Removing captured stones in a timed game

I have not spent much time playing Go in the “real world.” Most of my experience with the game has been online, although I did purchase a goban a few weeks ago. I have been considering buying or making a clock, but I had a question about how to use a timer in a face-to-face game:

Imagine that I am playing with 20-second byo-yomi, and I capture a large group of my opponents stones. Do I have exactly 20 seconds to make the move, remove all of the captured stones from the board, and push the timer? How is this normally dealt with in face-to-face games?

One can pause the clock if there is a capture of three or more stones.

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I didn’t know that was allowed. I learned something today.

That’s a fairly common rule in blitz tournaments, rather than a universal truth. In slow tournaments you usually can’t pause the clock even for big captures. I was once playing a game with 50 stones in 5 minutes accelerating overtime with no such rule and I pre-emptively captured dozens of dead stones in a semeai rather than playing a useful move as I was miles ahead and my opponent could have played atari on me at the end of a byo-yomi period to win on time.

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If memory serves, in America it is an official aga rule. I had the impression it was standard in Europe also.

I was able to find this in Senseis Library:

http://senseis.xmp.net/?CommonClockRules#toc4

Stopping clock for removing big captures

For how many stones may the clock be stopped?
EGF: 3 (Clock neutralisation - 5.)
AGA: 2 (VI. E. Timekeeping. 10. c.)

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It’s like @Pempu say you can find it in EGF rules Chapter 5, paragraph 6. [1]