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I've read somewhere that Fan Hui was ranked between 600th and 700th world Baduk player. Knowing he's 2P whereas some players are up to 9P, it seems reasonable to me.
Is there any official and accessible world ranking ? What is the exact rank of Fan Hui ?
Just to add a few notes in addition to Pieter's answer, and with a hint to your implied question (can AlphaGo beat Lee Sedol?):
First off, I'm not sure if you thought being 9p automatically means being stronger than 2p. This is not the case.
However, in this particular instance, other matters are of more importance. Fan Hui has not been competing in Asian (i.e. highest level) tournaments for many years, and his competition in Europe is limited - that's why he's the current European champion, after all.
However, this also means that it can be assumed that he's not quite as sharp as an active, competing pro in Asia. His focus simply shifted towards teaching, as teaching was the reason he came to Europe. That is to say, and with no disrespect to Fan Hui's great skill, Lee Sedol, an active top level competitive pro, is quite a bit stronger than Fan Hui - 2 stones, goes the rumor among pros.
Obviously, the closer we get to perfect moves, the more difficult it becomes to improve further: For instance, doubling AlphaGo's calculation power does not at all lead to doubled strength. Think of it more like a logarithmic scale: To improve another stone in strength, you have to put in just as much work as you did for all previous stones together (roughly speaking). It remains to be seen if AlphaGo's improvements since the Fan Hui games are large enough.
While we cannot compare pros by their rank, we can get a rough idea of their relative strength by using Dr. Taeil Bai's chart, of which I reproduce the beginning of the most recent version I could find (from cyberoro, 2014):
![[3]](https://i.stack.imgur.com/Prazi.png)
I am not aware if Fan Hui is included in the list, too - if he was, that might be the source for your 600th-700th information.
I believe your information comes from this unofficial rating system:
Fan Hui's page on that site:
http://www.goratings.org/players/1480.html
Fan Hui only only played a few pro games - none recently - so his ranking there (or any other pro ranking system) is unreliable.
1P-9P rankings are not ratings (you only go up) and don't necessarily reflect the player's current strength.
Is there any official and accessible world ranking ?
No; Rankings are done by national Go organizations, with some variance existing between them.
What is the exact rank of Fan Hui ?
As reported here,
Fan [Hui] earned a 2-dan professional ranking in China before emigrating to France, so it appears that go software has reached the level of professional play.
and
..., but it is worth noting that the AlphaGo programming team reports that AlphaGo can beat the best rival computer programs with a four-stone handicap. That is something that several other 9-dan pros have had trouble doing in the past few years.
