Abstract
We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order $\sqrt{n}$ from the naïve law-of-large numbers allocation. Upon rescaling by $\sqrt{n}$ and sending $n\to\infty$, we show that optimal play's random deviations always have bounded support and have marginal distributions that are absolutely continuous with respect to Lebesgue measure.
Citation
James Fill. David Wilson. "Two-Player Knock 'em Down." Electron. J. Probab. 13 198 - 212, 2008. https://doi.org/10.1214/EJP.v13-485
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