tag:blogger.com,1999:blog-6883415296937284014.post6779589779107196891..comments2016-06-09T23:11:19.160-07:00Comments on Religion, Sets, and Politics: A brief note on non-transitive diceJoshuahttp://www.blogger.com/profile/00637936588223855248noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6883415296937284014.post-63961206589854026512012-10-16T00:38:17.494-07:002012-10-16T00:38:17.494-07:00This comment has been removed by a blog administrator.John Wardhttp://www.blogger.com/profile/07618127475423216346noreply@blogger.comtag:blogger.com,1999:blog-6883415296937284014.post-35886841965921274482012-06-16T01:36:23.367-07:002012-06-16T01:36:23.367-07:00good information ... I have read and will be added...good information ... I have read and will be added to my personal knowledge... thankstoko baju muslimhttp://toko-baju-muslim.comnoreply@blogger.comtag:blogger.com,1999:blog-6883415296937284014.post-84211880775576282152011-10-18T04:21:48.195-07:002011-10-18T04:21:48.195-07:00A=(12,12,12,12,1,1)
B=(10,10,10,7,7,7)
C=(18,18,4,...A=(12,12,12,12,1,1)<br />B=(10,10,10,7,7,7)<br />C=(18,18,4,4,4,4)<br />do a triple reversal. <br /><br />This can probably be generalized to a construction of an "n-reversible" set of dice {A,B,C} with the following properties:<br />For all odd k<=n, k dice of type A beat k dice of type B, which in turn beat k dice of type C, which, counter-intuitively, beat k dice of type A.<br />For all even k<=n, k copies of B beat k copies of A, which beat k copies of C, which beat k copies of B.TGnoreply@blogger.comtag:blogger.com,1999:blog-6883415296937284014.post-38096189070067268982011-09-26T19:29:36.253-07:002011-09-26T19:29:36.253-07:00Intuitively, I think the answer is yes. I'm pl...Intuitively, I think the answer is yes. I'm playing with A=(12,12,2) B=(8,8,8) C=(16,3,3). If that doesn't work, I can always use 6 or 12 or 18 sides and re-jigger a single side til it works.<br /><br />I just saw Moneyball, about the Oakland A's use of statistical analysis to produce a team with just as many wins as the Yankees with one-third the salary. It reminded me of this problem- the Yankees kept beating the A's in the post-season because they used all that extra to buy players in July at exorbitant prices because performance in April, May and June is a more reliable predictor of performance in September than last season's stats. I was especially reminded of this because the A's drafting strategy involves avoiding top-of-the-line players for more under-ranked above-average players. If you'll humor me, 162 dice As will "beat" 162 dice Ys, but 5 dice Ys will "beat" 5 dice As.TGnoreply@blogger.com