{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T10:19:34Z","timestamp":1773224374780,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove a conjecture of Droste and Kuske about the probability that $1$ is minimal in a certain random linear ordering of the set of natural numbers.  We also prove generalizations, in two directions, of this conjecture: when we use a biased coin in the random process and when we begin the random process with a specified ordering of a finite initial segment of the natural numbers.  Our proofs use a connection between the conjecture and a question about the game of gambler's ruin.  We exhibit several different approaches (combinatorial, probabilistic, generating function) to the problem, of course ultimately producing equivalent results.<\/jats:p>","DOI":"10.37236\/1920","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:56Z","timestamp":1578719516000},"source":"Crossref","is-referenced-by-count":3,"title":["Random Orders and Gambler's Ruin"],"prefix":"10.37236","volume":"12","author":[{"given":"Andreas","family":"Blass","sequence":"first","affiliation":[]},{"given":"G\u00e1bor","family":"Braun","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1r23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:49:50Z","timestamp":1579322990000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1r23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1920","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5,13]]},"article-number":"R23"}}