Don,

I agree that more time generally leads to better moves. Also in Go. Where I think Go differs from Chess is the qualitative difference between a move that was thought about for 10 sec. or 2 hrs. is much smaller in Go than in Chess. And that's really because of the different nature of the games. Chess really is a tactical game, so looking at more positions improves the results considerably. To move up 200 ELO points in Go is usually not achieved by looking at more positions but by acquiring new concepts. To acquire a new concept in just a few hours is a rare thing. Some of these concepts would maybe take years to acquire if there wasn't someone to teach it to them.

You wrote:
If you are given twice as much thinking time, there is bound to be 2 or
        3 moves in a 300 move game where it makes a difference in the quality
        of those 2 or 3 moves.   And that is worth 1 or more ranks of strength.

Two or three superior moves would most likely be worth a few points, not a whole rank. Two or three blunders, that would maybe make a rank or two difference. But I really don't think doubling the thinking time would reduce the number of blunders by 2 or 3. And definitely not another 2 when doubling again. (Also I think the numbers are deceiving, the vital part of a Go game rarely lasts more than 200 moves and that is only 100 moves each. And many moves are forced.)

The example you gave about studying a position for two hours and then showing it to someone 600 ELO points stronger. I think in Go someone who is 600 ELO points stronger can let the other player think about every move for a whole day and still beat him using on average just 10-20 sec. per move. It doesn't scale the way it does with Chess.

I must admit this opinion is not very scientifically based, just on personal observations of seeing players of many different levels play.


Mark

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