(;AB[aq]AB[bq]AB[cq]AB[dq]AB[er]AB[es]AW[bp]AW[cp]AW[dp]AW[eq]AW[fr]AW[fs]AW[ap]C[Black to get the best result (using Japanese rules); assume there are no large ko threats for Black.]AW[ep]AW[fq]AP[goproblems]
(;B[dr];W[cs]
(;B[br];W[bs]
(;B[as];W[ar]C[A 1000 year ko. If Black wins it Black cannot connect and must play C2 or D1, after which White retakes. If White wins it White can connect to make a seki (1 point for the captured stone) or give atari at C2 or D1 after which Black retakes. Neither wants to start this ko; hence its name. This is worse for Black than a regular seki.]MA[cr]MA[ds])
(;B[cr];W[as]C[Bent 4 in the corner; Black is dead.])
(;B[ar])
(;B[ds];W[as]C[Bent 4 in the corner; Black is dead.]))
(;B[cr];W[bs]
(;B[as];W[ar])
(;B[br];W[as]C[Bent 4 in the corner; Black is dead.])
(;B[ds];W[ar]))
(;B[bs];W[br]
(;B[ar];W[as]C[Ko])
(;B[cr];W[as]C[Black is dead. White can create a one-eye lump at B1 first, then A2, then (if Black captures) B1 again.])
(;B[as];W[ar])
(;B[ds];W[ar]))
(;B[as];W[br]
(;B[cr];W[bs])
(;B[bs];W[ar])
(;B[ds];W[ar]))
(;B[ar];W[bs])
(;B[ds];W[br]
(;B[bs];W[ar])
(;B[cr];W[ar])
(;B[ar];W[bs])))
(;B[cr];W[bs]
(;B[cs];W[ar]C[Sente seki, no points. If next B2 then White plays D1 (atari); Black takes at A1, White takes at D2. 4 points each, still equal to seki. This is one point worse than the solution.]MA[br]MA[ds])
(;B[ds];W[cs])
(;B[br];W[cs]
(;B[as];W[ar]C[Ko])
(;B[ds];W[dr])
(;B[ar];W[dr])
(;B[dr];W[as]C[Bent 4 in the corner; Black is dead.]))
(;B[dr];W[cs]
(;B[as];W[ar])
(;B[br])
(;B[ds];W[ar]))
(;B[as];W[cs]
(;B[br];W[ar]C[Ko])
(;B[ar];W[dr])
(;B[ds];W[dr])
(;B[dr];W[ar]))
(;B[ar];W[cs]))
(;B[cs]
(;W[dr]
(;B[ds];W[bs]
(;B[cr];W[ar]C[Sente seki; also Black has a point (the captured stone)RIGHT])
(;B[br];W[cr])
(;B[as];W[cr])
(;B[ar];W[cr]))
(;B[cr];W[ds])
(;B[br];W[ds])
(;B[as];W[ds])
(;B[bs];W[ds])
(;B[ar];W[ds]))
(;W[bs];B[dr]C[Black lives with points, White won't play like this.RIGHT]))
(;B[ds];W[cs]
(;B[dr];W[br]
(;B[bs])
(;B[cr];W[ar])
(;B[ar];W[bs]))
(;B[cr];W[bs])
(;B[bs];W[dr]
(;B[cr];W[ar])
(;B[ar];W[cr])
(;B[ds];W[cr])
(;B[er];W[cr]))
(;B[br];W[dr]))
(;B[bs];W[dr]
(;B[cr];W[ds]
(;B[ar]C[Black lives but White has sente and 3 points more than in the solution.])
(;B[cs];W[ar]))
(;B[ar];W[cr])
(;B[ds];W[cs]
(;B[cr];W[ar])
(;B[ar];W[cr])
(;B[ds];W[cr])
(;B[er];W[cr]))
(;B[cs];W[ds]))
(;B[br];W[dr]
(;B[cr];W[cs])
(;B[cs];W[ds])
(;B[ds];W[cs]))
(;B[ar];W[dr]
(;B[cr];W[bs]
(;B[ds];W[cs])
(;B[cs];W[ds]))
(;B[bs];W[cr])
(;B[ds];W[cs]
(;B[cr];W[bs])
(;B[bs];W[cr]))
(;B[cs];W[ds]))
(;B[as];W[dr]
(;B[cr];W[cs])
(;B[cs];W[ds])
(;B[ds];W[cr])
(;B[br];W[cr])))