A silly question: What's the highest obtainable score in a game of Go?

This question occurred to me, which seems at first glance relatively easy to determine, but actually becomes very complex when you consider capturing, ko fights, handicap stones (ignoring handicap komi which is arguably infinite), etc. No doubt the ruleset has significant impact here too!

I will offer my “Fermat’s Theorem”, that a score over 361 is possible for a single player, and moreover I suspect over several thousand can be obtained (though my knowledge of the rules is functional at best).

Anyway, mathematicians and pedants welcome.

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361+komi for AGA and NZ rules. Semantics of Chinese scoring would lead to 180.5+komi/2.

Japanese rules allow repetition of the same board state, so you can drive the score to any value with a cycle in which one player passes more often than the other.
If you forbid passing the upper bound is again 361+komi if white plays the last move (+1 if black is playing last).
Edit: assuming komi is >=0 for white.

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Chinese sums stones and territory, right?
So, if all white stones are dead, black should have exactly 361 points.
If all black stones are dead, white should have 361+komi.

Am I missing something?

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With Japanese rules, Black plays 79 times and White passes 79 times, Black plays so we get position 1 below:


Then White captures 80 stones and we get position 2:

Black places 79 stones (everywhere except J1 and J2), White passes 79 times, then Black captures 1 stone and we are back to position 1.

In the cycle, Black has made 1 capture and White 80 captures so White gained 79 points. If we make n cycles, White can make 79n points in the process.

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That works only because Japanese rule forgot to give a prisoner for each pass (did that change in some new Japanese ruleset? I don’t know.)

Yes, that’s correct. The semantics that @flovo are referring to is just a different, but equivalent, way of recording the same score. See the “half counting” section of Chinese Counting at Sensei's Library. Basically, you can just count one player’s score and compare it against the size of the board (minus any unplayed dame) divided by two, while also adding or subtracting half-komi (depending on if you counted for black or white).

I don’t think the official Japanese rules tradition has ever used pass stones.

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I believe AGA invented this technique to allow area rules to be counted using territory counting. AFAIK they are the only ruleset that implements pass stones.

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Agree.
But knowing "if Black’s score is more or less than this ‘half count’ " (from Sensei’s) doesn’t mean that black has to divide by two his own score.

If all white groups are dead, black’s score is 361, which is more than the half count.
180.5 isn’t the highest score. It’s the half count and also it’s the amount of points black has other than the half count.
So we can say “black wins because he has 180.5 points more than the half count”, which means also “black has 361 points”.

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Yes, that’s true. It’s purely a matter of semantics of how one defines “score”. Some might say that the “score” refers to each individual player’s count, while others might use “score” to refer to the margin of the outcome, like calling things like “B+3.5” as the “score”.

See, every discussion on this forum comes back to linguistics.

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Gotta say… You’re sounding a bit pedantic there :wink:

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This is not about forgetting something. :slight_smile: Japanese rules use territory scoring. Giving prisoner for pass is area scoring.

It’s forgetting if you want to have the same scoring. Japanese scoring was elaborated after the Chinese way in an attempt to get a more sophisticated scoring but my guess not in an attempt to modify the score. To have a perfect equivalence, they shouldn’t have forgotten this prisoner for a pass rule (Especially for this kind of uncommon problematic of this topic)

Besides, giving a prisoner for a pass is used in similar scoring as Japanese scoring (Territory) to make it always equivalent to a Chinese scoring (area)

Area scoring is enclosed area + stones on the board. No use for pass stones there. Equivalence scoring needs pass stones. Territory scoring can use them, but usually doesn’t.

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The basic difference between area and territory is temperature - whether dame worth more than pass. With pass stones you get points for dame (if the opponent needs to pass, like one-sided dame for example) - or from the other viewpont you lose points for passing but not for dame. Territory scoring cannot use pass stones (as that would make dame valuable compared to pass).

You probably thought about hybrid scoring rules (like Spight), that include a territory phase followed by an area phase. Those rules use pass stones, but only in the area phase.

Edit: You are right that area scoring remains area scoring regardless of pass stones (which are not counted). Territory scoring, on the other hand, becomes area scoring with pass stones.

This is a popular misbelief. In reality Japanese scoring was invented much earlier than today’s Chinese scoring. History went like this: stone scoring → territory scoring → area scoring. (I remember I was also surprised when learned about this.)

Area scoring - today’s Chinese way - is relatively new. Btw, Japanese theorists are very aware of the theoretical differences in scores/results and are actually proud of them (like finer granularity, no free reinforcement, no pts for one-sided dame etc.).

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Do you have some sources elaborating on this timeline?

I was under the impression before that both the modern Chinese and Japanese rules descended from stone scoring, which is likely the form of the game that propagated to Japan over a thousand years ago. However, that is not the same as to say that one descended from the other, but rather they diverged from a common ancestor.

It seems a bit tricky to determine the exact evolution of these things, since both types of rules were not so formally codified and written down precisely until the 20th century, and long existed as just commonly understood tradition.

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By the way, see here for a source where I’m basing on my understanding from:

Depends on how many times white is willing to play at A:

Screen Shot 2021-10-22 at 17.41.10

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I cannot cite sources off hand, but I’m sure of this. You can try to google - IIRC Bill Spight wrote about this a few times on L19, plus others as well.

This is not even a doubtful detail in history, the difference is probably several centuries. I’m not sure but the transfer of the game from China to Japan may already have used territory scoring, at least there are records of very old Chinese games that already used territory scoring. Even in China area scoring is new.

Edit: just to clarify, I’m not saying area scoring necessarily evolved DIRECTLY FROM territory scoring, but was invented several centuries later, and was likely influenced by it.

No the pass stone is a prisoner to put on the board, and the scoring will be proceed like a Territory scoring (counting the emptyness only)

In my post, i was very careful to not talk about China or Japan, as i know already that which rule was used before here and there is notably not clear.

What do you call stone counting ? Is it the way where you fill all the Territories (without pass) until the loser will have to suicide? (A counting which doesn’t give exactly the same result as multiplicity of groups is a desavantage )