  Past efforts to classify impartial three-player combinatorial games (the
theories of Li and Straffin) have made various restrictive assumptions about
the rationality of one's opponents and the formation and behavior of
coalitions. One may instead adopt an agnostic attitude towards such issues, and
seek only to understand in what circumstances one player has a winning strategy
against the combined forces of the other two. By limiting ourselves to this
more modest theoretical objective, and by regarding two games as being
equivalent if they are interchangeable in all disjunctive sums,as far as
single-player winnability is concerned, we can obtain an interesting analogue
of Grundy values for three-player impartial games.
