{"title":"赌徒的废墟和第一次穿越时间","authors":"J. Vrbik","doi":"10.3888/TMJ.14-8","DOIUrl":null,"url":null,"abstract":"Our first objective is to find the probability that our player wins the game, ending up with a+ b dollars. To do this, we have to imagine that the game has been going on for some time, and the player has reached the point of having exactly i dollars in his pocket, so that his opponent has a+ bi. Given that, we denote our player’s probability of winning the game by wi. If one more round is played, one can see that","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2012-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Gambler's Ruin and First Passage Time\",\"authors\":\"J. Vrbik\",\"doi\":\"10.3888/TMJ.14-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Our first objective is to find the probability that our player wins the game, ending up with a+ b dollars. To do this, we have to imagine that the game has been going on for some time, and the player has reached the point of having exactly i dollars in his pocket, so that his opponent has a+ bi. Given that, we denote our player’s probability of winning the game by wi. If one more round is played, one can see that\",\"PeriodicalId\":91418,\"journal\":{\"name\":\"The Mathematica journal\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Mathematica journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3888/TMJ.14-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Mathematica journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3888/TMJ.14-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Our first objective is to find the probability that our player wins the game, ending up with a+ b dollars. To do this, we have to imagine that the game has been going on for some time, and the player has reached the point of having exactly i dollars in his pocket, so that his opponent has a+ bi. Given that, we denote our player’s probability of winning the game by wi. If one more round is played, one can see that
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