{"53837":{"#nid":"53837","#data":{"type":"event","title":"Sheldon M. Ross - Some Multiple Player Gambler\u0027s Ruin Problems","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u003C\/strong\u003E Some Multiple Player Gambler\u2019s Ruin Problems\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E Sheldon M. Ross\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003ESuppose there are r gamblers, with gambler i initially having a fortune of n\u003Csub\u003Ei\u003C\/sub\u003E.\u0026nbsp; In our first model we suppose that at each stage two of the gamblers are chosen to play a game, equally likely to be won by either player, with the winner of the game receiving 1 from the loser. Any gambler whose fortune becomes 0 leaves, and this continues until there is only a single gambler left.  We are interested in the probability that player i is the one left, and in the the mean number of games played between specified players i and j. In our second model we suppose that all remaining players contribute 1 to a pot, which is equally likely to be won by each of them. The problem here is to determine the expected number of games played until one player has all the\u003Cbr \/\u003Efunds.\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003ESome Multiple Player Gambler\u0027s Ruin Problems\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Some Multiple Player Gambler\u2019s Ruin Problems"}],"uid":"27187","created_gmt":"2010-02-23 12:09:37","changed_gmt":"2016-10-08 01:49:08","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2010-03-16T13:00:00-04:00","event_time_end":"2010-03-16T14:00:00-04:00","event_time_end_last":"2010-03-16T14:00:00-04:00","gmt_time_start":"2010-03-16 17:00:00","gmt_time_end":"2010-03-16 18:00:00","gmt_time_end_last":"2010-03-16 18:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[{"id":"8778","name":"gambler"},{"id":"8909","name":"or-seminars"},{"id":"167286","name":"statistics-seminars"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}