This online article about King Safety in chess programming discusses Stockfish toward the end. https://chessprogramming.wikispaces...

And it really doesn't matter how much processing power was given to Stockfish because all AlphaZero is doing is searching through its database that it collected from past games involving the same position, games which AlphaZero compiled by playing against itself, and then choosing the best moves based on its win ratio. So, AlphaZero is 100s of moves ahead because with every move AlphaZero makes, it already sees checkmate in X number of moves, or a draw from current position. Stockfish just cannot even compare.

"In 100 games from the normal starting position AlphaZero won 25 games as White, won 3 as Black, and drew the remaining 72, with 0 losses.[32] AlphaZero also played twelve 100-game matches against Stockfish starting from twelve popular openings for a final score of 290 wins, 886 draws and 24 losses, for a point score of 733:467.[33][note 1] The research has not been peer reviewed and Google declined to comment until it is published.[32]"

Yes, we all agree on this. I've tried writing an AlphaZero member to get the additional games, but he begged me off citing a pending submitted article's publication.

If I worked for Google, I would consider copying the games and giving it to Wikileaks.

<tonsillolith: Let's also not forget that the time controls Stockfish was made to use were not the ones it was optimized for. If we saw an Alphago vs Stockfish match that was organized by Stockfish's creatora instead of by Alphago's, this could be a very different outcome>

I don't think that you understand how AlphaZero in partcular or neural networks in general work. AlphaZero does not have an explicit database of all the games it has played or all the games it was provided to analyze. Instead, AlphaZero, like all neural network-based chess engines, uses that information to calculate the proper weights for its nodes to use when calculating the best move to make at any one time. So the information derived from its neural network training is <implicit> in AlphaZero's memory but not <explicitly>.

<We can consider chess solved with AlphaZero, because chess really only has a finite number of moves.>

Chess does have a finite number of possible moves or, more appropriately. Possible positions. But that number is so high that it might as well be infinite. It has been estimated anywhere from 10^43 (the Shannon number) to 10^52 positions. This measure of complexiity is referred to as state space complexity since it counts every possible position once regardless of how it was reached; i.e. ignoring move transpositions. This is equivalent of the information contained in each chess engine's hash table.

Using the lower number of 10^43 and assuming that the chess computer can evaluate 1 position / attosecond (10^-15 seconds, with 12 attoseconds currently being the best timing control of laser pulses), it would mean that computer would need about 3.17*10^21 years to evaluate all possible positions. Given that the age of the universe is estimated at 1.47*10^10 years, it's not practical in the near future to completely solve the game of chess.

<Perhaps Google will one day allow us to search positions through AlphaZero's database. To be honest, AlphaZero reminded me of Paul Morphy's reckless game play. But at least Morphy's games were analyzable!>

This reminds me of one of my favorite jokes:

A man is driving along a road in his car when suddenly an animal jumps across his path. The man swerves to avoid it but as a result he drives his car into a ditch. As the man is considering what to do he spots a farmer in the field next to the road and goes to meet him.

Man: "Excuse me, do you by chance have a rope?"

Farmer: "Yes I do."

Man: "Great. My car went into a ditch as I swerved to avoid hitting an animal that suddenly jumped the road. Can I borrow your rope to pull my car out of the ditch?"

Farmer: "I'm sorry, no. I need the rope to tie up my milk."

Man (puzzled): "But you can't use a rope to tie up your milk?"

Farmer: "When you don't want to do something, one answer is as good as another."

I think that it's even more pertinent to compare the relative power of the hardware used by AlphaZero with the hardware used by Stockfish in their match. After all, if you want to compare the relative performance of two <software> chess engines, you want to have them run either on similar <hardware> or <hardware> with equivalent performance. That's why the TCEC championships and the various chess engine tournaments like CCRL and CEGT are all run on the same hardware.

The hardware use by AlphaZero during its match with Stockfish consisted of 4 second generation and proprietary Tensor Processing Units rated at 45 TFlops each for a total performance capability of about 180 TFlops. Stockfish ran on a Linux system consisting of, supposedly, 64 cores, since the DeepMind AlphaZero paper (https://arxiv.org/pdf/1712.01815.pdf indicated that it used 64 threads. Assuming a system of something like 16 Intel i5s each with 4 cores running at 3.4 GHz the total performance capability of the hardware running Stockfish was about 1.68 TFlops. So the hardware running AlphaZero during the match was > 100 times more powerful than the hardware running Stockfish.

Stockfish's opening book and tablebase support were disabled during the match. This might seem fair since AlphaZero doesn't have either, but they represent part of the strongest Stockfish configuration, even though the default Stockfish installation, at least in Arena, does not include the use of their . And, they also represent some of what Stockfish has "learned" about the opening and endgame so, whether it "learned" by having it available during game play doesn't seem to be any different than what AlphaZero learned during its training. But that's clearly a matter of opinion.

As you mentioned, Todd Romstad, one of Stockfish's original creators, also talked by the effective disabling of Stockfish's time management algorithm by using a fixed time/move, saying that a lot of effort was spent in incorporating "smarts" into Stockfish to determine which positions were not critical and therefore did not need much analysis time, thus making more analysis time available for the critical positions that required it. AlphaZero did not have a time management function because this was, after all, a proof of concept and not a production chess engine so that again may or may not be a fair comparison of the two engines' playing strength.

Disabling tablebases in Stockfish, to be fair, probably had little to no effect on the outcome; the slowdown in accessing SSD data probably eliminates almost all advantage accruing to perfect information on 6-piece endgames, especially at 60-second-per-move time controls.

It wasn't clear to me that they disabled opening books per se. The AlphaZero team's preprint says: "Table 2 analyses the most common human openings (those played more than 100,000 times in an online database of human chess games (1)). Each of these openings is independently discovered and played frequently by AlphaZero during self-play training. When starting from each human opening, AlphaZero convincingly defeated Stockfish..." The last sentence evidently means that they started the AlphaZero-Stockfish games from some set of common openings. Indeed, on page 6 of the preprint, they indicate that AlphaZero and Stockfish played (at least) 1200 games, consisting of a 100-game match in each of 12 openings. For example, they report that in E61, the King's Indian Defense, AlphaZero beat Stockfish +16 -2 =82. In C00, the French Defense, AlphaZero beat Stockfish +43 -0 =57. I guess "the" 100-game match that AlphaZero won +28 -0 =72 was a separate set of games. If so, they never explicitly say whether or how openings were chosen. In this game at least, AlphaZero and Stockfish do stay in book for quite a while.

At any rate, I'm pretty sure that you would get better performance from 64 physical cores without hyperthreading rather than from 32 physical cores with hyperthreading, so I gave the presumable Stockfish configuration the benefit of the doubt and I assumed 64 physical cores without hyperthreading. If the Stockfish configuration used was indeed 32 physical cores with hyperthreading then the performance advantage for AlphaZero would be greater than 100X, possibly in the 130X – 150X range. And I also have no idea how alpha-beta pruning would be impacted by hyperthreading, although I'm reasonably sure that it would be slower with 32 hyperthreaded physical cores than with 64 physical cores without hyperthreading. Which is why I always wondered why Google/Deep Mind indicated that the Stockfish configuration used "64 threads". If indeed it was 32 hyperthreaded cores, then that would be somewhat misleading with regards to the performance capability of the system used to run Stockfish.

For a similar perspective you can look here: https://chess.stackexchange.com/que.... But I don't know how old the system where Stockfish ran was, I doubt that it consisted of Intel I9 Extreme Processors, so I suspect that the system used for Stockfish was substantially slower. For more information about TPUs, see https://en.wikipedia.org/wiki/Tenso.... But basically a TPU is designed for a high volume of low precision computations of the types that are common to neural network-based calculations. You could presumably run AlphaZero on an Intel processor by implementing the TPU calculations in software but at great impact on performance, but I have no idea of the magnitude of the effort required. Some enterprising,, dedicated, and independently wealthy person(s) could probably do that to satisfy their curiosity, but I'm 100% sure that Google/Deep Mind will not spend the time and money to do this and make AlphaZero perform less capably in another match with Stockfish.

With respect to the openings I read the AlphaZero paper again and every time I read it I get more confused. I also apparently didn't pay much attention to pages 5 and 6. It now seems clear, at least to me, that separately (a) AlphaZero and Stockfish played "the" 100-game match starting from the initial position with AlphaZero performing considerably better than Stockfish and (b) they presumably played 12 100-game matches (a total of 1200 games) from each of the positions shown in Table 2. So I don't think that Stockfish necessarily had its opening book enabled for part (b), the board was set according to the final position in each of the openings and play resumed from there, with AlphaZero playing White for 50 games of each opening and Stockfish playing White for 50 games of each opening. I don't know how either AlphaZero OR Stockfish selected their openings in their "Initial Position" match.

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This is almost certainly a draw. Consider the following position that might eventually be reached:

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This 6-man endgame position is a draw, although Stockfish8 evaluates this position at greater than <+2.00>! It seems that Stockfish could improve its evaluation of unbalanced endgame positions.