Reply to thread

Message: <blockquote data-quote="Elric" data-source="post: 4694964" data-attributes="member: 1139">I can post a calculation for him.  As I mention in my previous post, doing it the way you do slightly increases the chance that Shield works.  Suppose that you are hit with an average of 4 successful attacks in an encounter (with each attack hitting you 50% of the time) and that 75% of the attacks that hit you target AC/Reflex.  What is the chance that Shield will work on one of them?The unconditional chance that Shield works on a given attack is 15%.  The chance that Shield works on a given attack, conditional on the attack hitting, is 30%.  If we start from n=8 attacks, each with a 50% chance of hitting, we get Prob (Shield works)= 1- (1-0.15)^8 = 72.75% of the time.If we start by assuming that there are 4 successful attacks, we get Prob (Shield works)= 1-(1-0.3)^4= 75.99% of the time.The latter calculation cannot be used as a proxy for the answer in the former calculation (as you seem to be implying it can be).  The answer you think you are getting is wrong.This occurs because the chance that Shield works is concave in the number of (edit- successful) attacks, and from there it's a consequence of <a href="http://en.wikipedia.org/wiki/Jensen%27s_inequality" target="_blank">Jensen's inequality</a>.</blockquote>