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How much stronger are human/computer teams vs. computers alone? My understanding is that that advantage is enough to be decisive, especially in correspondence play, but just how large is it?

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    The general consensus until recently has been than human+software > software, but the human has to be one of the best GM for the difference to be significant. However, the recent AlphaZero revolution will probably cause a serious reassessment, and a gloomy one for human's pride. – Evargalo Dec 11 '17 at 10:43
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Well, humans have the advantage of identifying potential long term positional ideas where as computers are better at calculating quite complex positions. I predict most of the games would end up in draws but in some situations (specially endgames where you need depth as well as complex strategic plannings), human and computer partnership would triumph. A famous example would be the Caruana vs Nakamura game where computers never identified the queen sacrifice. https://www.youtube.com/watch?v=dMjj9SPnlBE.

Also it's self evident that artificial intelligence programs such as Alpha-go-zero has both human like abilities (long term strategic plannings) as well as computer like abilities (deep calculations). So it would be a great example for you to see the games played between Alpha go zero and chess programs like Stockfish (https://www.youtube.com/watch?v=vP2J4WNN4Qg)

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It pretty mcuh depends who the human is. Me + SF can almost always beat SF alone with longer thinking time. It does not take much insight to do that, as I know by heart precisely what moves in precisely what lines SF misplays and precisely what pawn structures it plays badly. Every second move or so, SF will make a mistake, of which the human might take advantage. 3 such mistakes/inaccuracies are sufficient to lose you the game. On the other hand, I will not blunder anywhere in the game as I could have if playing alone, as SF will assist me in tactics, so me + engine could theoretically win every single game. Of course, this will not happen, but this is just the theoretical side of it. If the human player does not know the engine's weaknesses, then there is not much added value to the team. For example, me + unknown engine versus unknown engine might end unexpectedly, even with a win for the unknown engine. In this case, the human might even be a burden, if he chooses not to follow the engine's recommendations. In general, however, a team should always be not only stronger, but significantly stronger, it is always like that when the fight is 2 on 1 and the single entity is of comparable strength.

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    I can only smile, here you go: :-) – Wlod AA Jan 22 '18 at 2:48

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