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Message: <blockquote data-quote="Elric" data-source="post: 4694928" data-attributes="member: 1139">Indeed, the number of successful attacks is the metric that directly matters.  What I am doing is generating a probability distribution of the number of successful attacks through a hit probability and a set number of attacks.  Now, you’ve both taken issue with my assuming a set number of attacks, which could in theory be changed as well at the cost of much more complication.  By looking at successful hits directly without any probability distribution on it, you have made a more restrictive assumption than what I am assuming—essentially, you have not only assumed the number of attacks, but you have also assumed that the results of those attacks will be the average number of successful hits.  If I assumed a set number of successful hits, I couldn’t evaluate the tradeoff of not using Second Chance now on a regular hit, which lessens the chance that you’ll get to use it at all, but raises the chance you’ll get to use it on a critical.  The way you do it also increases the chance Shield gets used at all.I assume optimality because it makes calculations easier.  If you would like to do calculations with a “makes mistake” term added, you can do so, but it means more work (and arguing about the manner in which people make mistakes), so I don’t do it.  When you’re near optimality in general, small deviations have a small effect on the result, so nearly optimal usage will produce the nearly optimal result.  I assume this because it’s easy to calculate and making assumptions about what PCs know about attacks remaining is much harder.  As long as you have a reasonable idea when the number of attacks remaining against you drops to a very low number, you’re OK here.  One simple assumption could be that the player is 1 more conservative than my optimal k, and this accounts for the loss due to uncertainty.  This doesn’t affect the “low” n=4 case, because you already use Second Chance every time you can.  In the “high” n=8 case, this lowers Second Chance to 96% of the expected damage blocked that it would otherwise get.  This strategy ends up being an 11% increase in average damage blocked over the “use Second Chance the first time you can” strategy.This is roughly correct, given my assumptions.  Actually, now that you bring this up, I spot a small error in my calculation- I wasn’t accounting for the chance that Second Chance changes a regular hit into a critical hit properly.  So this makes Second Chance a little worse in general, but increases the relative value of the “wait for a critical hit” strategy (because I was correctly accounting for the fact that on a critical hit, Second Chance can’t hurt you).  This doesn’t change the optimal k.In particular, the Low case (n=4) number for Second Chance goes from 0.53 to 0.49, and the high case number for Second Chance goes from 0.64 to 0.605.  So this error had a noticeable impact on Second Chance’s average damage blocked.No, the expected value is the average damage prevented.  This accounts for the times when you don’t get to use it because of waiting and Second Chance prevents 0 damage.Indeed, waiting too long can cause other problems, as you suggest with the healing surge example.  Knowing whether you need healing can be valuable in and of itself.  To the extent that the optimal k=4 I calculated occurs very close to the end of the encounter, this could give us pause, but for n=8, it means waiting halfway through the encounter, which seems reasonable.</blockquote>

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