tag:blogger.com,1999:blog-5234436246664688381.post7026288176056258201..comments2018-01-25T18:05:31.348-08:00Comments on Mathematics, biology and recreation: Sucker betJonathan Dushoffhttp://www.blogger.com/profile/03197609136976213552noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-5234436246664688381.post-28142005893287814952014-07-10T20:32:05.095-07:002014-07-10T20:32:05.095-07:00Please see http://lalashan.mcmaster.ca/theobio/mat...Please see http://lalashan.mcmaster.ca/theobio/math/index.php/Sucker_bet for more discussion (and a link to the answer).<br />Jonathan Dushoffhttps://www.blogger.com/profile/03197609136976213552noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-57515219253032650452014-07-08T16:51:28.261-07:002014-07-08T16:51:28.261-07:00Please see my apology to Tom.Please see my apology to Tom.Jonathan Dushoffhttps://www.blogger.com/profile/03197609136976213552noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-28416019598433188662014-07-08T16:51:04.994-07:002014-07-08T16:51:04.994-07:00And my apologies for not making the question more ...And my apologies for not making the question more clear! A bad start to my blog, and I'll do better in future.Jonathan Dushoffhttps://www.blogger.com/profile/03197609136976213552noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-71816593524876138622014-07-08T16:50:04.268-07:002014-07-08T16:50:04.268-07:00Your math argument is the standard (wrong) one tha...Your math argument is the standard (wrong) one that makes this a trick question. Your sims need to simulate a whole string of rolls, not just the first two. Hard to imagine how it can be different, which is of course the point.<br />Jonathan Dushoffhttps://www.blogger.com/profile/03197609136976213552noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-2650816853836572742014-07-08T16:48:09.167-07:002014-07-08T16:48:09.167-07:00Not that kind of trick :-). Yes, Bob wins if ther...Not that kind of trick :-). Yes, Bob wins if there is an 8 followed immediately by a 7, and Alice wins if there is a 7 followed immediately by a 7 (there's a typo in your question -- the numbers are backward).<br />Jonathan Dushoffhttps://www.blogger.com/profile/03197609136976213552noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-89492596752322921782014-07-08T08:33:15.942-07:002014-07-08T08:33:15.942-07:00Followup based on Tom's comment : if they'...Followup based on Tom's comment : if they're allowed to keep rolling until one of them wins, keeping the last 7 or 8 into account, then it turns out Bob wins. <br /><br />Intuition :<br /><br />If a 7 is rolled, that can be a win for both Alice and Bob, depending on the last 7 or 8. If it was a 7, Alice wins. If it's an 8, Bob wins. However, for any given roll of an 8, the next 7 cannot allow Alice to win, but Bob will win. <br /><br />Bob wins about 2.35x as frequently as Alice. Well played, Bob. Well played.Quentin CAUDRONhttps://www.blogger.com/profile/02589691583848421234noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-66032859437369406712014-07-08T08:18:54.920-07:002014-07-08T08:18:54.920-07:00I'm going to be thinking about this incorrectl...I'm going to be thinking about this incorrectly ( which is why these types of questions always come with unexpected solutions ), but...<br /><br />- Assume the two rolls are IID<br />- Seven is more likely than eight for the first roll<br />- Second roll, they both need the same, we can just ignore; even if we don't ignore it, it's equally likely for both of them<br />- Assume that, if we don't get either a (7, 7) or (8, 7), then neither win<br /><br />So... Beer is on Alice ?<br /><br />Sims confirm that Alice wins 2.79% of the time, and Bob only gets there 2.31% of the time.Quentin CAUDRONhttps://www.blogger.com/profile/02589691583848421234noreply@blogger.comtag:blogger.com,1999:blog-5234436246664688381.post-53329790180784009602014-07-08T08:17:36.138-07:002014-07-08T08:17:36.138-07:00Does the 8 have to follow the 7 immediately?Does the 8 have to follow the 7 immediately?Tom Cutrofellohttps://www.blogger.com/profile/01937787618646704157noreply@blogger.com