Kuhn poker: the value −1/18, all optimal strategies, and the solution at every ante and bet
A Lean 4 development of Kuhn's simplified two-person poker (Kuhn 1950): three cards 1 0 and bet b > 0 (Kuhn's pp. 102-103, stated there without proof, and the region b > 2a he does not state): the value is -b^2/(6(2a + b)) for b = 2a, with explicit guaranteeing strategies in each case; in Case 3 the calling probability eta with the 2 ranges over [(2a - b)/(2a + b), b/(2a + b)], and the interval printed on p. 102, b/(2a + b) = 2a never bets the 1 or the 2 first, folds them, and with the 3 is cut out by one inequality (a single strategy at b = 2a; beyond it a two-dimensional set in which I may…
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