{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T09:47:50Z","timestamp":1771494470124,"version":"3.50.1"},"reference-count":14,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T00:00:00Z","timestamp":1748822400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["ICGA Journal: The Journal of the Computer Games Community"],"published-print":{"date-parts":[[2025,8]]},"abstract":"\n Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and height six, in alternating turns. Mis\u00e8re Connect Four is played by the same rules, but with the opposite objective:\n do not<\/jats:italic>\n connect four. This article announces that Mis\u00e8re Connect Four is solved: perfect play by both sides leads to a second-player win. More generally, this article also announces that Mis\u00e8re Connect\n \n \n k<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n played on a\n \n \n w<\/mml:mi>\n \u00d7<\/mml:mo>\n h<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n board is also solved, but the outcome depends on the game\u2019s parameters\n \n \n k<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n ,\n \n \n w<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n , and\n \n \n h<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n , and may be a first-player win, a second-player win, or a draw. These results are constructive, meaning that we provide explicit strategies, thus enabling readers to impress their friends and foes alike with provably optimal play in the mis\u00e8re form of a table-top game for children.\n <\/jats:p>","DOI":"10.1177\/13896911251342484","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T16:46:37Z","timestamp":1767631597000},"page":"118-129","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Mis\u00e8re Connect Four is Solved"],"prefix":"10.1177","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7567-2747","authenticated-orcid":false,"given":"Robert","family":"Steele","sequence":"first","affiliation":[{"name":"NYU Langone Health, New York, NY, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5273-5234","authenticated-orcid":false,"given":"Daniel B","family":"Larremore","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Colorado Boulder, Boulder, CO, USA"},{"name":"BioFrontiers Institute, University of Colorado Boulder, Boulder, CO, USA"},{"name":"Santa Fe Institute, Santa Fe, NM, USA"}]}],"member":"179","published-online":{"date-parts":[[2025,6,2]]},"reference":[{"key":"e_1_3_3_2_1","volume-title":"The Complete Book of Connect Four: History, Strategy, Puzzles","author":"Allen J. D.","year":"2010","unstructured":"Allen J. D. (2010). The Complete Book of Connect Four: History, Strategy, Puzzles. Sterling. Available online at https:\/\/fabpedigree.com\/james\/connect4.htm."},{"key":"e_1_3_3_3_1","doi-asserted-by":"publisher","DOI":"10.3233\/ICG-1988-11410"},{"key":"e_1_3_3_4_1","doi-asserted-by":"crossref","unstructured":"Allis L. V. (1994). Searching for solutions in games and artificial intelligence. PhD thesis Maastricht University. doi:https:\/\/doi.org\/10.26481\/dis.19940923la.","DOI":"10.26481\/dis.19940923la"},{"key":"e_1_3_3_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvd58spj.13"},{"key":"e_1_3_3_6_1","doi-asserted-by":"crossref","unstructured":"Edelkamp S. Kissmann P. (2008). Symbolic classification of general two-player games. In KI 2008: Advances in Artificial Intelligence: 31st Annual German Conference on AI KI 2008 Kaiserslautern Germany September 23\u201326 2008. Proceedings 31 (pp. 185\u2013192). Springer.","DOI":"10.1007\/978-3-540-85845-4_23"},{"key":"e_1_3_3_7_1","doi-asserted-by":"crossref","unstructured":"Fraenkel A. S. Garey M. R. Johnson D. S. Schaefer T. Yesha Y. (1978). The complexity of checkers on an N\u00d7 N board. In 19th Annual Symposium on Foundations of Computer Science (SFCS 1978) (pp. 55\u201364). IEEE.","DOI":"10.1109\/SFCS.1978.36"},{"key":"e_1_3_3_8_1","article-title":"Simplification of partizan games in mis\u00e9re play","volume":"7","author":"Mesdal G.","year":"2007","unstructured":"Mesdal G., Ottaway P. (2007). Simplification of partizan games in mis\u00e9re play. Integers, 7, G06.","journal-title":"Integers"},{"key":"e_1_3_3_9_1","first-page":"113","article-title":"Restricted developments in partizan mis\u00e9re game theory","volume":"5","author":"Milley R.","year":"2018","unstructured":"Milley R., Renault G. (2018). Restricted developments in partizan mis\u00e9re game theory. Games of No Chance, 5, 113\u2013123.","journal-title":"Games of No Chance"},{"key":"e_1_3_3_10_1","doi-asserted-by":"publisher","DOI":"10.1126\/science.1144079"},{"key":"e_1_3_3_11_1","unstructured":"Steele R. Larremore D. B. (2024). Mis\u00e9re Connect Four is Solved. arXiv preprint arXiv:2410.05551."},{"key":"e_1_3_3_12_1","unstructured":"Tromp J. (1995a). John\u2019s Connect Four Playground. Website. Accessed September 1 2024. https:\/\/tromp.github.io\/c4\/c4.html"},{"key":"e_1_3_3_13_1","unstructured":"Tromp J. (1995b). Connect-4. UCI Machine Learning Repository. DOI:https:\/\/doi.org\/10.24432\/C59P43."},{"issue":"2","key":"e_1_3_3_14_1","first-page":"123","article-title":"Losing Chess: 1. E3 Wins for White","volume":"39","author":"Watkins M.","year":"2017","unstructured":"Watkins M. (2017). Losing Chess: 1. E3 Wins for White. Journal of the International Computer Games Association, 39(2), 123\u2013125.","journal-title":"Journal of the International Computer Games Association"},{"key":"e_1_3_3_15_1","doi-asserted-by":"crossref","unstructured":"Yamaguchi Y. Yamaguchi K. Tanaka T. Kaneko T. (2012). Infinite connect-four is solved: Draw. In Advances in Computer Games: 13th International Conference ACG 2011 Tilburg The Netherlands November 20\u201322 2011 Revised Selected Papers 13 (pp. 208\u2013219). Springer.","DOI":"10.1007\/978-3-642-31866-5_18"}],"container-title":["ICGA Journal: The Journal of the Computer Games Community"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/13896911251342484","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/13896911251342484","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/13896911251342484","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T08:41:34Z","timestamp":1771490494000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/13896911251342484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,2]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["10.1177\/13896911251342484"],"URL":"https:\/\/doi.org\/10.1177\/13896911251342484","relation":{},"ISSN":["1389-6911","2468-2438"],"issn-type":[{"value":"1389-6911","type":"print"},{"value":"2468-2438","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,2]]}}}