  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 naive law-of-large numbers
allocation. Upon rescaling by sqrt(n) and sending n to infinity, 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.
