Tiger's mouth applications
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With the tiger's mouth of . Black creates a weakness in White's wall.
Vice versa, White creates cutting points in Black's position.
For either player, simply connecting is too soft. may even be omitted.
In this joseki a tiger's mouth appears, creating better eyeshape. It is a very strong shape. An alternative to is playing at a, which intends to reduce White's base along the side.
However compared with a, has much more eye potential. A single black move at b instantly creates a live shape with two eyes at c and d.
Bulge and anti-bulge
prevents White from making a tiger shape. The result can be seen as a weak player's diagonal for White. See also bulge and anti-bulge