What is the Elo rating of Stockfish version that played AlphaZero?

Question

AlphaZero has defeated Stockfish with all novelties and brilliant strategic sacrifices. But some people were disputing its win, because Stockfish was running on weak hardware (1 GB RAM), not access to opening book, not having free time control, maybe not have endgame table base, etc.

This setting by DeepMind is understandable from a scientific perspective though. It is to test intuitive/strategic play by deep learning technique vs. counting/tactical play by brute force search. However, this leaves chess lovers with many questions like what is the true strength of AlphaZero? What is the true advantage of strategic/positional sacrifice play? Were Morphy, Tal, and others correct and Stockfish wrong? Or full version Stockfish is still the best?

One work around is to replicate the Stockfish version that played AlphaZero, to see how strong it is compared to the full version and other engine and human. Thus we could infer the Elo rating of AlphaZero and answer most questions.

So, did anyone test it? Is anyone interested in testing it? Maybe Stockfish developers, because Stockfish's pride is at stake? Or is there other way to approach the problem?

Thanks

Edit:

• Note that Stockfish had good 64 threads CPU and could evaluate 70 million positions/second.
• The Stockfish Elo rating provided in the paper is the full version, thus this replication is needed.
• The paper.

Answer 1

The Stockfish version that played agaist AlphaZero was significantly compromised in several different aspects:

1. There was no opening book available
2. Time control was 1 minute/move, which throws out of the window various optimizations re: using more time thinking about difficult moves
3. Stockfish had threads=64 set, but the actual hardware had only 8 CPU cores, that effectively slowed things down quite a lot
4. The hardware was quite different -- an average $1k PC (Stockfish) against a bunch of specialized hardware that might cost millions and is not accessible to anyone
5. There are more, but these are main points.

Answering your question, there's no way to measure how much rating Stockfish had in a very handicapped conditions it had to run.

Nonetheless, winning over Stockfish is quite an achievement, no matter how handicapped it was and how much was the difference in hardware cost.

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UPDATE: in the recent article "AlphaZero: Shedding new light on the grand games of chess, shogi and Go" the rating for Stockfish was drawn as a line at 3500. Besides that, the article provides the new games played with a reasonable time control for SF as well as opening books.

Answer 2

AlphaZero vs. Stockfish 8, 1000-game match as in the latest paper (with Stockfish operating at full power) yielded a score of +155 -6 =839. Using this calculator gives an elo difference of 52.

Stockfish 8's elo rating on computer chess rating lists is about 3378, giving AlphaZero a rating of about 3430.

Disclaimer: these rating lists are generated with hundreds of thousands of games between all the engines. With only 1000 games against a single engine, this 3430 rating is unlikely to be accurate. AlphaZero is certainly one of the stronger engines out there, but it's not clear exactly how strong.