Aside from these 2 things, I'd say this new feature is perfect.
I especially like the arrows drawn on the board for the currently considered "best move". This is quite helpful when the engine fluctuates between several moves too frequently to actually read the suggested move.
I also like that the local analysis isn't triggered automatically, so you can alyways analyze a posisition on your own first.
#21

1. Converting UCI notation to algebraic notation is not trivial and is always done server-side. As this is client-side analysis, the code to do this isn't available and is unlikely to be written any time soon (very tedious).

2. Seems like a fair critique to allow computer analysis on moves already analysed server-side to get a second opinion.
There seems to be a cap on the depth (18) for client side analysis. Is there a reason for this? I would want it to be infinite as:
1. Power consumption / Battery Life is not a concern on plugged in devices
2. Some endgame positions, stockfish is able to reach immensely high depths quite easily and so the (18) limit might produce lower quality evaluations.
Amazing the 'power' of open source and team-work.
github.com/nmrugg/stockfish.js

#23
current depth 18 limit is due to quick response only.
Stockfish.js online:
nmrugg.github.io/kingdom/

(but for deep analysis it is better to use installed c++ version, compiled javascript is not as fast as compiled c++, and stockfish.js can only use one cpu-core yet)
yeah, the depth cap is unfortunate.

Never knew that stockfish is actually available on javascript, amazing.
I totally agree with the second point of #21. I think it's very important to be able to turn on the local analysis for games previously analyzed by the server. You can find yourself in a totally lost position without ever playing an "inaccuracy" just by making subpar moves that lose you less than 49 centipawns and never know why.

Another feature that would be convenient is a button that automatically plays the top computer move. For example, you want to follow a computer line 10 moves deep to see the point. Currently you can do this by finding and dragging the appropriate piece around the board one at a time for both sides. Instead, if the "best move: e1c1" line was actually a button that made the move it suggests, you could keep your mouse in one place and just click 10 times in a row. I think this is a pretty common feature in chess analysis software, but I'm not sure how much work it would be for Lichess to implement.
Yes this site is TOP right now at chess for sure. That new computer analysis on real time is a dream come true for everybody. Simply outstanding :-))
I just threw another $5 in the donation box bringing my September total to $15. More to come over time. I have no problem putting money into a project that makes such good use of it.
Suggestion about client side analysis: Show 3 best possible moves with their weights on each turn. And also paint arrows for those moves on the board using different opacity.

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