{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:15Z","timestamp":1753893855426,"version":"3.41.2"},"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 show that there is an $m=2n+o(n)$, such that, in the Maker-Breaker game played on $\\mathbb{Z}^d$ where Maker needs to put at least $m$ of his marks consecutively in one of $n$ given winning directions, Breaker can force a draw using a pairing strategy. This improves the result of Kruczek and Sundberg [Electronic Journal of Combinatorics 15(1):N42, 2008] who showed that such a pairing strategy exists if $m\\ge 3n$.  A simple argument shows that $m$ has to be at least $2n+1$ if Breaker is only allowed to use a pairing strategy, thus the main term of our bound is optimal.<\/jats:p>","DOI":"10.37236\/482","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:00:16Z","timestamp":1578715216000},"source":"Crossref","is-referenced-by-count":0,"title":["Asymptotically Optimal Pairing Strategy for Tic-Tac-Toe with Numerous Directions"],"prefix":"10.37236","volume":"17","author":[{"given":"Padmini","family":"Mukkamala","sequence":"first","affiliation":[]},{"given":"D\u00f6m\u00f6t\u00f6r","family":"P\u00e1lv\u00f6lgyi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,10,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1n33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:22:47Z","timestamp":1579303367000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1n33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/482","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,10,15]]},"article-number":"N33"}}