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When I watch the live coverage of the match between Lee Sedol and Alpha Go with 9 Dan professional Michael Redmond, I can't believe it.
That's probably because "it's not counting as we know it, jum."
They are not normally counting up each point of sure territory, and then doing a raft of hypothetical boundary-play sequences around more open areas, and counting those 1, 2, 3, 4.... They can do that, and may, at least once or twice, actually do it. But in fast games there are more important things to think about in the brief moments available.
So they use various alternative techniques.
A common one is to count just the mistakes. They start with the premise that the game starts even and (between pros) almost all moves are NOT mistakes. So when they spot the few mistakes, it is easy to make a mental note of them. Mistake in this context tends to mean things like overconcentration or some similar inefficiency. For example, making a ponnuki capture with five stones instead of four. Pros furthermore have a very good intuitive sense, based on long experience, of what each type of mistake is worth.
There are other similar heuristic techniques, some of which are beyond the ken even of normal pros. Yi Ch'ang-ho was famous for "counting", which too many people seem to think is the 1, 2, 3, 4 type. It was rather his ability to
sense how many points he would get out of fuzzy shapes in the centre, which he could superimpose on the other heuristic techniques, that made him the envy of other pros.
There are also non-heuristic techniques, of course. The main one is sheer memorisation. A typical pro will know by heart the de-iri or miai count (ways of counting the value of a move rather than a position) of maybe 1,000 common positions. The very first book on boundary-play counting, Genan Inseki's
Igo Shukairoku of 1844, was of this type.
And add to all that the fact that many pros do actually have the ability to make a pretty accurate 1, 2, 3, 4 type of count at high speed. They may have to sacrifice some precious time, but that's often easy to do. For example, in 30 seconds a move, if the opponent plays an atari that forces you to connect, don't do it at once but spend your 30 seconds counting. Plus you can count in your opponent's time.
Having said all of that, pros DO miscount, and - believe it or not - even sometimes make mistakes in counting up the game at the every end when the game is over and time is no longer a problem (though maybe fatigue is).