tag:blogger.com,1999:blog-13306522.post111893879683492094..comments2022-04-27T17:28:39.018-07:00Comments on Adventures of BruteForce: Cyclical DominanceBrute Forcehttp://www.blogger.com/profile/10214183612902971524noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-13306522.post-1119550045121349562005-06-23T11:07:00.000-07:002005-06-23T11:07:00.000-07:00Perhaps I confused you with my usage of EV in my l...Perhaps I confused you with my usage of EV in my last comment. I suspect that you were thinking of what the expected value of the spin from each spinner would be. I was talking about EV in terms of expected win rate over the long-run. If you chose spinner A and I chose spinner B, and we were to bet 1 unit each spin. If you spin a bigger number you win, otherwise you lose. After N spins, how many units do you expect to be up or down?<BR/><BR/>In any case, here are the 5 solutions:<BR/><BR/>* { (168), (249), (357) }<BR/>* { (159), (267), (358) }<BR/> { (168), (239), (457) }<BR/> { (178), (249), (356) }<BR/> { (178), (239), (456) }<BR/><BR/>The ones marked with * are "fair" configurations. Each spinner is dominated by one and dominates another with a 5 to 4 edge. The others are not "fair," because some are dominated by or dominate another with a a 6 to 3 edge.Brute Forcehttps://www.blogger.com/profile/10214183612902971524noreply@blogger.comtag:blogger.com,1999:blog-13306522.post-1119542714249126242005-06-23T09:05:00.000-07:002005-06-23T09:05:00.000-07:00Well, I don't think that it would be possible then...Well, I don't think that it would be possible then. Maybe I am missing something here, but if A>B and B>C, how could C ever be greater than A? By transitivity A > C.Anonymoushttps://www.blogger.com/profile/13441809988487585009noreply@blogger.comtag:blogger.com,1999:blog-13306522.post-1119424602022693722005-06-22T00:16:00.000-07:002005-06-22T00:16:00.000-07:00Yes, a spinner dominates another if the EV is grea...Yes, a spinner dominates another if the EV is greater. So, we want to find a set of 3 spinners where if you were to choose one first, I could always choose one that beats yours. As Spud put it in a private chat, we want a Ro-Sham-Bo cycle.Brute Forcehttps://www.blogger.com/profile/10214183612902971524noreply@blogger.comtag:blogger.com,1999:blog-13306522.post-1119405801634376552005-06-21T19:03:00.000-07:002005-06-21T19:03:00.000-07:00I am not understanding the problem. What does it m...I am not understanding the problem. What does it mean for a spinner to be dominant, are we talking about the EV of one spinner greater than another? If so, given that A's EV is greater than B's greater than C's. I don't see any way C's EV can be greater than A's. What am I missing?Anonymoushttps://www.blogger.com/profile/13441809988487585009noreply@blogger.com