Nash's 1952 RAND report speculates an unproven "dualization"-type pairing strategy for Hex, distinct from his existence proof

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Nash's 1952 RAND report goes beyond the bare non-constructive existence proof already recorded in the vault's prior note on the same document. In the same passage where he states that "the winning strategy is, as yet, unknown", Nash goes on to speculate about what an explicit strategy might look like: "It is possible, however, that he has a dualization type strategy." He sketches the idea concretely, as a guess rather than a proof: "If such were the case he could guide his play by a division of the board into 3 classes of hexagons: (a) His first move (b) A class of paired hexagons (c) A class of dummy hexagons" — with the second player's occupation of one hexagon in a pair answered by the first player occupying its partner.

This is a second, distinct move within the same report: not the existence proof itself, but an unproven conjecture about the shape a constructive strategy might take, offered decades before pairing-strategy arguments became a standard tool in combinatorial game theory. Nash does not claim the scheme works, and no source read at capture time confirms, refutes, or traces this specific 1952 conjecture forward to the field's later constructive results.