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Message: <blockquote data-quote="Elric" data-source="post: 4695759" data-attributes="member: 1139">Indeed, I’ve been quite up front from the beginning that I’m setting the number of attacks constant as a simplification.  As I have mentioned repeatedly, thinking about an optimal use of Second Chance (in terms of average damage blocked) requires a simplifying assumption.  One could, I suppose, think of the number of rounds as known constant and the chance a character would be attacked per round as another known constant, and solve from there for optimal strategies for Second Chance use as a function of the number of rounds, but I haven’t done that.  Changing from 8 rounds at 1 attack/round to 16 rounds at a 50% of an attack per round changes the probability distribution over the number of successful hits (as you can see, in the former case it’s not possible to get successfully hit 9 times, but this is possibly in the latter case), even though the average number stays the same.  Changing to 32 rounds at a 25% chance of an attack per round would change the odds as well, though the average number of attacks would be the same in each case.  As I said in a previous post, which addressed this issue quite directly:It’s not that my first equation must be in a deep and abiding sense correct.  It’s that it involves fewer simplifying assumptions.  We could do this calculation at any level of simplification desired.  For example, assuming a distribution of the number of rounds and a distribution of the number of attacks on a given round (round 1, round 2, etc.) would generate its own probability distribution for the number of successful attacks, would be less simplified still.  I wouldn't want to try doing it, but it's theoretically possible.This requires the assumption that each attack has a set and independent percentage chance to target Reflex/AC in every encounter.  As I indicated above in a response to APC, this is only an approximation to a varied set of encounters each with their own separate independent chance of an attack targeting AC/Reflex, which averages out over those encounters to 75% (and again, the approximation works slightly to Shield’s favor).Indeed, you will change the odds for Shield and Second Chance slightly (and in their favor) with your assumptions.  However, the effect is going to be much larger for Shield if you are considering a “use it at the first opportunity” strategy for Second Chance.  The reason, as I’ve indicated before, is being able to use Shield is much more dependent on being attacked by a decent number of attacks than Second Chance is.</blockquote>

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