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Since rush success rate is based on average S.P.E.C.I.A.L. used of that room and luck, I'm pretty sure it can go lower than that.
And health lost by Mr. Handy depends on how long he stays in a fight and what he's fighting.
Your calculations being based on falsely estimated datas, your results are flawed.
I had no problems with 1 Mr Handy auto collecting (when he broke down i repaired him).
Now i have no problem with 5 Mr Handy's auto collecting.
There are so many little things that make vault encounters harder.
Merged multiple rooms = harder enemies / fires
Leveld rooms / merged = harder enemies / fires
Vault Dwellers cap ranges = harder enemies / fires
etc etc.. go read.lol
but in a nutshell : Do NOT upgrade rooms or even merge them untill you ahve dwellers that can defend them or are strong enouggh for 3 alarm fires.
PS: chance of failure has been as low as 10% for me now that dwellers are trained. again. that info is also in the wiki and forums.
u missed the point that higher chance of success also mean lesser money, lets say you have 10% failure, you can only get 10 caps per rush, so back to the formula, 20 failure will kill mr.handy, with only 10% failure, you can do 90 successful rush, you should be getting 10 caps x 90 rush = 900 caps, 2000 caps to repair, you lose 1100 caps.
and if you need to make caps by rushing.. you got some serious prolems.
My formula is only rush rooms mid game to late game when the chance of failure is as low as possible, and only when you absolutely have too complete Objective missions or u need more Stimpacks now and can not wait.
Complete the mission / Quest for Bottle and Cappy. Then they will visit your base and you clokc on them for more free caps and even nuca cola bottles.
etc etc.
your question was so long.. i didnt really know the point untill just now.
Definately Not worth it.
good luck. have fun