{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T05:39:43Z","timestamp":1789105183200,"version":"build-2803163510"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of coming up this way depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high\u2010speed photography are reported. For natural flips, the chance of coming up as started is about .51.<\/jats:p>","DOI":"10.1137\/s0036144504446436","type":"journal-article","created":{"date-parts":[[2007,4,30]],"date-time":"2007-04-30T18:00:35Z","timestamp":1177956035000},"page":"211-235","source":"Crossref","is-referenced-by-count":119,"title":["Dynamical Bias in the Coin Toss"],"prefix":"10.1137","volume":"49","author":[{"given":"Persi","family":"Diaconis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Susan","family":"Holmes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Montgomery","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,5,1]]},"reference":[{"key":"R1","unstructured":"R. Barnhart,\n                      Beating the Wheel: Winning Strategies at Roulette\n                      , Lyle and Stuart, New York, 1992."},{"key":"R2","unstructured":"T. Bass,\n                      The Eudaemonic Pie\n                      , Houghton\u2010Mifflin, Boston, 1985."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(79)90082-0"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.2307\/2695798"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"E. Engel,\n                      A Road to Randomness in Physical Systems\n                      , Springer\u2010Verlag, New York, 1992.","DOI":"10.1007\/978-1-4419-8684-9"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"A. Ercan, F. Xiao, X. Q. Liu, S. H. Lim, A. El Gamal, and B. Wandell,\n                      Experimental High Speed CMOS Image Sensor System and Applications\n                      , in Proceedings of IEEE Conference on Sensors 2002, IEEE, 2002, pp. 15\u201320.","DOI":"10.1109\/ICSENS.2002.1036979"},{"key":"R7","unstructured":"O. Faugeras,\n                      Three\u2010Dimensional Computer Vision\n                      , MIT Press, Cambridge, MA, 1993."},{"key":"R8","unstructured":"R. P. Feynman, with R. Leighton,\n                      Surely You\u2019re Joking, Mr. Feynman!\n                      , Norton, New York, 1985."},{"key":"R9","unstructured":"R. Feynman, R. Leighton, and M. Sands,\n                      The Feynman Lectures on Physics\n                      , Vol. I, Addison\u2010Wesley, New York, 1963."},{"key":"R10","unstructured":"H. Flanders,\n                      Differential Forms with Applications to the Physical Sciences\n                      , Dover, Mineola, New York, 1989."},{"key":"R11","unstructured":"V. Fremont and R. Chellali,\n                      Direct Camera Calibration Using Two Concentric Circles from a Single View\n                      , in Proceedings of the International Conference on Artificial Reality and Telexistence (ICAT), 2002, pp. 93\u201398."},{"key":"R12","doi-asserted-by":"crossref","unstructured":"W. Gander, G. Golub, and R. Strebel,\n                      Fitting of Circles and Ellipses: Least Square Solution\n                      , Tech report SCCM\u201094\u201008, SCCM, Stanford University, Stanford, CA, 1994.","DOI":"10.1016\/B978-044482107-2\/50036-4"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1198\/000313002605"},{"key":"R14","unstructured":"H. Goldstein,\n                      Classical Mechanics\n                      , Addison\u2010Wesley, Reading, MA, 1950."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1002\/sapm193413151"},{"key":"R16","first-page":"179","volume":"46","author":"Hopf E.","year":"1936","journal-title":"Jahresber. 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Kweon,\n                      A Camera Calibration Method Using Concentric Circles for Vision Applications\n                      , ACCV2002, Melbourne, Australia, 2002."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1109\/4.972156"},{"key":"R24","unstructured":"Heads or Tails\n                      , pamphlet, Murphy\u2019s Magic Supplies, Rancho Cordova, CA, 2006."},{"key":"R25","doi-asserted-by":"crossref","unstructured":"L. Landau and E. Lifschitz,\n                      Mechanics\n                      , 3rd ed., Pergamon Press, Oxford, UK, 1976.","DOI":"10.1515\/9783112569122"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1017\/S0031819100050361"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.2307\/2589049"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"J. E. Marsden and T. S. Ratiu,\n                      Introduction to Mechanics and Symmetry\n                      , Texts Appl. 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Strevens,\n                      Bigger than Chaos: Understanding Complexity through Probability\n                      , Harvard University Press, Cambridge, MA, 2003.","DOI":"10.4159\/9780674044067"},{"key":"R35","unstructured":"A. Toomre,\n                      Personal communication\n                      , 1981."},{"key":"R36","doi-asserted-by":"crossref","unstructured":"J. Von Plato,\n                      Creating Modern Probability: Its Mathematics, Physics and Philosophy in Historical Perspective\n                      , Cambridge University Press, Cambridge, UK, 1994.","DOI":"10.1017\/CBO9780511609107"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.33.576"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1007\/BF01895515"},{"key":"R39","doi-asserted-by":"crossref","unstructured":"Z. Zhang,\n                      Flexible camera calibration by viewing a plane from unknown orientations\n                      , in Proceedings of the 7th International IEEE Conference on Computer Vision, Greece, 1999, pp. 666\u2013673.","DOI":"10.1109\/ICCV.1999.791289"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036144504446436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:19:25Z","timestamp":1787231965000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036144504446436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1137\/S0036144504446436"],"URL":"https:\/\/doi.org\/10.1137\/s0036144504446436","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}