5 progress is always better even if SE chance is so low, but you can always convert those TLS for some extra E.
(not using big rat personally)
22.125 expected return from Sealed Archive with 5% rare success chance.
22.125 / 13 actions = ~1.70 EPA
27 echo return from Baseborn’s Papers.
27 / 15 actions = 1.80 EPA
Baseborn’s Papers is better, assuming 5% rare success chance, which seems probable at this point. It could be any arbitrary percentage chance, but between 5 and 10 is starting to split hairs.
If Baseborn’s Papers is worse, I’d say it is because of higher risk. Each of my 3 attempts I got stuck with 4 bad cards in my hand and was occasionally forced to play them. This may bump up the expected action count high enough to offset its greater (ideal) profitability.
edited by Kaijyuu on 3/3/2017
If the difference is over 4 echoes, then papers will sometimes be better even if it means taking more actions. I have been in situations where I already had the prize card, less than 7 progress, and enough guaranteed progress cards to get to 7 in one or two actions.