Cutting point is a term from the game of Go (Wei Qi/Badouk). It refers to an unoccupied point on the board where one player can play in order to "cut" an opponent's group apart into two separate (and presumably weaker) groups. They often occur where two stones of the same colour are only touching diagonally, with an opponent's stone in one of the two intersections that adjoin both of them (this is the kind of cutting point shown in the example below). Other kinds of cutting points exist, of course. An important part of mid-game tactics in Go is looking for cutting points in your own formation (so as to protect them) and your opponent's (by exploiting them). Here is an example, showing the initial situation (white represented by O, black by X) and the sequence of cutting moves and responses (shown by numbers, white being the odd numbers and black being the evens).

. . . . . . . . . .

O O . . . . . . . .

X X O O O . . . . .

8 3 X X O . . . . .

9 6 4 X O . O . . .

117 5 1 X O . . . .

. . . . 2 X O O O .

. . . . . X X X O .

(Black 10 at 3) The numbers are a bit confusing, so here's the final situation (white's stone #3 was captured, and black 10 will be in the hole): ..........
OO........
XXOOO.....
XXXXO.....
OXXXO.O...
OOOOXO....
....XXOOO.
.....XXXO.

Black is now quite clearly cut into two pieces, and the awful lump of black stones at the left is probably going to be captured (depending on what stones there are out of sight on the left). Black probably should have let white capture the first stone he ataried.

Disclaimer: I am a very weak Go player, only around 18k (22k* on IGS) at the time of this writing. Given the situation shown here, there are no doubt better ways to cut (which would also depend on surrounding stones), but I'm just trying to illustrate the concept.

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