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Analysis is wrong

Why in this game http://fr.lichess.org/b4DSCrdb/black#80, at the move 40, analyse advice the move c5 and 41.Bd2 but if white play the move Bd2 there is a mat in 2 for black with 41. Bd2 - Qe2+ 42. Kg1 - Qg2#, so why the analysis advice a white move who lead to a checkmate ?
Maybe he server that did the analysis was using its cpu for other things when computing that move/line and didn't have time to look ahead that far.
A couple things probably combined there.

1) As flugsio pointed out, it's likely the engine performed a VERY short analysis on that move.

That alone isn't enough to explain it, though since a check like Qe2+ is going to get extended and the mate seen basically immediately.

2) Moves towards the end of displayed variations cannot be trusted. Part of this is because they are based on shallower analysis, but another big part is that the moves towards the end of the displayed variation are often not even part of the actual main line calculated by the engine.

The reasons are strange and complicated, but ultimately the take home message is that you shouldn't rely on moves shown deep in a displayed variation.

In this particular case, the fact that the displayed variation is only 2 ply shows that something very unusual was going on with the computational time allotted, or with how the variation was displayed.

Both are good reasons not to trust the variation. Just as a confirming side-note, it's not at all uncommon at TCEC to see the main lines of top engines ending in positions with simple tactics for one side. The engines aren't overlooking those; it's just a quirk of how they reconstruct the principal variation for display purposes.

'Tis a funny world :)

C5 was a better move, because you needed that queen that you had relied on for most of the game. Bd2 would just turn the game around for white.
Also plus the computer just calculates the best moves for each side to achieve checkmate the fastest.

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