CDAM: Computational, Discrete and Applicable Mathematics@LSE 

CDAM Research Report, LSECDAM200820September 2008 
On Ruckle's Conjecture on Accumulation Games
Steve Alpern, Robbert Fokkink, and Kensaku Kikuta
In an accumulation game, the Hider secretly distributes his given total wealth h among n locations, while the Searcher picks r locations and confiscates the material placed there. The Hider wins if what is left at the remaining nr locations is at least 1; otherwise the Searcher wins. Ruckle's Conjecture says that an optimal Hider strategy is to put an equal amount h=k at k randomly chosen locations, for some k: We extend the work of Kikuta and Ruckle by proving the Conjecture for the following cases, among others: r = 2 or n2; n≤ 7; n = 2r 1; h < 2 + 1/(nr1) and n ≤ 2r. The last result uses the ErdosKoRado theorem. We establish a connection between Ruckle's Conjecture and the difficult Hoeffding problem of bounding tail probabilities of sums of random variables.A PDF file (244 kB) with the full contents of this report can be downloaded by clicking here.
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