Disjunctive compounds of short combinatorial games have been studied for many years under a variety of assumptions. A structure theory for normal-play impartial games was established in the 1930s by the Sprague–Grundy theorem [Grundy 1939; Sprague 1935; 1937]. Every such game G is equivalent to a Nim-heap, and the size of this heap, known as the nim value of G, completely describes the behavior of G in disjunctive sums. The Sprague–Grundy theorem underpins virtually all subsequent work on impartial combinatorial games.

Decades later, Conway generalized the Sprague–Grundy theorem in two directions [Berlekamp et al. 2003; Conway 2001]. First, he showed that every partizan game G can be assigned a value that exactly captures its disjunctive behavior, and this value is represented by a unique simplest form for G. Conway’s game values are partizan analogues of nim values, and his simplest form theorem directly generalizes the Sprague–Grundy theorem.

Conway also introduced a misère-play analogue of the Sprague–Grundy theorem. He showed that every impartial game G is represented by a unique misère simplest form [Conway 2001]. Unfortunately, in misère play such simplifications tend to be weak, and as a result the canonical theory of misère games is less useful in practice than its normal-play counterparts.

In each case—normal-play impartial, normal-play partizan, and misère-play impartial—the identification of simplest forms proved to be a key result, at once establishing a structure theory and opening the door to further investigations. In this paper, we prove an analogous simplest form theorem for the misère-play partizan case. The proof integrates techniques drawn from each of Conway’s advances, together with a crucial lemma from [Mesdal and Ottaway 2007].