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Go strategy is extremely complex and well-studied, so we won't try to cover more than the basics. You can find more at external sites like Sensei's Library.
Life and death is an important concept:
- A group is dead if the opponent can eventually capture it, and alive if they can't.
- A group with two eyes (two small territories) is alive, because the opponent can't fill up both eyes at the same time.
Basic strategy:
- Go is a race to surround territory as fast as possible, so play the biggest moves first. Generally these are those that decide the life or death of big groups, or that stake out large territories.
- Starting in the corners is more economical than starting in the middle or on the sides. For illustration, think of how much area can be surrounded by 4 stones in the corner (4 points) compared to the side (2 points) and the middle (1 point).
- Don't waste moves trying to capture stones that save a group that can't be saved.
- Don't worry about losing individual stones. You get another one every turn.