tag:blogger.com,1999:blog-15628310.post112545203536361633..comments2022-07-26T20:48:08.865-04:00Comments on Question of the day: Pistols at DawnAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-15628310.post-1125580530159179052005-09-01T09:15:00.000-04:002005-09-01T09:15:00.000-04:00You are A, 1/3 accuracyB is 1/2 accurateC is alway...You are A, 1/3 accuracy<BR/>B is 1/2 accurate<BR/>C is always accurate<BR/> <BR/>x X y = x shoots at y<BR/> <BR/>As A, you can either:<BR/>1) shoot at B<BR/>2) shoot at C<BR/>3) shoot at the ground (deliberately miss).<BR/> <BR/>1) a X b<BR/>if you hit (1/3 of the time), you lose, and C fires next and takes you out<BR/>otherwise (2/3 of the time) b X c as C is B's biggest threat. 1/2 the time B takes out C, which leaves a X b to resolve. 1/2 the time B misses, C kills B, and you have 1/3 chance to take out C before he takes you out.<BR/> <BR/>First, a X b (with C out of the picture) is<BR/>1/3 + 2/3 * 1/2 * 1/3 + 2/3 * 1/2 * 2/3 * 1/2 * 1/3 + ...<BR/>= 1/3 + (1/3)^n * 1/3<BR/>= 1/3 + 1/6 = 1/2<BR/> <BR/>So a X b (with C there) is<BR/>2/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/3 = 10/36 chance of winning<BR/> <BR/>2) a X c<BR/>if you hit C, B shoots are you, 1/2 the time you survive and it boils down to the a X b (C out of picture) calculated above.<BR/>if you miss C, B shoots at C, 1/2 the time hits and it boils down to a X b above. 1/2 the time B misses, C takes B out, and you have 1/3 chance to take C out.<BR/> <BR/>So a X c is<BR/>1/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/2 + 2/3 * 1/2 * 1/3<BR/>= 1/12 + 1/6 + 1/9 = 13/36 chance of winning<BR/> <BR/>This makes sense, relatively, as you best hope is to take out the most accurate shooter.<BR/> <BR/>3) option 3, you skip your turn by firing into the ground.<BR/>b X c, 1/2 the time B hits and it becomes a X b calculated above. The other 1/2, C takes out B and you have 1/3 chance to take out C.<BR/> <BR/>So, A miss on purpose is<BR/>1/2 * 1/2 + 1/2 * 1/3 = 1/4 + 1/6 = 15/36 chance of winning.<BR/> <BR/>So your best option, at 15/36 = 41.7% of winning, is to miss your first shot on purpose!!Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.com