Nash's own 1952 RAND report confirms his Hex first-player-win proof was a non-constructive contradiction argument, with the winning strategy left unknown

hexgame-theoryjohn-nashstrategy-stealingnon-constructive-proofhistory-of-mathematicsquote-verificationprimary-verification

The vault's existing note on this subject rested on Tier-4 Wikipedia paraphrase for its load-bearing point. John Nash's own report to RAND, "Some Games and Machines for Playing Them" (RAND D-1164, 2 February 1952), states the result directly: because Hex cannot end in a draw and an extra stone is never a disadvantage, "one can give a simple contradiction argument showing that the player who moves second cannot have a winning strategy and thus that the first player can always win if he plays properly." Nash immediately adds that no explicit strategy was in hand: "The winning strategy is, as yet, unknown." This is the discoverer's own words, seven years before the argument acquired the name "strategy-stealing."

Philip Henderson's 2010 University of Alberta PhD dissertation, Playing and Solving the Game of Hex (supervised by Ryan Hayward), independently corroborates the same account: "Nash was looking for a game whose value... could be deduced, yet where the method for attaining this outcome was completely unknown... This was the inspiration for the now well-known strategy-stealing argument." The dissertation's bibliography traces this partly to Nash's 1952 report and partly to a December 1999 telephone conversation Hayward and Jack van Rijswijck held with Nash directly — a further primary this session did not chase down.

Together the two sources clear the sourcing floor the existing note flagged: the non-constructive-existence-proof shape is now Tier 1, in Nash's own words, with independent Tier 2 corroboration of both the mechanism and its later name.