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In Demis Hassabis' presentation at the the Kinds of Intelligence Symposium in January 2018, grandmasters are compared to AlphaZero and Stockfish along an interesting metric: how many moves are searched per decision made? It is claimed that ``human grandmasters'' considers 10 of moves per decision they make, AlphaZero tens of thousands, and Stockfish tens of millions. Is there any scientific evidence regarding the number of moves per grandmaster or human in general? 10 seems to me a very arbitrary number. Where does it come from?

PS. I didn't know that grandmasters can be non-humans as well!

Edit. I missed this answer but my question is not about what make a grandmaster special? Or how many moves can foresee a grandmaster? I understand that any number would depend on the position. My question is I guess more precise: is there any scientific evidence, experiment, or study that tried to measure the average number of moves a human can consider during a certain amount of time?

My attempt was to read Alexander Kotov's book "Think like a grandmaster". Kotov asks this simple question: How many candidate moves a grandmaster examine? Kotov does not give any precise answer: ``they are unusual cases where there can be five or six, where in the next they are actually seven'' but his book dates back from the seventies (1971 for the English translation) and I was wondering if someone tried to test this more scientifically, by estimating an average number.

marked as duplicate by Brian Towers, Glorfindel, fuxia, Phonon, GloriaVictis Dec 30 '18 at 15:39

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I assume you're wondering about the speed of calculating moves. I'm not sure how you would go about figuring out the max #moves a GM can calculate (I guess the experiment runs until they fall asleep?).

I'm an FM and I can calculate a couple of moves per second (1-3), assuming the calculation is trivial enough. For more complicated positions where I need to analyze in the middle of my calculations, the speed significantly slows down to how long I need to analyze. This depends entirely on the complexity of the position. GMs are probably slightly faster than me on average. I'm not sure where the "10 moves per decision" figure came from.

From what I understand of AlphaZero, it uses a very strong intuitive (generated from playing itself thousands of times) combined with Monte Carlo Tree Search. This search plays out random simulations of games, starting from where AlphaZero is calculating, and then the move that ends up scoring the highest is chosen.

Stockfish uses the typical minimax with alpha-beta search algorithm, combined with other algorithms which increase efficiency (esp. iterative deepening). It doesn't calculate to the end of the game in each branch, but instead goes up to a certain point and evaluates the resulting position based off its evaluation heuristics.

As for the speed of moves/second between AlphaZero and Stockfish, it comes down to how fast (on average) they can evaluate one position/node. The overall way they traverse the calculation tree is irrelevant when talking about raw calculation speed. Calculation speed comes down to two things:

  • The speed of the computer the Engine is running on.
  • The algorithm used to evaluate a position.

Assuming Stock and AlphaZero are given equal computers, then on average I would assume AlphaZero is faster (I don't have any official sources for this though). This is because it evaluates based off a very fined tuned intuition which it learned by playing itself over and over. Meanwhile, Stockfish uses evaluation heuristics thought up by humans. They're very good heuristics, but still only human made.

On ChessBase, Stockfish evaluates over 1 million nodes/positions per second. I don't know what AlphaZero's speed is, but when they eventually publish the engine you could check it out then.

  • Thanks for those insights. As a FM myself, I can attest that GMs are much faster than me on average! But I also don't know where the "10 moves per decision" figure came from. The experiment I have in mind could have been done during, say, half an hour... For instance, counting at loud the number of moves a human can calculate during a certain period of time. – Kortchnoi Dec 28 '18 at 23:35
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    @Kortchnoi For sure, that'd probably give you a rough ballpark. But when you mentally calculate a move and record it (or say something to signal someone else to record) it takes time and interrupts your calculation flow. So the results would need to be adjusted accordingly. – Inertial Ignorance Dec 28 '18 at 23:55

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