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Analysis of adversarial binary search game
Introduction Alice and Bob are at it again, this time playing a game called Binary Search. Alice begins by secretly selecting an integer key from 1 to $latex n=100$, then Bob makes a series of inte…
But presumably Bob is then allowed similar leeway, not being forced to execute textbook binary search that always guesses the midpoint of the interval of remaining possible numbers. I wrote some Mathematica code (on GitHub) to compute exact optimal strategies for Alice and Bob for smaller versions of this problem, up to . My suspicion is that this sawtooth behavior persists, continuing to straddle zero expected return, so that it seems difficult to predict whether the particular game at has Alice in the red or the black, when both she and Bob use truly optimal strategies.
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