Can chess engines calculate Mikhail Tal's sacrifices?

Spock didn't always understand Captain Kirk's thinking.

Not 2 exp to 64  -1, but 2 exp to 63  +1. That is not so much as 1645 times the global production of wheat in 2014.

Interesting proposition, since a high level chess engine might look at the same position and find a far better line of play, or at least find a way to refute some of Tal's sacrifices.

It's also possible that certain engines would find and play those sacrifices, and other engines will go for less risky play, going for more of a positional, long term advantage.

Part of the issue, is that Tal (who I admire greatly), is a human being and not a chess engine.

What sacrifice that Tal spotted and brilliantly played, and thought long and hard over, might be instantly disregard by a high level engine as being refuted by play most human GMs might not consider.

Best comment. Short but enough. Mikhail Tal's sacrifices on chess board are ever remembered. Thanks @fabelhaft.  

As it happens, I have created such an engine a couple of years ago, see http://www.pkoziol.cal24.pl/opental/

It runs best under Arena chess interface and has some problems with Fritz GUI. Also, there's one feature that might be confusing: program can read opening books, but it will always prefer a move from internal book made from Tal's games.

Hi Pawel, glad to see you again. I'm curious about Brendan, who has apparently gone invisible. Any information on whether he's still involved with chess engines these days?

Sadly, no contact with Brendan - his web page went missing, my last contact with him 3 months ago, his last social media outings were 2 months ago, more about global politics than about chess.

how many player like Tal? 

That is why I AM afraid of him

(This explanation is only for sacrifices that are not part of a tactical sequence)

Chess engines will always be able to calculate much further into the future (and with perfect accuracy) than humans. Engines always give the best possible move, which means the move given by the engine will always give the greatest advantage possible to that side. Often times that involves gaining as much space as possible while not giving your opponent any possible openings for a good move that gives them the advantage. Chess engines not recommending most of Tal's crazy sacrifices does not mean the engine cannot calculate or comprehend the move, it means the engine sees a refutation to the sacrifice that gives the opponent the advantage. Tal's moves are incredibly effective again'st humans because they deeply complicate the position making calculation very hard, therefore making the best move for the opponent very unclear. Calculation and finding the best move in a deeply complicated position for an engine is a joke, it can calculate any position 15+ moves in advance in a matter of seconds, far superior than any human could hope to be. If you set up a position vs a computer on chess.com by clicking on the "Learn" tab on the left, then click "analysis", and then in the options just to the right of the chess board click "Setup", you can set up a position from any game and see the computer's recommendations/lines. Arrange a crazy Tal sacrifice on the board and look at the computer's suggestions. If the position is equal before the sacrifice you will see that the computer can refute the sacrifice quite well and probably take advantage from it. If the position is in favor of Tal's pieces, you will likely see the computer refute it in a way that gives Tal's side the smallest possible advantage. Tal's moves seem incredible because they often work, but they do not work because they are the overall best move, they work because they complicate the position so much that the opponent (a human) blunders (or just makes a small mistake), which results in Tal gaining advantage from the move. If the opponent managed to find the best refutation to the sacrifice (and the correct following moves) then in most cases Tal would not gain advantage from the series of moves. If the position is equal, it would likely stay equal or the opponent would gain advantage because Tal sacrificed a piece, if Tal had the advantage the position would likely stay at that advantage or Tal's advantage would decrease because again, he sacrificed a piece.  As stated at the top, moves that are part of a tactical sequence that give advantage will often be suggested as one of the top picks by the engine. For example, if sacrificing your knight on f6 leads to a forced checkmate or severe material loss for the opponent within the next 5-6 moves, this would likely be the engines top recommendation (unless there is another move that leads to a forced checkmate or that causes even more severe material loss). A tactical move like this that has a clear benefit to the player in the foreseeable future AND that has no good refutations (the opponent has no possible moves that save them from checkmate AND severe material losses) is not considered a Tal move. This is a tactical sequence that happens all the time when players get checkmated. Tal moves are random pawn pushes or piece sacrifices that complicate positions deeply and makes it very difficult for the opponent to find the correct moves. Again, engines can calculate these moves, but they can also calculate the refutations. If the engine sees one possible move from the opponent that gets them out of trouble, the Tal sacrifice would likely be considered very poor because the opponent is no longer in trouble AND you just sacrifices a piece, likely putting you at a massive disadvantage to the point that you might as well resign. That is all, hope it makes sense

The computer is correct, it is by no means "TOO COMPLICATED" for computers to understand. 20...Bxc7 21.Rxf6 Nxf6 simply refutes your sacrifice and black is equal if not better. The much stronger sacrifice was 20.Bb5!! cxb5 21.Nxd5 Qe6 22.Ng6 and white is just crushing.