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Message: <blockquote data-quote="Elric" data-source="post: 4694923" data-attributes="member: 1139">This is an example of different powers of attacks, which I’m not trying to quantify.  I can quantify, say, the difference between having half of your  encounters with 50% of attacks targeting AC/Reflex and half of your encounters with 100% of attacks targeting AC/Reflex, versus having every encounter with 75% of attacks targeting AC/Reflex.I’ll assume n=8 in both cases.  In the former case, Shield is 96.3% as effective in terms of attacks stopped as in the latter case (0.701 attacks stopped vs. 0.728 attacks stopped).  I think this distribution across encounters leads to changes at least as extreme as what you’re likely to see in practice, and it’s still not a big difference.This idea that it doesn’t matter if you don’t end up using Second Chance because then you weren’t hit again is more consistent with a “mini-max” strategy of trying to minimize the maximum damage you take, rather than what I’m doing, which is trying to minimize the average (i.e., expected) damage you take.  Doing a calculation related to a minimax strategy would involves assuming players who are risk averse over the amount of damage they take, and would be quite a bit harder.Indeed, I mention this in my initial post.  If you don’t know the number of attacks you’ll face, this doesn’t impact Shield at all in my example (since my assumption is that you use it as soon as possible), but does weaken Second Chance (because you don’t know if you’ll get another chance to use it, which makes optimization more difficult).  I could do a calculation letting the number of future attacks be a variable, but that would be more difficult and would require stronger assumptions.Expectation means average damage blocked, since that’s the metric I’m using.  I’ve made a lot of assumptions, but a nice result is that I can calculate a number.This number is the additional average damage blocked you get by saving Second Chance and not using it initially on any hit (only critical hits).  The baseline calculation already takes into account that some hits will be critical hits, but assumes you use it the first time available.  Your 40% statistic is the answer you get if you compare “optimal waiting to use Second Chance vs. using it on the first available hit” (with hit chance=50%, crit=1.5 regular hits, and optimal k=4) and assume n=16-17 attacks.  Assuming n=8 gives you 15.7%, actually, not 13% as I said before.  See my post below.  I had a minor error here- I wasn’t handling the fact that Second Chance sometimes turns a regular hit into a critical hit, which makes saving it for critical comparatively better.  But Second Chance is slightly worse overall as a result.</blockquote>

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