A contact play, sometimes just referred to as "contact," is a type of move from the game of Go (Wei Qi/Badouk). A contact play arises when one player plays orthogonally adjacent to a stone of his opponent's (contrast with a shoulder hit, which is diagonally adjacent). In the diagram below, a Black play at any of the points marked "*" would be a contact play on the White stone marked "o":

.....
..*..
.*o*.
..*..
.....

Although it is not essential for either stone to be isolated for the play to be considered contact, if either is connected to a larger group, one usually talks about the move in different terms, and some of what I'm going to say here does not apply.

The most important thing for a beginner to learn about a contact play is that, although it looks like an aggressive attacking move, since it reduces the liberties of both stones, one should never use a contact play as a form of attack (unless engaged in something like a semeai, but that's different). The reason for this is that the usual follow-up sequences to a contact play tend to strengthen both sides. Since the purpose of an attack is to weaken the opponent's group, a contact play is almost always counter-productive. Instead, contact plays should be used as a form of defense; play contact to an opponent's stone that is already so strong that his strength gain is minimal, and your group will benefit from the exchange.

The most common response to a contact play is hane, also known as a bend. It's a kind of wrap-around move. In the diagram shown here, Black (x) has just played contact to White's (o) stone. White will usually respond at "a" or "b.":

....
.a..
.xo.
.b..
....

When an opponent plays hane on one of your isolated stones, one of the most common responses is to play a nobi or stretch to increase the liberties of that stone and prevent an atari. If White plays "a" in the above diagram, Black will probably play "c" or "d" in the diagram below, although if he wants to make a fight out of it, he might play the more severe crosscut at "e":

.....
..oe.
.cxo.
..d..
.....

From here there are many possible continuations. For instance, if Black plays at "c" and White makes a tiger's mouth, the situation would look like this:

.....
...o.
..o..
.xxo.
.....

To anyone who has played Go a few times, it should be clear that White's three stones are now significantly stronger than the isolated stone was. Thus, if Black was intending to attack, he has accomplished exactly the opposite of what he wanted to. White is connected, has plenty of liberties and even a bit of potential eye space that wasn't there previously.

More rarely, one sees nobi as a response to a contact play. This is played in situations where the player who had contact played against them has reason (real or imagined) to fear a crosscut if they play hane. I play nobi way too often, because crosscuts scare me to death. A White nobi response to a Black contact play would be at "a" or "b" (or, much more rarely, "c") in the below diagram.

.....
..a..
.xoc.
..b..
.....

Note that although nobi is a less common response to most contact plays, it is almost always the correct response to a contact play if the contacting stone is played as a kosumi (diagonal connection) to another stone of the same color. So, if Black has just played kosumi contact as shown in the next diagram, White should nobi at "a." The result is sometime's referred as "the weak player's diagonal" for Black, and the kosumi contact is usually a mistake on his part, although it appears as the correct move in at least one common joseki.

.....
.x.a.
..xo.
.....

In conclusion, two well-known Go proverbs essentially sum up how to use, and how not to use, a contact play:

"Attack from a distance."

"Defend with contact."

Many weak players would get a stone or two stronger by breaking the habit of attacking with contact, just because it looks aggressive.

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