Protein 3-dimension structure prediction has been the “crown jewel” of life sciences – AlphaFold2 provided a pivotal tool to 2M researchers to better understand life, develop pharmaceuticals & therapies, and much more.
2021 AlphaFold paper https://www.nature.com/articles/s41586-021-03819-2
Similarly Go game on a 2-dimensional board also has the 3rd-dimension. Amid classical views of territory vs influence, or the perspectives in fighting tactics and quantitative value, Ko adds a critical long-distance, third dimension.
How? When a Ko takes place, all four factors above must be reevaluated: territory, influence, tactics and value, because a player can play two moves in a row anywhere on the board when the opponent resolves the Ko. The gain from consecutive moves is usually vast. Ko of Go is unique among board games, which connects seemingly irrelevant groups or areas.
In opening or early game, Ko can be a huge “bomb” as hardly any Ko threat is big enough to trade for. In attacking, strong players could hold on the Ko variation and aim for creating weak groups, which lead to more Ko threats later on. In a game of mine on OGS, I waited over 100 moves for a better timing to play Ko.
In settling or defense, Ko is often the solution in complicated, Fa Yang Lun-level life-and-death positions. In an exciting 2024 Lanke Cup North America Qualifier, Michael Chen 1P and Alex Qi 1P played six Ko fights in the final match: Video commentaries
In endgame Ko can still be a “dagger” or “buzzer beater”. Ryan Li 4P’s endgame Ko ranks No. 1 among 60+ brilliant moves evaluated by a judge committee consisted of 3 Pros and 3 strong players, for the National Go Artistry Contest.
2016 Breakthrough with AlphaGo https://www.nature.com/articles/nature16961
Nature full-paper https://www.davidsilver.uk/wp-content/uploads/2020/03/unformatted_final_mastering_go.pdf
A famous small-endgame Ko strategy is taking dames while maintaining the Ko. This CAN decide a game sometimes – turning a White 0.5-point win into a Black 0.5-point or 1.5-point win. Ko is also the major cause that some games officially end with a draw, a rare result in Go.
It’s so fortunate of me to see the “3-dimensional beauty" in both DeepMind’s AlphaFold2 and Go game’s Ko.
2021 AlphaFold paper https://www.nature.com/articles/s41586-021-03819-2
Photo credits: Nature; AFP/Getty Images; Google Blog