# Maximum stone disparity

I am wondering what is the maximum disparity you have seen in any game, where the winner of the game had fewer stones on the board?

For a hypothetical maximum I am sure the difference could be quite large.

In a nonsense game under Chinese scoring, the winner might continually pass while the loser fills up his own territory with stones.

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Thatâ€™s an interesting question, but I have no idea, since itâ€™s not something that I have ever thought to consider.

Does â€śstones on the boardâ€ť only count the living stones or all physically present stones at the end of the game?

The theoretical maximum is easy to work out if you assume that all groups left on the board are alive, ie. the last phase of scoring is complete. Black should have the minimum number of points, 2, and White one more, 3. The smallest three-point group is, I think, seven stones with an area of ten.

So, White has seven stones. How many does Black have? Blackâ€™s stones could form a single group covering the rest of the board. 361 - 10 = 351. Remove two stones for the eyes and you get 349. The difference between the number of stones, then, is 349 - 7 = 342. Black can have a maximum 342 more stones on the board than White in a lost game.

(Edit: had to correct this, mixed up stones and group area)

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You can use seki and let white win by komi to get an even worse result with Japanese rules: white only has three stones on A2, A3, A4, black has filled all other intersections with exception of B2 and B4. That gives white a win by 6.5, while there is a difference of 353 stones.

Iâ€™m not sure this is the smallest possible, but I have a feeling it is.

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so youâ€™re looking for games where one side captures many many stones but still loses the game because of the strategy

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I think these are two very different questions:

1. Whatâ€™s the hypothetical maximum (allowing nonsensical games where both players just conspire to inflate the disparity)?
2. Whatâ€™s the largest disparity that youâ€™ve seen in a â€śnormalâ€ť, sensible game (where both players, preferably stronger ones, are playing well and just trying to win)?

The first is a mathematical problem, while the second requires examining actual games. I think @Skurj means to ask about the second question, which I am quite curious about as well. I hope that people provide some examples to respond to the second question.

The same could happen in a Japanese rules game.

If you consider Japanese rules and let white win by komi, then white does not need to put any stones on the board. Black can put 359 living stones on the board, with two eyes giving only two points of territory.
Thus, the largest (uncontroversial) disparity seems to be 359.

We could consider whether 360 is possible, but I think that would involve a rules debate to resolve. If black has 360 stones on the board (all but one point occupied), and then both players pass, are blackâ€™s stones alive?

The Japanese rules have an interesting way of defining â€śaliveâ€ť:

[Article 7.1] Stones are said to be â€śaliveâ€ť if they cannot be captured by the opponent, or if capturing them would enable a new stone to be played that the opponent could not capture.

Even though a 360-stone group with just one eye could be immediately captured, doing so would leave an almost wide-open board, where black could clearly play additional stones that would live. So, I believe that a 360-stone group, if both players pass and agree to end the game, would be considered alive. White would have no interest in capturing that group to continue the game, since komi already gives white the win.
Thus, if you accept my line of reasoning, then 360 seems to be the maximum disparity.

Reconsidering the definition of â€śdisparityâ€ť, if we simply count all stones present after both players pass, but before we remove any â€śdeadâ€ť stones, then clearly, the above rules debate is not necessary, and we could say that 360 is the maximum disparity, even if we were to argue that a 360-stone group is ultimately dead.

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Exactly thus. Hypothetical maximums are an interesting, but brief, exercise.

Iâ€™m more curious to know how extreme the ratio can get when both (high-level?) players are doing their level best to bag the win.

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What about " average stone disparity in pro games" or similar concepts ?
(and perhaps limited by time-range/geography/levels, and so for)

Is there any way to query existing and preferably large databases of Go games and find out? I took a quick look at the few database options listed on Sensei.net and could not find out how, but perhaps someone more familiar with these products could?

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Thereâ€™s a possible scenario where two players make big dragons and then trade them, like through a ko. One player, in the endgame, is forced to actually take the captured dragon off the board because the capturing stones are short of liberties; but the other player isnâ€™t. That could easily mean a 50+ difference in the number of stones really sitting on the board.

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I think the hypothetical maximum that could be reached without passing is, perhaps, a more accurate maximum score.

Figure that, without passing unevenly, Chinese and Japanese scoring are the same. If white wins, the minimum number of stones required to create territory by which she could do so would be to have a wall down the middle of the board. The minimum winning margin would be to have 7 stones on the 10th line, and 12 on the 9th, for a score of 183.5, with 5.5 point komi, to blackâ€™s 183. Black can have a living group with two eyes, exactly, for a total of 181 stones to whiteâ€™s 19. This board would be achievable if white continuously played in blackâ€™s territory, and black continuously responded and captured whiteâ€™s stones until only two 1-point eye spaces remained. Black would have 162 more stones than white.

In that scenario, though, black could easily invade whiteâ€™s territory. Perhaps a follow up might be: whatâ€™s the minimum number of additional stones white would need to solidify her side? It definitely seems possible with 4: two on the 3-3s and two between those stones. It might be possible with three? Iâ€™m not sure. With 4 stones, the maximum difference would seem to be 158 stones.

While still nonsense: it at least guides us to what must happen for a huge disparity to happen: someone needs to sacrifice a lot of stones to secure a large, open area. The games with the biggest capturing disparities will, naturally, lead to the biggest stone disparities.

Pro games see differences far less than that, and the only massive sacrifice and win games Iâ€™ve found end in resignation. Hereâ€™s a decent first contender, though: http://gokifu.com/s/2ttq.js I think white is up by 26 stones when he resigns, but I may be miscountingâ€¦

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So the primary cap in that scenario is the modesty/humility of a professional player.

If we had a really tenacious individual who insisted on playing out an effectively lost game, what would be his/her strategy and how far could the scale continue to tip?

If someone played inside their own territory, thatâ€™d tip things.

Thatâ€™s still contrived, though, so Iâ€™m not sure itâ€™s a meaningful exercise compared to just calculating the theoretical maximum.

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Well, I once gave my younger brother (13 at the time I think) fifteen stones on a 13x13 board and wonâ€¦ Yes, he knew the rules.

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