{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-G7RWY3S3/4E32029D-D596-48C5-B8D5-26495CF20F8F/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-G7RWY3S3/98df0f83-ba44-4636-b73e-6612007e707b/PDF","dcterms:extent":"667 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-G7RWY3S3/b0cf5e9a-dc1e-4051-94d6-e47a6e0683af/TEXT","dcterms:extent":"62 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-G7RWY3S3","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2011","dc:creator":["Addona, Vittorio","Wagon, Stan","Wilf, Herbert S."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:4"},{"@xml:lang":"sl","#text":"str. 29-62"}],"dc:identifier":["COBISSID:16261977","ISSN:1855-3966","URN:URN:NBN:SI:doc-G7RWY3S3"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"game theory"},{"@xml:lang":"en","#text":"Legendre polynomials"},{"@xml:lang":"sl","#text":"Legendrovi polinomi"},{"@xml:lang":"en","#text":"probability"},{"@xml:lang":"sl","#text":"simbolno seštevanje"},{"@xml:lang":"en","#text":"symbolic summation"},{"@xml:lang":"sl","#text":"teorija iger"},{"@xml:lang":"sl","#text":"verjetnost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"How to lose as little as possible|"},"dc:description":{"@xml:lang":"sl","#text":"Suppose Alice has a coin with heads probability ?$q$? and Bob has one with heads probability ?$p>q$?. Now each of them will toss their coin ?$n$? times, and Alice will win iff she gets more heads than Bob does. Evidently the game favors Bob, but for the given ?$p, q$?, what is the choice of n that maximizes Alice's chances of winning? We show that there is an essentially unique value ?$N(q, p)$? of ?$n$? that maximizes the probability ?$f(n)$? that the weak coin will win, and it satisfies ?$\\left\\lfloor \\frac{1}{2(p-q)} - \\frac{1}{2} \\right\\rfloor \\leq N(q, p) \\leq \\left\\lceil \\frac{\\max(1-p,q)}{p-q} \\right\\rceil$?. The analysis uses the multivariate form of Zeilberger's algorithm to find an indicator function ?$J_n(q, p)$? such that ?$J > 0$? iff ?$n < N(q,p)$? followed by a close study of this function, which is a linear combination of two Legendre polynomials. An integration-based algorithm is given for computing ?$N(q,p)$?"},"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-G7RWY3S3","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-G7RWY3S3"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-G7RWY3S3/4E32029D-D596-48C5-B8D5-26495CF20F8F/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-G7RWY3S3/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-G7RWY3S3"}}}}