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What are the differences? And do these differences influence strategy?

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In france and america, the AGA rule is very nice: it makes every situation to be played to be resolved (where Japanese rules have many special cases treated according to the rule). the AGA/french/? rules also allow one to use both Japanese or Chinese counting, therefore quite nice to use (as both players play the same amount of stones, the counting will be equivalent in "almost every cases") –  Olivier Dulac Nov 26 '13 at 20:00
    
I like to teach Go by presenting only the Chinese rules (It focus on the main goal: occupy territory! Everything is played out. Prisonners are not important "per se" [and it's nice to show that you can just hand them over to the opponent]. So the learner knows she/he has to focus on occupying territory instead of capturing stones. Do NOT confuse them with 2 set of rules. Later, I do use Japanese COUNTING, as it's fast: put prisonners back into opponent's territory, arrange empty areas in multiple of 10 [5x2, 10xn, 3x4-minus2stones] so that it's both easy to count AND to re-count if unsure. –  Olivier Dulac Nov 26 '13 at 20:02
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up vote 15 down vote accepted

From Wikipedia:

Although there are some minor differences between rule sets used in different countries, most notably in Chinese and Japanese scoring rules, these differences do not seriously affect the tactics and strategy of the game.

There are two basic scoring systems used to determine the winner at the end of a game; they almost always give the same result. Territory scoring counts the number of empty points your stones surround, together with the number of stones you captured. While it originated in China, today it is commonly associated with Japan and Korea. Area scoring counts the number of points your stones occupy and surround. It is associated with contemporary Chinese play and was probably established there during the Ming Dynasty in the 15th or 16th century.

Read the full article here.

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