(;GM[1]FF[4]CA[UTF-8]AP[CGoban:3]ST[2]
RU[Japanese]SZ[19]KM[0.00]
PB[Black to play]AW[ep][fp][bq][dq][gq][cr][dr][bs]AB[dn][co][cp][dp][cq][eq][br][er]C[This is the problem position. Black to play.]
(;B[ar]C[The proverb says to always sacrifice two stones
instad of one. This is the correct move.]
;W[aq]C[This atari is the only possible move for white.]
;B[ds]C[Black calmly plays atari knowing the two stones can be taken.]
;W[as]C[It looks like white has an eye and lots of liberties...]
;B[br]C[... but black plays inside to catch white short.]
(;W[ar]C[This is white's strongest move.]
;B[es]C[Black now has 4 liberties and white 4 but
the common liberty is in black's favour.]
(;W[fr]C[If white tries and outside liberty...]
;B[cs]C[.... then the eye becomes false when black plays here so
losing a liberty.]
;W[br]C[White is clearly a liberty behind now.]
;B[bp]
;W[fs]
;B[ap])
(;W[cs]C[If white makes the solid eye it is three liberties
each with black tom play. ]
;B[bp]
;W[fr]
;B[ap]
;W[fs]
;B[br]))
(;W[cs]C[This white connection is self-atari.]
;B[ar]))
(;B[ds]
;W[ar]C[This is two eyes for white, so a failure for black.])
(;B[bp]
;W[ar]
;B[ds]C[This is also two eyes for white.])
(;B[aq]C[This move can sometimes lead to a ko.]
;W[bp]
;B[ap]
;W[ar]
;B[bo]
;W[ao]
;B[ap]C[But no ko in this position white is already alive.])
(;B[cs]C[This may look like threateing a snap-back shape...]
;W[ar]C[...but white is already alive.]
;B[ds]
;W[es]
;B[ds]C[Still white is alive.]))
