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As an avid chess player looking to improve my game, I am curious about the tools that top-level players, especially grandmasters, use for analysis. Specifically, I am interested in knowing which chess engine is currently the most preferred among grandmasters for deep game analysis.

Furthermore, I am also keen to learn about the current state of chess engines in terms of speed and overall performance. Which chess engine is considered the fastest and best for analysis purposes right now?

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Stockfish is the unchallenged strongest engine right now. It has won the last eight TCEC competitions, often by crushing margins. Its dominance is not seriously challenged; there are some engines that can win an occasional opening* against it, but as a whole Stockfish wins more than it loses.

However if the question is "most preferred ... for analysis", then absolute strength is not all there is. It's not irrelevant, but it's not the be-all-end-all either, because in opening preparation you are aiming to reach a position which you are familiar with while the opponent is not, while retaining scope to play for a win. This is not the same as "the position which is better for you". In this case analysis by a weaker engine can actually be preferable. Sure, the weaker engine's preferred move might lose a couple of centipawns in Stockfish's eval, but you're playing against a human, not Stockfish, and humans might not be able to capitalize. In this case, you should make use of all the strongest engines, perhaps crosscheck their preferred lines against each other. The strongest CPU engines are Stockfish, Torch, Komodo, Berserk, and Ethereal. If you have an exceptionally high-end GPU,** then the GPU engines might be more useful for you, in which case the strongest is Leela Chess Zero. (Stoofvlees is also a strong GPU engine, but it's not widely available.)

For most people, Stockfish suffices. It's only when you're at the upper echelons of chess skill where surprising the opponent is more important than achieving the objectively-best position, that you might consider the other engines.

*In engine chess, the opening is predetermined, and both engines take turns to play white. To win an opening, you need to either score 1.5-0.5, or 2-0 (known as a "double kill" or "reverse kill").

**These days there are two basic kinds of engines: the ones that use NNUE run on CPU, and the ones that use NNs largely run on GPU. Simplifying a little, the two kinds of engines are incompatible with each other's hardware. Your particular hardware is likely to be CPU-focused, making the CPU engines more useful; but if you for whatever reason have a lot of GPU resources (crypto mining, AI enthusiast, gamer ...) then the GPU engines might be preferable.

PS: You also ask about the "fastest". For your purposes this is almost surely an irrelevant metric, because speed - or nps, short for nodes (i.e. positions searched) per second - depends on how complicated an engine's evaluation function is. If you write a really simple evaluation function, your speed goes up, but your playing strength goes down, because you've lost the ability to evaluate a position as accurately.

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Not long ago, I attended a public lecture by Jon Edwards, the winner of the 2022 World Correspondence Chess Championship. In modern correspondence chess, unlimited engine use is permitted. To get an edge, the top players need to be able to make better use of all the tools available than their competitors can. Edwards said that in addition to the "usual suspects" such as Stockfish and Leela, he found that Houdini would sometimes be able to generate ideas not found by the other engines—but usually only if you were prepared to run it for several days on a position.

Edwards also emphasized the importance of databases of chess games. He said that the databases of correspondence chess games were the most important, and that even non-correspondence players at the elite level rely heavily on correspondence chess databases, and not just on databases of human-versus-human games.

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