Where Is the " Thousand-Dollar Ko ''?

This paper features a problem that was composed to illustrate the power of combinatorial game theory applied to Go endgame positions. The problem is the sum of many subproblems, over a dozen of which have temperatures significantly greater than one. One of the subproblems is a conspicuous four-point ko, and there are several overlaps among other subproblems. Even though the theory of such positions is far from complete, the paper demonstrates that enough mathematics is now known to obtain provably correct, counterintuitive, solutions to some very difficult Go endgame problems.