{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:54Z","timestamp":1787323254333,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"8","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>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 $n-r$ 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 several cases, e.g., $r=2$ or $n-2$; $n\\leq7$; $n=2r-1$; $h\\leq2+1\/\\,(n-r)$ and $n\\leq2r$. The last result uses the Erd\u0151s\u2013Ko\u2013Rado theorem. We establish a connection between Ruckle's conjecture and the Hoeffding problem of bounding tail probabilities of sums of random variables.<\/jats:p>","DOI":"10.1137\/080741926","type":"journal-article","created":{"date-parts":[[2010,10,19]],"date-time":"2010-10-19T18:09:09Z","timestamp":1287511749000},"page":"5073-5083","source":"Crossref","is-referenced-by-count":14,"title":["On Ruckle's Conjecture on Accumulation Games"],"prefix":"10.1137","volume":"48","author":[{"given":"Steve","family":"Alpern","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robbert","family":"Fokkink","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ken","family":"Kikuta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,10,19]]},"reference":[{"key":"R1","unstructured":"S. Alpern and R. J. Fokkink,\n                      Accumulation Games on Graphs\n                      , Research report 2008-18, Centre for Discrete and Applicable Mathematics, London School of Economics, 2008."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0326077"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1989-0972227-7"},{"key":"R4","unstructured":"B. Bollob\u00e1s,\n                      Combinatorics\n                      , Cambridge University Press, Cambridge, UK, 1986."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/27.1.25"},{"key":"R6","first-page":"93","volume":"8","author":"Erd\u0151s P.","year":"1965","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/12.1.313"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728543"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.2307\/2282952"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728489"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022639813629"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004609529766"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/1520-6750(199410)41:6<821::AID-NAV3220410610>3.0.CO;2-Y"},{"key":"R14","unstructured":"L. E. Meester,\n                      Extremal Distributions for Tail Probabilities of Sums of iid Random Variables on\n                      [0,1], preprint, 2008; available online from http:\/\/arxiv.org\/abs\/0808.1669."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-7998.1962.tb01601.x"},{"key":"R16","unstructured":"W. Ruckle,\n                      Geometric Games and Their Applications\n                      , Res. Notes in Math. 82, Pitman, Boston, 1983."},{"key":"R17","first-page":"173","volume":"54","author":"Ruckle W.","year":"2001","journal-title":"Sci. Math. Jpn."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177697279"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021765121940"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080741926","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:51:12Z","timestamp":1787320272000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080741926"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":19,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080741926"],"URL":"https:\/\/doi.org\/10.1137\/080741926","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}