In my online History of Game Theory I have an entry dated 1713 on the first use of a mixed strategy,
In a letter dated 13 November 1713 James Waldegrave provided the first, known, minimax mixed strategy solution to a two-person game. Waldegrave wrote the letter, about a two-person version of the card game le Her, to Pierre-Remond de Montmort who in turn wrote to Nicolas Bernoulli, including in his letter a discussion of the Waldegrave solution. Waldegrave's solution is a minimax mixed strategy equilibrium, but he made no extension of his result to other games, and expressed concern that a mixed strategy "does not seem to be in the usual rules of play" of games of chance.The reference I gave for the belief that James was the author of the letter was to a work by Professor Harold Kuhn,
On Waldegrave see Kuhn, H. W. (1968), Preface to Waldegrave's Comments: Excerpt from Montmort's Letter to Nicholas Bernoulli, pp. 3-6 in Precursors in Mathematical Economics: An Anthology (Series of Reprints of Scarce Works on Political Economy, 19) (W. J. Baumol and S. M. Goldfeld, eds.), London: London School of Economics and Political Science and Waldegrave's Comments: Excerpt from Montmort's Letter to Nicholas Bernoulli, pp. 7-9 in Precursors in Mathematical Economics: An Anthology (Series of Reprints of Scarce Works on Political Economy, 19) (W. J. Baumol and S. M. Goldfeld, eds.), London: London School of Economics and Political Science, 1968.
But James was not the only Waldegrave who could have written the letter. Professor David Bellhouse published a paper in 2007 arguing that Charles, not James, Waldegrave was the author of the famous letter. Charles was an uncle to James.
This morning I received an email from Professor Kuhn alerting me to the fact that Professor Bellhouse has been continuing his research into which Waldegrave wrote the letter and now believes that it was neither James nor Charles but Charles's brother Francis. In light of this I have amended my history to show Francis as the likely author of the letter.
Professor Bellhouse is working on a new paper about Montmort, Bernoulli and Waldegrave. I look forward to seeing this in print so we can get the whole story.