Repeating Positions Can End the Game with “No Result”
It is possible for the game to wind up in a loop, where the same board positions repeat in a cyclical sequence. When this happens, the game might (but does not always have to) end with “No Result”. Here is the relevant rule.
Article 12. No result
When the same whole-board position is repeated during a game, if the players agree, the game ends without result.
A game that ends in “no result” is viewed as an inconclusive outcome that is different than the game ending with a tied score (jigo), which would only be possible if using an integer komi. The latter can be considered a draw, but the former should not. Traditionally, if a decisive result is needed (e.g., in a tournament), the players would have to replay an entire new game to make up for a game that ends with no result.
Further, a key provision of the rule is the phrase “if the players agree”. In this post and several of the following ones, we will explore the nuances of that provision.
The classic triple lo example for no result
A Triple Ko is perhaps the most commonly given example of a cycle that can lead to a no result. Broadly speaking, any position where there are three active kos could perhaps be called a triple ko, however the exact specifics can wildly affect what happens. Hence, let’s start with a basic “self-contained” triple ko, where all of the kos are part of the same local position:
Starting with Black’s turn to play, Black can give reprieve to their stones in atari by capturing one of the kos (move 1 in the diagram below). Now, White’s stones are in atari, and since White cannot recapture the ko, they must take another ko with move 2, which in turn forces Black to take the third ko with move 3.
Note that after 3 moves, the parity of the kos have flipped:
However, it’s White’s turn to play, and White must similarly continue by recapturing the first ko with move 4, which further compels moves 5 and 6, if both players wish to save their stones.
After move 6, the entire position has returned to where we had started. If neither player wishes to give up their stones, they could continue this loop indefinitely, and hence trigger the rules to end the game with “no result”.
Side note: a helpful way to visualize triple ko is to imagine each ko in the diagrams above as a light switch. Black is trying to flip all of the switches down, while White is trying to flip all of them up. They take turns flipping one switch at a time, but they cannot flip the switch that their opponent last touched.
Triple ko does not have to end with no result
The no result outcome for the basic triple ko discussed above requires this loop to occur and for both players to agree. If one of the players was so far ahead in score that it did not matter whether their stones were captured, then their best play would be to abandon this loop (assuming that they would rather win than end the game with no result). However, even if one player was far enough ahead, they could mistakenly persist with the cycle and have a winning game turned into a no result.
In general, three active kos does not necessary mean that the players are locked into playing the cycle indefinitely either. Moonshine Life is an interesting example, which I will talk more about in another post, where there are three active kos, but should not end in no result (unless one player makes the blunder of insisting on the cycle rather than winning).
Just a few more notes for now
- Triple ko involves a six-move cycle, but a four-move cycle (that could force a no result) is also possible with a position called Eternal Life.
- The are “three-move” and “five-move” cycles the do not cause a “no result” since they have an unbalanced number of captures.
- The possibility of abusing double ko seki is perhaps another reason for requiring both players to agree to a no result.
- The exact timing/procedures for compelling players to break a cycle (if they do not agree to a no result) is somewhat unclear, and it could have strategic implications.
- Comparing the preference between jigo vs no result would perhaps depend on external factors, such as specific tournament procedures, rating systems, prestige, etc.
- Moonshine Life is also very interesting, as mentioned above.
- I plan to write more about most of these topics on this list. If you thought my earlier posts revealed some really weird quirks about the Japanese rules, then buckle-up, since kos are where things really get crazy.
- There are many more examples of longer and more complex cycles, but I can’t hope to cover or even understand them all.