If Black had defended correctly (see problem 4890) then Black should live unconditionally.
Black A19 however is a costly mistake, though it is not easy to find the best way to exploit it.
(;AB[ca]AB[cb]AB[cc]AB[cd]AB[be]AB[bf]AW[af]AW[bg]AW[cf]AW[ce]AW[dd]AW[dc]AW[db]AW[da]AB[ad]AB[aa]AW[ab]AW[cg]AW[bi]TR[aa]C[White has played a 3 point endgame move at A18, and Black has a frivolous reply. Try to find the optimal response.]AP[goproblems]
(;W[ac]
(;B[bb]
(;W[ba]
(;B[bd]C[If Black has no big ko threat B16 is imminent.]
(;W[aa];B[bc]
(;W[ab];B[aa]
(;W[ba]C[Ko, and Black still needs to find the first threat. Nice.RIGHT])
(;W[ag];B[ac])
(;W[ae];B[ac]))
(;W[aa];B[ab])
(;W[ag];B[ab]))
(;W[ag];B[aa]C[Ko, White needs to find the first threat. Close but not good enough; you should make Black find the first threat, especially so when there aren't any.])
(;W[ae];B[aa]C[Ko, White needs to find the first threat and Black has an internal ko threat to boot. What a waste.]MA[ag])
(;W[bc];B[aa]))
(;B[de]C[This shows what happens if Black tenukis or plays a threat that White can ignore...]
(;W[bd]
(;B[aa];W[ae]C[RIGHT])
(;B[bc];W[bd]C[RIGHT]))
(;W[bc];B[aa]C[This time the ko favors Black.])
(;W[ag];B[aa]C[Ko, White to find a threat first.])
(;W[ae]
(;B[aa];W[bd]C[RIGHT])
(;B[ag];W[bd]
(;B[bc];W[bd]C[RIGHT])
(;B[aa]
(;W[ae]C[Bizarre but correct anyway.RIGHT])
(;W[af];B[bc])
(;W[ba]C[NOTTHIS]))))
(;W[aa];B[bc])))
(;W[bd];B[bc])
(;W[bc];B[bd])
(;W[ae];B[bd]
(;W[ba];B[ag]
(;W[af];B[aa]C[Ko, White needs to find the first threat. Not good enough; it would be better to make Black have to find the first threat, especially so if there aren't any.])
(;W[aa];B[af])
(;W[ah];B[af]))
(;W[ag];B[bc]))
(;W[ag];B[bc]))
(;B[bc]C[In case you wonder why Black does not play like this?];W[ba];B[bb];W[bd]C[That's why.RIGHT])
(;B[bd]C[Surely White won't fall for this?]
(;W[ba];B[bb]
(;W[aa];B[bc]
(;W[ab];B[aa]
(;W[ba]C[Ko, and Black still needs to find the first threat. Nice.RIGHT])
(;W[ag];B[ac])
(;W[ae];B[ac]))
(;W[aa];B[ab])
(;W[ag];B[ab]))
(;W[ag];B[aa]C[Ko, White needs to find the first threat. Close but not good enough; you should make Black find the first threat, especially so when there aren't any.])
(;W[ae];B[aa]C[Ko, White needs to find the first threat and Black has an internal ko threat to boot. What a waste.]MA[ag])
(;W[bc];B[aa]))
(;W[bb]C[The beauty of nakade fills the heart with joy.RIGHT]))
(;B[ba]
(;W[bc]C[RIGHT])
(;W[bd];B[bc];W[ag];B[bb];W[ae]C[RIGHT])
(;W[ag];B[bc];W[ae]C[RIGHT])))
(;W[ba]
(;B[bb]
(;W[ac];B[aa]C[Ko, White needs to find the first threat. You should make Black needing the first threat, especially so if there aren't any.])
(;W[aa];B[ac])
(;W[bc];B[bd]
(;W[ag];B[ac])
(;W[ae];B[ag])
(;W[ac];B[aa])
(;W[aa];B[ac]))
(;W[bd];B[bc]C[Black lives.])
(;W[ae];B[ac]
(;W[bd];B[aa]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.]MA[be]MA[bf])
(;W[ag];B[aa]MA[be]MA[bf]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.])
(;W[bc];B[aa]
(;W[bd];B[be]C[])
(;W[ag];B[bd])))
(;W[ag];B[ac]
(;W[ae];B[aa]MA[be]MA[bf]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.])
(;W[bd];B[aa]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.]MA[be]MA[bf])
(;W[bc];B[aa])))
(;B[ac]C[Black would never even think about playing this, wouldn't Black?];W[bc];B[bd];W[bb];B[aa];W[bb]C[Definitely not! ;)]))
(;W[bb];B[bc]
(;W[ba];B[ac]
(;W[ag];B[aa]
(;W[ae];B[bb]MA[be]MA[bf]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.])
(;W[ab];B[bb])
(;W[ba];B[bb])
(;W[bb];B[ae]))
(;W[ae];B[ag]))
(;W[ag];B[ae]
(;W[ba]C[Black lives in seki and has sente.])
(;W[ac];B[ba]))
(;W[ae];B[ag])
(;W[ac];B[ba]))
(;W[bc];B[bb]
(;W[ba];B[bd]
(;W[ag];B[ac])
(;W[ae];B[ag])
(;W[ac])
(;W[aa];B[ac]))
(;W[ac];B[bd])
(;W[bd];B[ac])
(;W[ag];B[ac])
(;W[ae];B[ag]
(;W[ba];B[bd])
(;W[af];B[ac])
(;W[ac])))
(;W[bd];B[bc]
(;W[ba];B[bb]C[Black lives.])
(;W[bb];B[ac]
(;W[ag];B[ae];W[ba];B[aa])
(;W[ba];B[aa])
(;W[ae];B[ag]))
(;W[ac];B[bb])
(;W[ag];B[ae]
(;W[ba];B[bb]C[Black lives.])
(;W[bb];B[ba])
(;W[ac];B[bb]))
(;W[ae];B[ag]))
(;W[ae];B[ag])
(;W[ag];B[bb]
(;W[ba];B[ac]
(;W[ae])
(;W[bd];B[aa]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.]MA[be]MA[bf])
(;W[bc];B[aa]))
(;W[ac];B[bc])
(;W[bc];B[ac])
(;W[bd];B[ac]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.]MA[be]MA[bf])
(;W[ae];B[ac]C[Black is more than glad to sacrifice 2 stones in exchange for unconditional life.])))