Just so others know how to calculate in the effect of a time instant as a daily prize, what you are doing is taking half the harmonic mean of the essences per 1 hour and the essences per daily prize divided by the number of hours offered. So let's say the daily prize is one 20 hour instant. The large chest would be requiring 1/(1/(412/20) + 1/24.524) = 11.20 essences per hour of instant. The small chest would be requiring 1/(1/(360.857/20) + 1/26.737) = 10.78 essences per hour of instant. Thus even an insignificant time prize for the daily will produce more total time with the small chest than with the large.
I'm nodding like I'm fascinated ... when all I see when I read this is,
"Numbers blah blah numbers blah blah blah more numbers blah blah numbers blah." I'm drooling idiot when it comes to the maths...!
Since reading this thread I've switched to opening just the small chests, instead of
only opening the large ones (as I've done for the longest time). From a practical point of view, I think it's a much better approach. I always thought I'd never be able to reach the third Grand Prize with the smalls, because there just aren't enough feathers there. But of course, that's all wrong.
Let me try my hand at some (much more basic!) math: Opening 2 large chests costs me 280 essence. Opening 6 small chests costs 300, roughly the same amount. But with the odds of getting free essence so much higher, I'm likely to get at least 2 shots of it somewhere in those 6 chests, so I wind up opening around 8 at the same cost (possibly even less, if I score the 90-point versions). It's
possible I'll get a free booster in those 2 large chests, but pretty iffy. If I don't, and I keep things even for this example, that means I wind up with 6 items from the smalls as opposed to just 2 items from the larges—with a pretty good chance that one of them will be the daily prize, along with some decent instants as well. They may not be as big as what you get from the large ones, but the aggregate gained over the course of an entire event would give you pretty much the same effect—and split into much more reasonable iterations, too. No more wrestling with whether to spend a 14-hour instant to wrap up a production with 5 hours left. Even a 10-hour production can be more practically dealt with, since I'll probably end up with a lot more 5-hour instants than 14s anyway. And the end result toward the Grand Prizes is the same: 40 feathers gained.
It's all odds and percentages and rolling the dice and such, but I can say that it
feels like I'm getting a lot more out of the small chests, and there's a lot less of the burden that comes with gambling so much essence on one roll—and a lot less frustration when it doesn't come through. Works for me.