{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T18:48:03Z","timestamp":1771267683125,"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>In the game of Penney Ante two players take turns publicly selecting two distinct words of length $n$ using letters from an alphabet $\\Omega$ of size $q$. They roll a fair $q$ sided die having sides labelled with the elements of $\\Omega$ until the last $n$ tosses agree with one player's word, and that player is declared the winner. For $n\\geq 3$ the second player has a strategy which guarantees strictly better than even odds. Guibas and Odlyzko have shown that the last $n-1$ letters of the second player's optimal word agree with the initial $n-1$ letters of the first player's word. We offer a new proof of this result when $q \\geq 3$ using correlation polynomial identities, and we complete the description of the second player's best strategy by characterizing the optimal leading letter.  We also give a new proof of their conjecture that for $q=2$ this optimal strategy is unique, and we provide a generalization of this result to higher $q$.<\/jats:p>","DOI":"10.37236\/1061","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:02:43Z","timestamp":1578718963000},"source":"Crossref","is-referenced-by-count":7,"title":["Optimal Penney Ante Strategy via Correlation Polynomial Identities"],"prefix":"10.37236","volume":"13","author":[{"given":"Daniel","family":"Felix","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,4,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:17:29Z","timestamp":1579321049000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4,4]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1061","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4,4]]},"article-number":"R35"}}